File: part8.html

package info (click to toggle)
nyquist 3.23%2Bds-1
  • links: PTS, VCS
  • area: main
  • in suites: trixie
  • size: 58,064 kB
  • sloc: ansic: 74,758; lisp: 18,104; java: 10,719; cpp: 6,688; sh: 171; xml: 58; makefile: 40; python: 15
file content (3740 lines) | stat: -rw-r--r-- 259,341 bytes parent folder | download 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
 
<!DOCTYPE html>
<html><head><title>Nyquist Functions</title>
<link rel="stylesheet" type="text/css" href="nyquiststyle.css">
<link rel="icon" href="nyquist-icon.png" />
<link rel="shortcut icon" href="nyquist-icon.png" />
</head>
<body bgcolor="ffffff">
<a href = "part7.html">Previous Section</a> | <a href = "part9.html">Next Section</a> | <a href = "title.html#toc">Table of Contents</a> | <a href = "indx.html">Index</a> | <a href = "title.html">Title Page</a>
<hr>
<a name = "82"><h2>Nyquist Functions</h2></a>
<p>This chapter provides a language reference for Nyquist.  Operations
are categorized by functionality and abstraction level.
Nyquist is implemented in two important levels: the &ldquo;high level&rdquo; supports
behavioral abstraction, which means that operations like <code>stretch</code> and
<code>at</code> can be applied.  These functions are the ones that typical users
are expected to use, and most of these functions are written in XLISP.</p>

<p>The &ldquo;low-level&rdquo; primitives directly operate on sounds, but know nothing of
environmental variables (such as <code>*warp*</code>, etc.).  The
names of most of these low-level functions start with &ldquo;<code>snd-</code>&rdquo;.  In
general, programmers should avoid any function with the &ldquo;<code>snd-</code>&rdquo;
prefix.  Instead, use the &ldquo;high-level&rdquo; functions, which know about the
environment and react appropriately.  The names of high-level functions
do not have prefixes like the low-level functions.  </p>

<p>There are certain low-level operations that apply directly to sounds (as
opposed to behaviors) and are relatively &ldquo;safe&rdquo; for ordinary use.  These
are marked as such.</p>

<p>Nyquist uses both linear frequency and equal-temperament pitch numbers to
specify repetition rates.  Frequency is always specified in either cycles
per second (hz), or pitch numbers, also referred to as &ldquo;steps,&rdquo; as in
steps of the chromatic scale.  Steps are floating point numbers such that 60
= Middle C, 61 = C#, 61.23 is C# plus 23 cents, etc.  The mapping from pitch
number to frequency is the standard exponential conversion, and fractional
pitch numbers are allowed:

<blockquote>frequency = 440 * 2<sup>((pitch - 69)/12)</sup></blockquote>

There are many
predefined pitch names.  By default these are tuned in equal temperament,
with A4 = 440Hz, but these may be changed.  (See Section <a href = "part2.html#16">Predefined Constants</a>).</p>
<a name = "83"><h3>Sounds</h3></a><a name="index256"></a>
<p>A sound is a primitive data type in Nyquist.  Sounds can be created, passed
as parameters, garbage collected, printed, and set to variables just like
strings, atoms, numbers, and other data types.  </p>
<a name = "84"><h4>What is a Sound?</h4></a>
<p>Sounds have 5 components:
<ul>
<li>
<code>srate<a name="index257"></a></code> &ndash; the sample rate of the sound.</li>
<li><code>samples<a name="index258"></a></code> &ndash; the samples.</li>
<li><code>signal-start<a name="index259"></a></code> &ndash; the time of the first sample.</li>
<li><code>signal-stop<a name="index260"></a></code> &ndash; the time of one past the last sample.</li>
<li><code>logical-stop<a name="index261"></a></code> &ndash; the time at which the sound logically ends, e.g. a 
sound may end at the beginning of a decay.  This value defaults 
to <code>signal-stop</code>,
but may be set to any value.  
</li></ul>
It may seem that there should be <code>logical-start</code> to indicate the
logical or perceptual beginning of a sound as well as a <code>logical-stop</code>
to indicate the logical ending of a sound.  In practice, only
<code>logical-stop</code> is needed; this attribute tells when the next sound
should begin to form a sequence of sounds.  In this respect, Nyquist sounds
are asymmetric: it is possible to compute sequences forward in time by
aligning the logical start of each sound with the <code>logical-stop</code> of the
previous one, but one cannot compute &ldquo;backwards&rdquo;, aligning the logical end
of each sound with the logical start of its successor.  The root of this
asymmetry is the fact that when we invoke a behavior, we say when to start,
and the result of the behavior tells us its logical duration.  There is no
way to invoke a behavior with a direct specification of when to
stop <a href = "foot.html#foot3">(Footnote 3)</a> .  </p>
<b><i>Note:</i></b> there is no way to enforce the
intended &ldquo;perceptual&rdquo; interpretation of 
<code>logical-stop</code>.  As far as Nyquist is concerned, these are just numbers to
guide the alignment of sounds within various control constructs.<a name = "85"><h4>Multichannel Sounds</h4></a><a name="index262"></a>
<p>Multichannel sounds are represented by Lisp arrays of sounds.  To create an
array of sounds the XLISP <code>vector</code> function is useful.  Most low-level 
Nyquist functions (the ones starting with <code>snd-</code>) do not operate on
multichannel sounds.  Most high-level functions do operate on multichannel
sounds.</p>
<a name = "86"><h4>Accessing and Creating Sound</h4></a>
<p>Several functions display information concerning a sound and can be used to
query the components of a sound. There are functions that access samples in
a sound and functions that construct sounds from samples.</p>
<dl>
<dt>
<code>sref(<a name="index263"></a><a name="Sound, accessing point264"></a><i>sound</i>, <i>time</i>)</code> [SAL]<br>

<code>(sref <i>sound</i> <i>time</i>)</code> [LISP]</dt>
<dd>Accesses <i>sound</i> at 
the point <i>time</i>, which is a local time. If <i>time</i> does not 
correspond to a sample time, then the nearest samples are linearly 
interpolated to form the result.  To access a particular sample, either 
convert the sound to an array (see <code>snd-samples</code> below), or use 
<code>snd-srate</code> and <code>snd-t0</code> (see below) to find the sample rate 
and starting time,  and compute a time (<i>t</i>) from the sample number (<i>n</i>):

<blockquote>t = (n / srate) + t0</blockquote>

Thus, the Lisp code to access the n<sup T>th</sup> sample of a sound would look like:

<p></p>
<pre>
(sref sound (global-to-local (+ (/ n (snd-srate sound)) (snd-t0 sound))))
</pre>

<p>
Or in SAL, it would look like:
</p>
<pre>
sref(sound, global-to-local(n / snd-srate(sound) + snd-t0(sound)))
</pre>

<p>
Here is why <code>sref</code> interprets its time argument 
as a local time (shown first in LISP and then in SAL syntax):
</p>
<pre>
&gt; (sref (ramp 1) 0.5) <i>; evaluate a ramp at time 0.5</i>
0.5
SAL&gt; print sref(ramp(1), 0.5) <i>; evaluate a ramp at time 0.5</i>
0.5
&gt; (at 2.0 (sref (ramp 1) 0.5)) <i>; ramp is shifted to start at 2.0</i>
		<i>; the time, 0.5, is shifted to 2.5</i>
0.5
SAL&gt; sref(ramp(1), 0.5) @ 2.0 <i>; ramp is shifted to start at 2.0</i>
		<i>; the time, 0.5, is shifted to 2.5</i>
0.5
</pre>

<p>
If you were to use <code>snd-sref</code>, which treats time as global, instead 
of <code>sref</code>, which treats time as local, then the first example above
would return the same answer (0.5), but the second example would return
0.  Why? Because the <code>ramp</code> behavior would be shifted to start at
time 2.0, but the resulting sound would be evaluated at global time 
0.5.  By definition, sounds have a value of zero before their start time.</p>
<dt><code>sref-inverse(<a name="index265"></a><i>sound</i>, <i>value</i>)</code> [SAL]<br>

<code>(sref-inverse <i>sound</i> <i>value</i>)</code> [LISP]</dt>
<dd>Search <i>sound</i> for the first point at which it achieves <i>value</i> and return the corresponding (linearly interpolated) time.  If no inverse exists, an error is raised.  This function is used by Nyquist in the implementation of time warping.<br><br>
<dt>
<code>snd-from-array(<a name="Sound, creating from array266"></a><a name="index267"></a><i>t0</i>, <i>sr</i>,
<i>array</i>)</code> [SAL]<br>

<code>(snd-from-array <i>t0</i> <i>sr</i> <i>array</i>)</code> [LISP]</dt>
<dd>Converts a lisp array of <code>FLONUM</code>s into a sound with starting
time <i>t0</i> and sample rate <i>sr</i>.  Safe for ordinary use.  Be aware that
arrays of floating-point samples use 14 bytes per sample, and an additional
4 bytes per sample are allocated by this function to create a sound type.<br><br>
<dt><code>snd-fromarraystream(<a name="index268"></a><i>t0</i>, <i>sr</i>, <i>object</i>)</code> [SAL]<br>

<code>(snd-fromarraystream <i>t0</i> <i>sr</i> <i>object</i>)</code> [LISP]</dt>
<dd>Creates a
sound for which samples come from
<i>object</i>. The starting time is <i>t0</i> (a <code>FLONUM</code>), and the sample rate is
<i>sr</i>. The <i>object</i> is an XLISP object (see Section <a href = "part19.html#235">Objects</a> for
information on objects.) A sound is returned.  When the sound needs samples,
they are generated by sending the message <code>:next</code> to <i>object</i>. If
<i>object</i> returns <code>NIL</code>, the sound terminates. Otherwise, <i>object</i>
must return an array of <code>FLONUM</code>s.  The values in these arrays are
concatenated to form the samples of the resulting sound. In the current
implementation, all arrays must have the same length.
There is no provision for <i>object</i> to specify the
logical stop time of the sound, so the logical stop time is the termination
time. <br><br>
<dt><code>snd-fromobject(<a name="index269"></a><a name="index270"></a><i>t0</i>, <i>sr</i>, <i>object</i>)</code> [SAL]<br>

<code>(snd-fromobject <i>t0</i> <i>sr</i> <i>object</i>)</code> [LISP]</dt>
<dd>Creates a sound for which samples come from
<i>object</i>. The starting time is <i>t0</i> (a <code>FLONUM</code>), and the sample rate is
<i>sr</i>. The <i>object</i> is an XLISP object (see Section <a href = "part19.html#235">Objects</a> for
information on objects. A sound is returned.  When the sound needs samples,
they are generated by sending the message <code>:next</code> to <i>object</i>. If
<i>object</i> returns <code>NIL</code>, the sound terminates. Otherwise, <i>object</i>
must return a <code>FLONUM</code>.  There is no provision for <i>object</i> to specify the
logical stop time of the sound, so the logical stop time is the termination
time.<br><br>
<dt><code>snd-extent(<a name="index271"></a><i>sound</i>, <i>maxsamples</i>)</code> [SAL]<br>

<code>(snd-extent <i>sound</i> <i>maxsamples</i>)</code> [LISP]</dt>
<dd>Returns a list of two numbers: the starting time of <i>sound</i> and the terminate time of <i>sound</i>.  Finding the terminate time requires that samples be computed.  Like most Nyquist functions, this is non-destructive, so memory will be allocated to preserve the sound samples.  If the sound is very long or infinite, this may exhaust all memory, so the <i>maxsamples</i> parameter specifies a limit on how many samples to compute.  If this limit is reached, the terminate time will be (incorrectly) based on the sound having <i>maxsamples</i> samples.  This function is safe for ordinary use.<br><br>
<dt><code>snd-fetch(<a name="index272"></a><a name="index273"></a><a name="index274"></a><a name="index275"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-fetch <i>sound</i>)</code> [LISP]</dt>
<dd>Reads samples
sequentially from <i>sound</i>. This returns a <code>FLONUM</code> after each call, or
<code>NIL</code> when <i>sound</i> terminates. <b><i>Note:</i></b> <code>snd-fetch</code> modifies
<i>sound</i>; it is strongly recommended to copy <i>sound</i> using
<code>snd-copy</code> and access only the copy with <code>snd-fetch</code>.<br><br>
<dt><code>snd-fetch-array(<a name="index276"></a><i>sound</i>, <i>len</i>,
<i>step</i>)</code> [SAL]<br>

<code>(snd-fetch-array <i>sound</i> <i>len</i> <i>step</i>)</code>
[LISP]</dt>
<dd>Reads 
sequential arrays of samples from <i>sound</i>, returning either an array
of <code>FLONUM</code>s or <code>NIL</code> when the sound terminates. The <i>len</i>
parameter, a <code>FIXNUM</code>, indicates how many samples should be
returned in the result array.  After the array is returned, <i>sound</i>
is modified by skipping over <i>step</i> (a <code>FIXNUM</code>) samples. If
<i>step</i> equals <i>len</i>, then every sample is returned once.  If
<i>step</i> is less than <i>len</i>, each returned array will overlap the
previous one, so some samples will be returned more than once. If
<i>step</i> is greater than <i>len</i>, then some samples will be skipped
and not returned in any array. The <i>step</i> and <i>len</i> may change at
each call, but in the current implementation, an internal buffer is
allocated for <i>sound</i> on the first call, so subsequent calls may not
specify a greater <i>len</i> than the first. When an array is returned,
it will have <i>len</i> samples. If necessary, <code>snd-fetch-array</code>
will read zeros beyond the end of the sound to fill the array. When
this happens, <code>*rslt*</code> is set to a FIXNUM number of samples in
the array that were read from the sound before the physical stop time 
of the sound. If all samples in the array are &ldquo;valid&rdquo; samples from
the sound (coming from the sound before the sound
terminates), <code>*rslt*</code> is set to <code>NIL</code>. The <code>*rslt*</code>
variable is global and used to return extra results from other
functions, so programs should not assume <code>*rslt*</code> is valid after
subsequent function calls. <b><i>Note:</i></b> <code>snd-fetch-array</code> modifies
<i>sound</i>; it is strongly recommended to copy <i>sound</i> using
<code>snd-copy</code> and access only the copy with <code>snd-fetch-array</code>.<br><br>
<dt><code>snd-flatten(<a name="index277"></a><i>sound</i>, <i>maxlen</i>)</code> [SAL]<br>

<code>(snd-flatten <i>sound</i> <i>maxlen</i>)</code> [LISP]</dt>
<dd>This function is identical 
to <code>snd-length</code>. You would use this function to force samples to be computed in memory. Normally, this is not a good thing to do, but here is one appropriate use: In the case of sounds intended for wavetables, the unevaluated 
sound may be larger than the evaluated (and typically short) one. 
Calling <code>snd-flatten</code> will compute the samples and allow the unit generators to be freed in the next garbage collection. <b><i>Note:</i></b> If a sound is computed from many instances of table-lookup oscillators, calling <code>snd-flatten</code> will free the oscillators and their tables. Calling <code>(stats)</code> will print how many total bytes have been allocated to tables.<br><br>
<dt><code>snd-length(<a name="index278"></a><a name="index279"></a><a name="index280"></a><i>sound</i>, <i>maxlen</i>)</code> [SAL]<br>

<code>(snd-length <i>sound</i> <i>maxlen</i>)</code> [LISP]</dt>
<dd>Counts the
number of samples in <i>sound</i> up to the physical stop time.  If the sound
has more than <i>maxlen</i> samples, <i>maxlen</i> is returned.  Calling this
function will cause all samples of the sound to be computed and saved in
memory (about 4 bytes per sample).  Otherwise, this function is safe for ordinary use.<br><br>
<dt><code>snd-maxsamp(<a name="index281"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-maxsamp <i>sound</i>)</code> [LISP]</dt>
<dd>Computes the maximum of
the absolute value of the samples in <i>sound</i>.  Calling this function will
cause samples to be computed and saved in memory.  (This function should
have a <i>maxlen</i> parameter to allow self-defense against sounds that would
exhaust available memory.)  Otherwise, this function is safe for ordinary use.
This function will probably be removed in a future version.  See <code>peak</code>, a replacement (<a href = "#103">Signal Operations</a>).<br><br>
<dt><code>snd-play(<a name="index282"></a><a name="index283"></a><a name="index284"></a><i>expression</i>)</code> [SAL]<br>

<code>(snd-play <i>expression</i>)</code> [LISP]</dt>
<dd>Evaluates <i>expression</i>
to obtain a sound, computes all of the samples (without
retaining them in memory), and returns the number of samples computed.
Originally, this was a placeholder
for a facility to play samples directly to an audio output device, but
playback is now accomplished by <code>s-save</code>.
Meanwhile, since this function does not write samples to a file, it is
useful in determining how much time is spent calculating samples.  See
<code>s-save</code> (Section <a href = "#100">Sound File Input and Output</a>) for saving samples to a file, and
<code>play</code> (Section <a href = "#100">Sound File Input and Output</a>) to play a sound.  This function is
safe for ordinary use. Note that it does not accept multichannel sounds.
To time mult-channel sound computation, you might try applying
<code>to-mono</code> (see Section <a href = "#87">Miscellaneous Functions</a>) to get a SOUND.<br><br>
<dt><code>snd-print-tree(<a name="index285"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-print-tree <i>sound</i>)</code> [LISP]</dt>
<dd>Prints an ascii
representation of the internal data structures representing a sound.  This
is useful for debugging Nyquist.  This function is
safe for ordinary use.<br><br>
<dt><code>snd-samples(<a name="index286"></a><a name="index287"></a><a name="index288"></a><a name="index289"></a><i>sound</i>, <i>limit</i>)</code> [SAL]<br>

<code>(snd-samples <i>sound</i> <i>limit</i>)</code> [LISP]</dt>
<dd>Converts the
samples into a lisp array.  The data is taken directly from the samples,
ignoring shifts.  For example, if the sound starts at 3.0 seconds, the first
sample will refer to time 3.0, not time 0.0.  A maximum of <i>limit</i> samples
is returned.  This function is safe for ordinary use, but like
<code>snd-from-array</code>, it requires a total of slightly over 18 bytes per
sample.<br><br>
<dt><code>snd-srate(<a name="index290"></a><a name="index291"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-srate <i>sound</i>)</code> [LISP]</dt>
<dd>Returns the sample rate of
the sound. Safe for ordinary use.
<br><br>
<dt><code>snd-time(<a name="index292"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-time <i>sound</i>)</code> [LISP]</dt>
<dd>Returns the start time of the
sound.  This will probably go away in a future version, so use <code>snd-t0</code>
instead.<br><br>
<dt><code>snd-t0(<a name="index293"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-t0 <i>sound</i>)</code> [LISP]</dt>
<dd>Returns the time of the
first sample of the sound.  Note that Nyquist operators such as add always
copy the sound and are allowed to shift the copy up to one half sample
period in either direction to align the samples of two operands.  Safe for
ordinary use.<br><br>
<dt><code>snd-print(<a name="index294"></a><i>expression</i>, <i>maxlen</i>)</code> [SAL]<br>

<code>(snd-print <i>expression</i> <i>maxlen</i>)</code> [LISP]</dt>
<dd>Evaluates
<i>expression</i> to yield a sound or an array of sounds, then prints up to
<i>maxlen</i> samples to the screen (stdout).  This is similar to
<code>snd-save</code>, but samples appear in text on the screen instead of in
binary in a file.  This function is intended for debugging<a name="index295"></a>.
Safe for ordinary use.<br><br>
<dt><code>snd-set-logical-stop(<a name="index296"></a><i>sound</i>,
<i>time</i>)</code> [SAL]<br>

<code>(snd-set-logical-stop <i>sound</i> <i>time</i>)</code> [LISP]</dt>
<dd>Returns a sound which is 
<i>sound</i>, except that the logical stop of the sound occurs at <i>time</i>.
<b><i>Note:</i></b> do not call this function.  When defining a behavior, use
<code>set-logical-stop</code> or <code>set-logical-stop-abs</code> instead.<br><br>
<dt><code>snd-sref(<a name="index297"></a><i>sound</i>, <i>time</i>)</code> [SAL]<br>

<code>(snd-sref <i>sound</i> <i>time</i>)</code> [LISP]</dt>
<dd>Evaluates <i>sound</i> 
at the global time given by <i>time</i>.  Safe for ordinary use, but normally, you should
call <code>sref</code> instead.<br><br>
<dt><code>snd-stop-time(<a name="index298"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-stop-time <i>sound</i>)</code> [LISP]</dt>
<dd>Returns the stop time of <i>sound</i>.
Sounds can be &ldquo;clipped&rdquo; or truncated at a particular time.  This function
returns that time or MAX-STOP-TIME if he programmer has not specified a stop
time for the sound.  Safe for ordinary use.<br><br>
<dt><code>soundp(<a name="index299"></a><i>sound</i>)</code> [SAL]<br>

<code>(soundp <i>sound</i>)</code> [LISP]</dt>
<dd>Returns true iff <i>sound</i> is a
SOUND.  Safe for ordinary use.<br><br>
<dt><code>stats(<a name="index300"></a><a name="index301"></a><a name="index302"></a>)</code> [SAL]<br>

<code>(stats)</code> [LISP]</dt>
<dd>Prints the memory usage status.  
See also the 
XLISP <code>mem</code> function.  Safe for ordinary use. This is the only way to find out how much memory is being used by table-lookup oscillator instances.<br><br>
<dt><code>snd-set-max-audio-mem(<a name="index303"></a><a name="index304"></a><a name="index305"></a><a name="index306"></a><i>bytes</i>)</code> [SAL]<br>

<code>(snd-set-max-audio-mem <i>bytes</i>)</code> [LISP]</dt>
<dd>Sets
a limit (a FIXNUM in bytes) on the amount of main memory that
Nyquist will allocate
for SOUNDs (this does not count table memory). The default is about 1GB.
The return value is the previous limit, in bytes. This is not a limit on
how big sounds can be. Since Nyquist computes sound incrementally, it can
generally play sounds or write sounds to files without storing them in
memory. However, if you store large sounds in variables, memory usage can
exceed your available RAM, causing extremely slow computation as main memory
is swapped to and from disk or Nyquist might run out of memory and crash. The
goal of placing a limit on audio memory is to terminate computations before
memory is totally exhausted, allowing Nyquist to print an error message and
allowing the user to view or save work. Generally, if you see the message
&ldquo;The maximum number of sample blocks has been reached, ...,&rdquo; you should
fix your code to avoid accumulating samples in memory, e.g. do not assign
sounds to global variables. Alternatively, you can use this function to
increase the limit, but of course you are still limited by the actual size
of memory on your computer, and exceeding that could cause severe performance
problems in Nyquist and and any other applications that are running.
See also Section <a href = "part2.html#7">Command Line</a> for command line options to limit
yquist memory, run time, and file access (these options are not available through
the NyquistIDE.)
</dd></dl><a name = "87"><h4>Miscellaneous Functions</h4></a>
<p>These are all safe and recommended for ordinary use.</p>
<dl>
<dt>

<code>to-mono(<a name="index307"></a><i>sound</i>)</code> [SAL]<br>

<code>(to-mono <i>sound</i>)</code> [LISP]</dt>
<dd>Returns the sum of all
channels of <i>sound</i> if it is a multichannel sound. If <i>sound</i>
is a SOUND, it is simply returned unchanged.
See <code>sim</code> (Section <a href = "#99">Combination and Time Structure</a>) for more details on how 
channels are summed.<br><br>
<dt><code>db-to-linear(<a name="index308"></a><i>x</i>)</code> [SAL]<br>

<code>(db-to-linear <i>x</i>)</code> [LISP]</dt>
<dd>Returns the
conversion of <i>x</i> from decibels to linear.  0dB is converted to 1.
20dB represents a linear factor of 10. If <i>x</i> is a sound, each
sample is converted and a sound is returned.  If <i>x</i> is a
multichannel sound, each channel is converted and a multichannel sound
(array) is returned.  <b><i>Note:</i></b> With sounds, conversion is only
performed on actual samples, not on the implicit zeros before the
beginning and after the termination of the sound.  Sample rates, start
times, etc. are taken from <i>x</i>. <br><br>
<dt><code>db-to-vel(<a name="index309"></a><i>x</i> [, <i>float</i>])</code> [SAL]<br>

<code>(db-to-vel <i>x</i> [<i>float</i>])</code> [LISP]</dt>
<dd>Returns the 
conversion of <i>x</i> from decibels to MIDI velocity using a rule that
maps -60 dB to 1 and 0 dB to 127. The MIDI velocity varies linearly 
with the square root of amplitude. The default value of <i>float</i> is
<code>nil</code> and the result is a <code>FIXNUM</code> clipped to fall in the
legal range of 1-127, but if a non-<code>nil</code> value
is provided, the result is a <code>FLONUM</code> that is not 
rounded or clipped. The input parameter must be a <code>FIXNUM</code> or
<code>FLONUM</code>. Sounds are not allowed.<br><br>
<dt><code>follow(<a name="index310"></a><a name="index311"></a><a name="index312"></a><a name="index313"></a><i>sound</i>, <i>floor</i>, <i>risetime</i>, <i>falltime</i>, <i>lookahead</i>)</code> [SAL]<br>

<code>(follow <i>sound</i> <i>floor</i> <i>risetime</i> <i>falltime</i> <i>lookahead</i>)</code> [LISP]</dt>
<dd>An envelope follower intended as a commponent for compressor and limiter functions. The basic goal of this function is to generate a smooth signal 
that rides on the peaks of the input signal. The usual objective is to 
produce an amplitude envelope given a low-sample rate (control rate) 
signal representing local RMS measurements. The first argument is the 
input signal. The <i>floor</i> is the minimum output value. The <i>risetime</i> 
is the time (in seconds) it takes for the output to rise (exponentially) 
from <i>floor</i> to unity (1.0) and the <i>falltime</i> is the time it takes 
for the output to fall (exponentially) from unity to <i>floor</i>. The 
algorithm looks ahead for peaks and will begin to increase the output 
signal according to <i>risetime</i> in anticipation of a peak. The amount 
of anticipation (in seconds) is given by <i>lookahead</i>.  The algorithm 
is as follows: the output value is allowed to increase according to 
<i>risetime</i> or decrease according to <i>falltime</i>. If the next input 
sample is in this range, that sample is simply output as the next output 
sample.  If the next input sample is too large, the algorithm goes back in 
time as far as necessary to compute an envelope that rises according to 
<i>risetime</i> to meet the new value. The algorithm will only work backward 
as far as <i>lookahead</i>.  If that is not far enough, then there is a final 
forward pass computing a rising signal from the earliest output sample. In 
this case, the output signal will be at least momentarily less than the 
input signal and will continue to rise exponentially until it intersects 
the input signal. If the input signal falls faster than indicated by 
<i>falltime</i>, the output fall rate will be limited by <i>falltime</i>, 
and the fall in output will stop when the output reaches <i>floor</i>. 
This algorithm can make two passes througth the buffer on sharply rising 
inputs, so it is not particularly fast. With short buffers and low sample 
rates this should not matter. See <code>snd-avg</code> for a function that 
can help to generate a low-sample-rate input for <code>follow</code>. 
See <code>snd-chase</code> in Section <a href = "#104">Filters</a> for a related filter.<br><br>
<dt>
<code>gate(<a name="index314"></a><a name="index315"></a><i>sound</i>, 
<i>lookahead</i>, <i>risetime</i>, <i>falltime</i>, <i>floor</i>, 
<i>threshold</i>)</code> [SAL]<br>

<code>(gate <i>sound</i> <i>lookahead</i> <i>risetime</i> <i>falltime</i> <i>floor</i> <i>threshold</i>)</code> [LISP]</dt>
<dd>Generate an exponential rise and decay intended 
for noise gate implementation. The decay starts when the signal drops 
below <i>threshold</i> and stays there for longer than <i>lookahead</i> (a 
<code>FLONUM</code> in seconds). (The signal begins to drop when the signal 
crosses <i>threshold</i>, not after <i>lookahead</i>.) Decay continues until 
the value reaches <i>floor</i> (a <code>FLONUM</code>), at which point the decay 
stops and the output value is held constant. Either during the decay or 
after the floor is reached, if the signal goes above <i>threshold</i>, then 
the output value will rise to unity (1.0) at the point the signal crosses 
the threshold. Because of internal lookahead, the signal actually begins 
to rise before the signal crosses <i>threshold</i>. The rise is a 
constant-rate exponential and set so that a rise from <i>floor</i> to unity 
occurs in <i>risetime</i>. Similary, the fall is a constant-rate exponential 
such that a fall from unity to <i>floor</i> takes <i>falltime</i>.<br><br>
<dt><code>noise-gate(<a name="index316"></a><i>sound</i> [, <i>lookahead</i>, <i>risetime</i>, <i>falltime</i>, <i>floor</i>, <i>threshold</i>] [, rms: <i>use-rms</i>, link: <i>link-option</i>])</code> [SAL]<br>

<code>(noise-gate <i>sound</i> [<i>lookahead</i> <i>risetime</i> <i>falltime</i> <i>floor</i> <i>threshold</i>] [:rms <i>use-rms</i> :link <i>link-option</i>])</code> [LISP]</dt>
<dd>A
simple noise gate implementation based on <code>gate</code>. All parameters
except <i>snd</i> are optional and default values are <i>lookahead</i>:
0.5, <i>risetime</i>: 0.02, <i>falltime</i>: 0.5, <i>floor</i>: 0.01,
<i>threshold</i>: 0.01. The keyword parameters <code>:rms</code> and <code>:link</code> are
also optional with default values of <i>use-rms</i>: <code>NIL</code> (false) and 
<i>link-option</i>: T (true). The result is the input <i>snd</i>, where 
below-threshold segments of sound are attenuated to a maximum of <i>floor</i> (see the
<code>gate</code> function above). If <i>use-rms</i> is non-NIL,
the <i>threshold</i> applies to the RMS of the <i>sound</i> computed with
10 ms non-overlapping rectangular windows. Otherwise, <i>threshold</i> applies
to the absolute value of each sample in <i>sound</i>. If <i>link-option</i> is
non-NIL, and if the input <i>sound</i> is multichannel, then a single gate
is computed and applied to all channels. The gate threshold is considered
to be exceeded when <i>any</i> channel would exceed the threshold and open 
the gate. (In other words, whether <i>use-rms</i> or not, a maximum value is
computed from all the channels and used to control the gate.)<br><br>
<dt><code>hz-to-step(<a name="index317"></a><i>freq</i>)</code> [SAL]<br>

<code>(hz-to-step <i>freq</i>)</code> [LISP]</dt>
<dd>Returns a step number for <i>freq</i> (in hz), which can be either a number of a <code>SOUND</code>. The result has the same type as the argument. See also <code>step-to-hz</code> (below).<br><br>
<dt><code>linear-to-db(<a name="index318"></a><i>x</i>)</code> [SAL]<br>

<code>(linear-to-db <i>x</i>)</code> [LISP]</dt>
<dd>Returns the conversion of <i>x</i> from linear to decibels.  1 is converted to 0.  0 is converted to -INF (a special IEEE floating point value.)  A factor of 10 represents a 20dB change.  If <i>x</i> is a sound,  each sample is converted and a sound is returned.  If <i>x</i> is a multichannel sound, each channel is converted and a multichannel sound (array) is returned.  <b><i>Note:</i></b> With sounds, conversion is only performed on actual samples, not on the implicit zeros before the beginning and after the termination of the sound.  Start times, sample rates, etc. are taken from <i>x</i>.<br><br>
<dt><code>linear-to-vel(<a name="index319"></a><i>x</i> [, <i>float</i>])</code> [SAL]<br>

<code>(linear-to-vel <i>x</i> [<i>float</i>])</code> [LISP]</dt>
<dd>Returns the 
conversion of <i>x</i> from linear amplitude to MIDI velocity using a rule that
maps -60 dB to 1 and 0 dB to 127. The MIDI velocity varies linearly 
with the square root of amplitude. The default value of <i>float</i> is
<code>nil</code> and the result is a <code>FIXNUM</code> clipped to fall in the
legal range of 1-127, but if a non-<code>nil</code> value
is provided, the result is a <code>FLONUM</code> that is not 
rounded or clipped. The input parameter must be a <code>FIXNUM</code> or
<code>FLONUM</code>. Sounds are not allowed.<br><br>
<dt><code>log(<a name="index320"></a><a name="index321"></a><i>x</i>)</code> [SAL]<br>

<code>(log <i>x</i>)</code> [LISP]</dt>
<dd>Calculates the natural log of <i>x</i> (a <code>FLONUM</code>). (See <code>s-log</code> for a version that operates on signals.)<br><br>
<dt><code>set-control-srate(<a name="index322"></a><a name="index323"></a><i>rate</i>)</code> [SAL]<br>

<code>(set-control-srate <i>rate</i>)</code> [LISP]</dt>
<dd>Sets the default sampling rate for control signals to <i>rate</i> by setting <code>*default-control-srate*</code> and reinitializing the environment.  Do not call this within any synthesis function (see the <code>control-srate-abs</code> transformation, Section <a href = "#98">Transformations</a>).<br><br>
<dt><code>set-sound-srate(<a name="index324"></a><a name="index325"></a><i>rate</i>)</code> [SAL]<br>

<code>(set-sound-srate <i>rate</i>)</code> [LISP]</dt>
<dd>Sets the default sampling rate for audio signals to <i>rate</i> by setting <code>*default-sound-srate*</code> and reinitializing the environment.  Do not call this within any synthesis function (see the <code>sound-srate-abs</code> transformation, Section <a href = "#98">Transformations</a>).<br><br>
<dt><code>set-pitch-names(<a name="index326"></a><a name="index327"></a><a name="index328"></a>)</code> [SAL]<br>

<code>(set-pitch-names)</code> [LIS]</dt>
<dd>Initializes pitch 
variables (<code>c0</code>, <code>cs0</code>, <code>df0</code>, <code>d0</code>, ... <code>b0</code>, 
<code>c1</code>, ... <code>b7</code>).  A440 (the default tuning) is represented by
 the step 69.0, so the variable <code>a4</code> (fourth octave A) is set to 69.0.  
You can change the tuning by 
setting <code>*A4-Hertz*</code><a name="index329"></a><a name="index330"></a><a name="index331"></a> to a 
value (in Hertz) and calling <code>set-pitch-names</code> to reinitialize the pitch 
variables.  Note that this will result in non-integer step values.  It does not
alter the mapping from step values to frequency.  There is no built-in 
provision for stretched scales or non-equal temperament, although users 
can write or compute any desired fractional step values.<br><br>
<dt><code>step-to-hz(<a name="index332"></a><i>pitch</i>)</code> [SAL]<br>

<code>(step-to-hz <i>pitch</i>)</code> [LISP]</dt>
<dd>Returns a frequency in hz
for <i>pitch</i>, a step number or a <code>SOUND</code> type representing a time-varying step number. The result is a <code>FLONUM</code> if <i>pitch</i> is a number, and a <code>SOUND</code> if <i>pitch</i> is a <code>SOUND</code>. See also <code>hz-to-step</code> (above).<br><br>
<dt><code>get-ioi(<a name="index333"></a><a name="index334"></a><i>dur</i>)</code> [SAL]<br>

<code>(get-ioi <i>dur</i>)</code> [LISP]</dt>
<dd>Gets the duration of of
something starting at a local time of 0 and ending at a local time of
<i>dur</i>. For convenience,  <code>*rslt*</code> is set to the global time
corresponding to local time zero. Note that sustain is ignored in this
calculation. The intent is to calculate the nominal start time of the
next event in a sequence (or the logical stop time of the current event)
rather than the actual sound duration of the current event.<br><br>
<dt><code>get-duration(<a name="index335"></a><i>dur</i>)</code> [SAL]<br>

<code>(get-duration <i>dur</i>)</code> [LISP]</dt>
<dd>Gets the actual duration of of something starting at a local time of 0 and ending at a local time of <i>dur</i> times the current sustain. For convenience,  <code>*rslt*</code> is set to the global time corresponding to local time zero.  See also <code>get-ioi</code> (above).<br><br>
<dt><code>get-loud(<a name="index336"></a>)</code> [SAL]<br>

<code>(get-loud)</code> [LISP]</dt>
<dd>Gets the current value of the <code>*loud*</code> environment variable.  If <code>*loud*</code> is a signal, it is evaluated at local time 0 and a number (<code>FLONUM</code>) is returned.<br><br>
<dt><code>get-sustain(<a name="index337"></a>)</code> [SAL]<br>

<code>(get-sustain)</code> [LISP]</dt>
<dd>Gets the current value of the <code>*sustain*</code> environment variable.  If <code>*sustain*</code> is a signal, it is evaluated at local time 0 and a number (<code>FLONUM</code>) is returned.<br><br>
<dt><code>get-transpose(<a name="index338"></a>)</code> [SAL]<br>

<code>(get-transpose)</code> [LISP]</dt>
<dd>Gets the current value of the <code>*transpose*</code> environment variable.  If <code>*transpose*</code> is a signal, it is evaluated at local time 0 and a number (<code>FLONUM</code>) is returned.<br><br>
<dt><code>get-warp(<a name="index339"></a>)</code> [SAL]<br>

<code>(get-warp)</code> [LISP]</dt>
<dd>Gets a function corresponding to 
the current value of the <code>*warp*</code> environment variable.  For 
efficiency, <code>*warp*</code> is stored in three parts representing a shift,
 a scale factor, and a continuous warp function.  <code>Get-warp</code> is used
 to retrieve a signal that maps logical time to real time.  This signal 
combines the information of all three components of <code>*warp*</code> into 
a single signal.  If the continuous warp function component is not present
 (indicating that the time warp is a simple combination of <code>at</code>
 and <code>stretch</code> transformations), an error is raised.  This 
function is mainly for internal system use.  In the future,
<code>get-warp</code> will probably be reimplemented to always return
 a signal and never raise an error.<br><br>
<dt><code>local-to-global(<a name="index340"></a><i>local-time</i>)</code> [SAL]<br>

<code>(local-to-global <i>local-time</i>)</code> [LISP]</dt>
<dd>Converts a score (local) time to a real (global) time according to the current environment.<br><br>
<dt><code>round(<a name="index341"></a><a name="index342"></a><i>x</i>)</code> [SAL]<br>

<code>(round <i>x</i>)</code> [LISP]</dt>
<dd>Round <i>x</i> to the nearest integer. If <i>x</i> is <i>n</i> + 0.5, where <i>n</i> is an integer, then return <i>n</i> + 1, even if <i>n</i> is negative.<br><br>
<dt><code>snd-set-latency(<a name="index343"></a><a name="index344"></a><i>latency</i>)</code> [SAL]<br>

<code>(snd-set-latency <i>latency</i>)</code> [LISP]</dt>
<dd>Set the latency requested when Nyquist plays sound to
<i>latency</i>, a <code>FLONUM</code>. The previous value is returned. The default is 0.3 seconds. To avoid glitches, the latency should be 
greater than the time required for garbage collection and message printing and any other system activity external to Nyquist.<br><br>
<dt><code>vel-to-db(<a name="index345"></a><i>x</i>)</code> [SAL]<br>

<code>(vel-to-db <i>x</i>)</code> [LISP]</dt>
<dd>Returns the conversion
of <i>x</i> from MIDI velocity to decibels using a rule that maps MIDI
velocity 1 to -60 dB and 127 to 0 dB. The amplitude is proportional to
the square of MIDI velocity. The input <i>x</i> can be a <code>FIXNUM</code> or
<code>FLONUM</code> but not a sound. The result is a <code>FLONUM</code>.<br><br>
<dt><code>vel-to-linear(<a name="index346"></a><i>x</i>)</code> [SAL]<br>

<code>(vel-to-linear <i>x</i>)</code> [LISP]</dt>
<dd>Returns
the conversion of <i>x</i> from MIDI velocity to linear amplitude
ratio using a rule that maps MIDI 
velocity 1 to -60 dB (0.001) and 127 to unity gain. The amplitude is proportional to
the square of MIDI velocity. The input <i>x</i> can be a <code>FIXNUM</code> or
<code>FLONUM</code> but not a sound. The result is a <code>FLONUM</code>.
</dd></dl><a name = "88"><h3>Behaviors</h3></a><a name="index347"></a><a name = "89"><h4>Using Previously Created Sounds</h4></a>
<p>These behaviors take a sound and transform that sound according to the
environment.  These are useful when writing code to make
a high-level function from a low-level function, or when cuing sounds
which were previously created:
<dl>
<dt>
<code>cue(<a name="index348"></a><i>sound</i>)</code> [SAL]<br>

<code>(cue <i>sound</i>)</code> [LISP]</dt>
<dd>Applies <code>*loud*</code>, the starting time from <code>*warp*</code>, <code>*start*</code>,
 and <code>*stop*</code> to <i>sound</i>.</p>
<dt><code>cue-file(<a name="index349"></a><i>filename</i>)</code> [SAL]<br>

<code>(cue-file <i>filename</i>)</code> [LISP]</dt>
<dd>Same as <code>cue</code>, except
the sound comes from the named file, samples from which are coerced to the current default <code>*sound-srate*</code> sample rate.<br><br>
<dt><code>sound(<a name="index350"></a><i>sound</i>)</code> [SAL]<br>

<code>(sound <i>sound</i>)</code> [LISP]</dt>
<dd>Applies <code>*loud*</code>, the starting
time and (possibly continuously varying) stretching from <code>*warp*</code>, 
<code>*start*</code>, and <code>*stop*</code> to <i>sound</i>.<br><br>
<dt><code>control(<a name="index351"></a><i>sound</i>)</code> [SAL]<br>

<code>(control <i>sound</i>)</code> [LISP]</dt>
<dd>This function is identical to
<code>sound</code>, but by convention is used when <i>sound</i> is a control signal
rather than an audio signal.
</dd></dl><a name = "90"><h4>Sound Synthesis</h4></a>
<p>These functions provide musically interesting creation behaviors that
react to their environment; these are the &ldquo;unit generators&rdquo; of Nyquist:</p>
<dl>
<dt>
<code>const(<a name="index352"></a><a name="index353"></a><i>value</i> [, <i>duration</i>])</code> [SAL]<br>

<code>(const <i>value</i> [<i>duration</i>])</code> [LISP]</dt>
<dd>Creates a constant function at the <code>*control-srate*</code>.  Every sample has the given <i>value</i>, and the default <i>duration</i> is 1.0.  See also <code>s-rest</code>, which is equivalent to calling <code>const</code> with zero, and note that you can pass scalar constants (numbers) to <code>sim</code>, <code>sum</code>, and <code>mult</code> where they are handled more efficiently than constant functions.<br><br>
<dt><code>env(<a name="index354"></a><i>t<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>t<sub>4</sub></i>, <i>l<sub>1</sub></i>, <i>l<sub>2</sub></i>, <i>l<sub>3</sub></i>, 
[<i>dur</i>])</code> [SAL]<br>

<code>(env <i>t<sub>1</sub></i> <i>t<sub>2</sub></i> <i>t<sub>4</sub></i> <i>l<sub>1</sub></i> <i>l<sub>2</sub></i> <i>l<sub>3</sub></i> <i>dur</i>)</code> [LISP]</dt>
<dd>Creates a 4-phase envelope.
<i>t<sub><i>i</i></sub></i> is the duration of phase <i>i</i>, and <i>l<sub><i>i</i></sub></i> 
is the final level of phase <i>i</i>.  <i>t<sub>3</sub></i> is implied by the duration
<i>dur</i>, and <i>l<sub>4</sub></i> is <code>0.0</code>.  If <i>dur</i> is not supplied, then
<code>1.0</code> is assumed.  The envelope duration is the product of <i>dur</i>,
<code>*stretch*</code>, and <code>*sustain*</code>.  If 
<i>t<sub>1</sub></i> + <i>t<sub>2</sub></i> + 2ms + <i>t<sub>4</sub></i> is greater than the envelope 
duration, then a two-phase envelope is
substituted that has an attack/release time ratio of <i>t<sub>1</sub></i>/<i>t<sub>4</sub></i>.
The sample rate of the returned sound is <code>*control-srate*</code>.  (See
<code>pwl</code> for a more general piece-wise linear function generator.)
The effect of time warping is to warp the starting time and ending time.
The intermediate breakpoints are then computed as described above.<br><br>
<dt><code>exp-dec(<a name="index355"></a><a name="index356"></a><i>hold</i>, <i>halfdec</i>, <i>length</i>)</code> [SAL]<br>

<code>(exp-dec <i>hold</i> <i>halfdec</i> <i>length</i>)</code> [LISP]</dt>
<dd>This convenient envelope shape is a special case of <code>pwev</code> (see Section <a href = "#92">Piece-wise Approximations</a>). The envelope starts at 1 and is constant for <i>hold</i> seconds. It then decays with a half life of <i>halfdec</i> seconds until <i>length</i>. (The total duration is <i>length</i>.) In other words, the amplitude falls by half each <i>halfdec</i> seconds. When stretched, this envelope scales linearly, which means the hold time increases and the half decay time increases.<br><br>
<dt>
<code>force-srate(<a name="index357"></a><a name="index358"></a><a name="index359"></a><i>srate</i>, <i>sound</i>)</code> [SAL]<br>

<code>(force-srate <i>srate</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Returns a sound which is up- or
down-sampled to <i>srate</i>.  Interpolation is linear, and no prefiltering is
applied in the down-sample case, so aliasing may occur. See also
<code>resample</code>.<br><br>
<dt><code>lfo(<a name="index360"></a><a name="index361"></a><i>freq</i> [, <i>duration</i>, <i>table</i>, <i>phase</i>])</code> [SAL]<br>

<code>(lfo <i>freq</i> <i>duration</i> <i>table</i> <i>phase</i>)</code> [LISP]</dt>
<dd>Just
like <code>osc</code> (below)
except this computes at the <code>*control-srate*</code> and frequency
is specified in Hz.  Initial <i>phase</i> is specified in degrees, defaulting to zero.
 The <code>*transpose*</code> and <code>*sustain*</code> is not
applied.  The effect of time warping is to warp the starting and ending
times.  The signal itself will have a constant unwarped frequency.<br><br>
<dt><code>fmlfo(<a name="index362"></a><i>freq</i> [, <i>table</i>, <i>phase</i>])</code> [SAL]<br>

<code>(fmlfo <i>freq</i> [<i>table</i> <i>phase</i>])</code> [LISP]</dt>
<dd>A low-frequency oscillator
that computes at the <code>*control-srate*</code> using a sound to specify a time-varying 
frequency in Hz. Initial <i>phase</i> is a <code>FLONUM</code> in degrees. The duration of the result is determined by <i>freq</i>.<br><br>
<dt><code>maketable(<a name="index363"></a><i>sound</i>)</code> [SAL]<br>

<code>(maketable <i>sound</i>)</code> [LISP]</dt>
<dd>Assumes that
the samples in <i>sound</i> constitute one period of a wavetable, and returns a wavetable
suitable for use as the <i>table</i> argument to the <code>osc</code> function (see
below).  Currently, tables are limited to 100,000,000 samples.  This limit is the compile-time constant <code>max_table_len</code> set in <code>sound.h</code>. A wavetable is a list of the form
<blockquote>
(<i>sound</i> <i>pitch-number</i> <i>periodic</i>)</blockquote> 
where the first element is a sound, the second is the pitch of the sound 
(this is not redundant, because the sound may represent any number of
periods), and the third element is <code>T</code> if the sound is one period of
a periodic signal, or <code>nil</code> if the sound is a sample that should not
be looped. Wavetables are used by <code>osc</code>, <code>osc</code>, <code>hzosc</code>,
<code>amosc</code>, <code>fmosc</code>, <code>lfo</code>, and <code>fmlfo</code>.<br><br>
<dt><code>build-harmonic(<a name="index364"></a><a name="index365"></a><i>n</i>, <i>table-size</i>)</code> [SAL]<br>

<code>(build-harmonic <i>n</i> <i>table-size</i>)</code> [LISP]</dt>
<dd>Intended for
constructing wavetables<a name="index366"></a><a name="index367"></a>, this function returns a sound of length <i>table-size</i>
samples containing <i>n</i> periods of a sinusoid.  These can be scaled and
summed to form a waveform with the desired harmonic content.  See <a href = "part2.html#11">Non-Sinusoidal Waveforms</a> for an example. A scaled sum of these harmonics can be passed to <code>maketable</code> to construct a wavetable suitable for <code>osc</code> and other oscillators.<br><br>
<dt><code>control-warp(<a name="index368"></a><i>warp-fn</i>, <i>signal</i>,   [<i>wrate</i>])</code> [SAL]<br>

<code>(control-warp <i>warp-fn</i> <i>signal</i> <i>wrate</i>)</code> [LISP]</dt>
<dd>Applies a
warp function <i>warp-fn</i> to <i>signal</i> using function composition.  If <i>wrate</i> is omitted, linear
interpolation is used.  <i>warp-fn</i> is a mapping from score (logical) time
to real time, and <i>signal</i> is a function from score time to real values.
The result is a function from real time to real values at a sample rate of
<code>*control-srate*</code>. See <code>sound-warp</code> for an explanation of
<i>wrate</i> and high-quality warping.<br><br>
<dt>
<code>mult(<a name="index369"></a><i>beh<sub>1</sub></i>, <i>beh<sub>2</sub></i>, <span style="font-style:normal">...</span>)</code> [SAL]<br>

<code>(mult <i>beh<sub>1</sub></i> <i>beh<sub>2</sub> <span style="font-style:normal">...</span></i>)</code> [LISP]</dt>
<dd>Returns the product of
behaviors.  The arguments may also be numbers, in which case simple multiplication is performed.  If a number and sound are mixed, the <code>scale</code> function is used to scale the sound by the number. When sounds are multiplied, the resulting sample rate is the maximum sample rate of the factors.<br><br>
<dt><code>prod(<a name="index370"></a><i>beh<sub>1</sub></i>, <i>beh<sub>2</sub></i>, <span style="font-style:normal">...</span>)</code> [SAL]<br>

<code>(prod <i>beh<sub>1</sub></i> <i>beh<sub>2</sub></i> <span style="font-style:normal">...</span>)</code> [LISP]</dt>
<dd>Same as <code>mult</code>.<br><br>
<dt>
<code>pan(<a name="index371"></a><a name="index372"></a><i>sound</i>, <i>where</i>)</code> [SAL]<br>

<code>(pan <i>sound</i> <i>where</i>)</code> [LISP]</dt>
<dd>Pans <i>sound</i> (a behavior) according  to <i>where</i> (another behavior or a number). <i>Sound</i> must be monophonic. <i>Where</i> may be a monophonic sound (e.g. <code>(ramp)</code> or simply a number (e.g. <code>0.5</code>). In either case, <i>where</i> should range from 0 to 1, where 0 means pan completely left, and 1 means pan completely right. For intermediate values, the sound to each channel is scaled linearly. Presently, <code>pan</code> does not check its arguments carefully.<br><br>
<dt><code>prod(<a name="index373"></a><i>beh<sub>1</sub></i>, <i>beh<sub>2</sub></i>, <span style="font-style:normal">...</span>)</code> [SAL]<br>

<code>(prod <i>beh<sub>1</sub></i> <i>beh<sub>2</sub></i> <span style="font-style:normal">...</span>)</code> [LISP]</dt>
<dd>Same as <code>mult</code>.<br><br>
<dt>
<code>resample(<a name="index374"></a><i>sound</i>, <i>srate</i>)</code> [SAL]<br>

<code>(resample <i>sound</i> <i>srate</i>)</code> [LISP]</dt>
<dd>Similar to <code>force-srate</code>, except
high-quality interpolation is used to prefilter and reconstruct the signal
at the new sample rate. Also, the result is scaled by 0.95 to reduce problems with
clipping. (See also <code>sound-warp</code>.)<br><br>
<dt>
<code>scale(<a name="index375"></a><i>scale</i>, <i>sound</i>)</code> [SAL]<br>

<code>(scale <i>scale</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Scales the amplitude of <i>sound</i> by the factor <i>scale</i>.  Identical function to <code>snd-scale</code>, except that it handles multichannel sounds.  Sample rates, start times, etc. are taken from <i>sound</i>.<br><br>
<dt><code>scale-db(<a name="index376"></a><i>db</i>, <i>sound</i>)</code> [SAL]<br>

<code>(scale-db <i>db</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Scales the amplitude of <i>sound</i> by the factor <i>db</i>, expressed in decibels.  Sample rates, start times, etc. are taken from <i>sound</i>.<br><br>
<dt><code>scale-srate(<a name="index377"></a><i>sound</i>, <i>scale</i>)</code> [SAL]<br>

<code>(scale-srate <i>sound</i> <i>scale</i>)</code> [LISP]</dt>
<dd>Scales the sample rate of <i>sound</i> by <i>scale</i> factor.  This has the effect of linearly shrinking or stretching time (the sound is not upsampled or downsampled).  This is a special case of <code>snd-xform</code> (see Section <a href = "#103">Signal Operations</a>).<br><br>
<dt><code>shift-time(<a name="index378"></a><i>sound</i>, <i>shift</i>)</code> [SAL]<br>

<code>(shift-time <i>sound</i> <i>shift</i>)</code> [LISP]</dt>
<dd>Shift <i>sound</i>
by <i>shift</i> seconds.  If the sound is 

f(t), then the result is

f(t - shift).
See Figure <a href = "#90">5</a>.  This is a special
case of <code>snd-xform</code> (see Section <a href = "#103">Signal Operations</a>).
</dd></dl>
<hr>
<blockquote>
</blockquote>
<img src="fig5.gif"><br><br>

<p><b>Figure 5: </b>The <code>shift-time</code> function shifts a sound in time
according to its <i>shift</i> argument.

</p>
<hr>
<dl>
<dt>
<code>sound-warp(<a name="index379"></a><i>warp-fn</i>, <i>signal</i> [, <i>wrate</i>])</code> [SAL]<br>

<code>(sound-warp <i>warp-fn</i> <i>signal</i> [<i>wrate</i>])</code> [LISP]</dt>
<dd>Applies a
warp function <i>warp-fn</i> to <i>signal</i> using function composition.  If the optional parameter <i>wrate</i> is omitted or NIL, linear
interpolation is used.  Otherwise, high-quality sample interpolation is used, and the
result is scaled by 0.95 to reduce problems with clipping (interpolated samples can
exceed the peak values of the input samples.) 
<i>warp-fn</i> is a mapping from score (logical) time
to real time, and <i>signal</i> is a function from score time to real values.
The result is a function from real time to real values at a sample rate of <code>*sound-srate*</code>.
See also <code>control-warp</code>.

If <i>wrate</i> is not NIL, it must be a number. The parameter indicates that
high-quality resampling should be used and specifies the sample rate for the
inverse of <i>warp-fn</i>. Use the lowest number you can.
 (See below for details.) Note that high-quality resampling is
much slower than linear interpolation. 

To perform high-quality resampling by a fixed ratio, as opposed to a
variable ratio allowed in <code>sound-warp</code>, use <code>scale-srate</code> to
stretch or shrink the sound, and then <code>resample</code> to restore the
original sample rate.

<code>Sound-warp</code> and <code>control-warp</code> both take the inverse of
<i>warp-fn</i> to get a function from real time to score time. Each sample
of this inverse is thus a score time; <i>signal</i> is evaluated at each of
these score times to yield a value, which is the desired result. The 
sample rate of the inverse warp function is somewhat arbitrary. With linear
interpolation, the inverse warp function sample rate is taken to be the
output sample rate. Note, however, that the samples of the inverse warp
function are stored as 32-bit floats, so they have limited precision. Since
these floats represent sample times, rounding can be a problem. Rounding
in this case is equivalent to adding jitter to the sample times. Nyquist
ignores this problem for ordinary warping, but for high-quality warping, the
jitter cannot be ignored. 

The solution is to use a rather low sample rate
for the inverse warp function. <code>Sound-warp</code> can then linearly
interpolate this signal using double-precision floats to minimize jitter
between samples. The sample rate is a compromise: a low sample rate
minimizes jitter, while a high sample rate does a better job of capturing
detail (e.g. rapid fluctuations) in the warp function. A good rule of thumb
is to use at most 1,000 to 10,000 samples for the inverse warp function. For
example, if the result will be 1 minute of sound, use a sample rate of
3000 samples / 60 seconds = 50 samples/second. Because Nyquist has no
advance information about the warp function, the inverse warp function
sample rate must be provided as a parameter.  When in doubt, just try
something and let your ears be the judge.<br><br>
<dt><code>integrate(<a name="index380"></a><a name="index381"></a><i>signal</i>)</code> [SAL]<br>

<code>(integrate <i>signal</i>)</code> [LISP]</dt>
<dd>Computes the integral of <i>signal</i>. The start time, sample rate, etc. are taken from <i>signal</i>.<br><br>
<dt><code>slope(<a name="index382"></a><a name="index383"></a><a name="index384"></a><i>signal</i>)</code> [SAL]<br>

<code>(slope <i>signal</i>)</code> [LISP]</dt>
<dd>Computes the first derivative (slope) of <i>signal</i>.  The start time, sample rate, etc. are taken from <i>signal</i>.
</dd></dl><a name = "91"><h5>Oscillators</h5></a><dl>
<dt>
<code>osc(<a name="index385"></a><i>pitch</i> [, <i>duration</i>, <i>table</i>, <i>phase</i>])</code> [SAL]<br>

<code>(osc <i>pitch</i> [<i>duration</i> <i>table</i> <i>phase</i>])</code> [LISP]</dt>
<dd>Returns 
a sound which
is the <i>table</i> oscillated at <i>pitch</i> for the given <i>duration</i>,
starting with the <i>phase</i> (in degrees).  
Defaults are:  <i>duration</i> <code>1.0</code> 
(second), <i>table</i> <code>*table*</code>,
<i>phase</i> <code>0.0</code>.  The default value of <code>*table*</code> is a sinusoid. Duration is stretched by <code>*warp*</code> and 
<code>*sustain*</code>, amplitude is nominally 1, but scaled by <code>*loudness*</code>, the start time is logical time 0, transformed by <code>*warp*</code>, and the sample rate is <code>*sound-srate*</code>.
The effect of time-warping is to warp the starting and ending times only; the
signal has a constant unwarped frequency.<br>

<b><i>Note 1:</i></b> A <code>table</code> is 3-element list. See <code>maketable</code> for a detailed
 description.<br>

<b><i>Note 2:</i></b> in the current implementation, it is assumed that the
output should be periodic.  See <code>snd-down</code> and <code>snd-up</code> for resampling one-shot sounds to a desired sample rate.  A future version of <code>osc</code>
will handle both cases.<br>

<b><i>Note 3:</i></b> When <code>osc</code> is called, memory is allocated for the table, and samples are copied from the sound (the first element of the list which is the <i>table</i> parameter) to the memory.  Every instance of <code>osc</code> has a private copy of the table, so the total storage can become large in some cases, for example in granular synthesis with many instances of <code>osc</code>. In some cases, it may make sense to use <code>snd-flatten</code> (see Section <a href = "#86">Accessing and Creating Sound</a>) to cause the sound to be fully realized, after which the <code>osc</code> and its table memory can be reclaimed by garbage collection. The <code>partial</code> function (see below) does not need a private table and does not use much space.<br><br>
<dt>
<code>partial(<a name="index386"></a><i>pitch</i>, <i>env</i>)</code> [SAL]<br>

<code>(partial <i>pitch</i> <i>env</i>)</code> [LISP]</dt>
<dd>Returns a sinusoid at
the indicated pitch; the sound is multiplied by <i>env</i>.  The start time and
duration are taken from <i>env</i>, which is of course subject to
transformations.  The sample rate is <code>*sound-srate*</code>.  The <code>partial</code>
function is faster than <code>osc</code>.<br><br>
<dt>
<code>sine(<a name="index387"></a><i>pitch</i> [, <i>duration</i>])</code> [SAL]<br>

<code>(sine <i>pitch</i> [<i>duration</i>])</code> [LISP]</dt>
<dd>Returns a sinusoid at
the indicated pitch.  The sample rate is <code>*sound-srate*</code>.  
This function is like <code>osc</code> with
respect to transformations.  The <code>sine</code> function is faster than
<code>osc</code>.<br><br>
<dt><code>hzosc(<a name="index388"></a><i>hz</i> [, <i>table</i>, <i>phase</i>])</code> [SAL]<br>

<code>(hzosc <i>hz</i> [<i>table</i> <i>phase</i>])</code> [LISP]</dt>
<dd>Returns a sound
which is the <i>table</i> oscillated at <i>hz</i> starting at <i>phase</i> degrees. The
default <i>table</i> is <code>*table*</code> and the default <i>phase</i> is <i>0.0</i>
degrees. The default duration is <code>1.0</code>, but this is stretched as
in <code>osc</code> (see above). The <i>hz</i> parameter may be a <code>SOUND</code>, in
which case the duration of the result is the duration of <i>hz</i>. The
sample rate is <code>*sound-srate*</code>.<br><br>
<dt><code>osc-saw(<a name="index389"></a><a name="index390"></a><i>hz</i>)</code> [SAL]<br>

<code>(osc-saw <i>hz</i>)</code> [LISP]</dt>
<dd>Returns a sawtooth waveshape at the indicated frequency (in Hertz). The sample rate is <code>*sound-srate*</code>. The <i>hz</i> parameter may be a sound as in <i>hzosc</i> (see above).<br><br>
<dt><code>osc-tri(<a name="index391"></a><a name="index392"></a><i>hz</i>)</code> [SAL]<br>

<code>(osc-tri <i>hz</i>)</code> [LISP]</dt>
<dd>Returns a triangle waveshape at the indicated frequency (in Hertz). The sample rate is <code>*sound-srate*</code>. The <i>hz</i> parameter may be a sound as in <i>hzosc</i> (see above).<br><br>
<dt><code>osc-pulse(<a name="index393"></a><a name="index394"></a><a name="index395"></a><a name="index396"></a><i>hz</i>, <i>bias</i> [, <i>compare-shape</i>])</code> [SAL]<br>

<code>(osc-pulse <i>hz</i> <i>bias</i> [<i>compare-shape</i>])</code> [LISP]</dt>
<dd>Returns a square pulse with variable width at the indicated frequency (in Hertz). The <i>bias</i> parameter controls the pulse width and should be between <code>-1</code> and <code>+1</code>, giving a pulse width from 0% (always at <code>-1</code>) to 100% (always at <code>+1</code>). When bias is zero, a square wave is generated. Bias may be a <code>SOUND</code> to create varying pulse width. If bias changes rapidly, strange effects may occur. The optional <i>compare-shape</i> defaults to a hard step at zero, but other shapes may be used to achieve non-square pulses. The <code>osc-pulse</code> behavior is written in terms of other behaviors and defined in the file <code>nyquist.lsp</code> using just a few lines of code. Read the code for the complete story.<br><br>
<dt>
<code>amosc(<a name="index397"></a><i>pitch</i>, <i>modulation</i> [, <i>table</i>,
<i>phase</i>])</code> [SAL]<br>

<code>(amosc <i>pitch</i> <i>modulation</i> [<i>table</i> <i>phase</i>])</code> [LISP]</dt>
<dd>Returns a
sound which is <i>table</i> oscillated at <i>pitch</i>.  The output
is multiplied by <i>modulation</i>
for the duration of the sound <i>modulation</i>.  
<i>osc-table</i> defaults to
<code>*table*</code>, and <i>phase</i> is the starting phase (default 0.0 degrees)
within <i>osc-table</i>.  The sample rate is <code>*sound-srate*</code>.  <br><br>
<dt>
<code>fmosc(<a name="index398"></a><i>pitch</i>, <i>modulation</i> [, <i>table</i>,
<i>phase</i>])</code> [SAL]<br>

<code>(fmosc <i>pitch</i> <i>modulation</i> [<i>table</i> <i>phase</i>])</code> [LISP]</dt>
<dd>Returns a
sound which is <i>table</i> oscillated at <i>pitch</i> plus <i>modulation</i>
for the duration of the sound <i>modulation</i>.  
<i>osc-table</i> defaults to
<code>*table*</code>, and <i>phase</i> is the starting phase (default 0.0 degrees)
within <i>osc-table</i>.  The <i>modulation</i>
is expressed in hz, e.g. a sinusoid modulation signal with an
amplitude of 1.0 (2.0 peak to peak), will cause a +/- 1.0 hz 
frequency deviation in <i>sound</i>.  Negative frequencies are correctly
handled.  The sample rate is <code>*sound-srate*</code>.  <br><br>
<dt>
<code>fmfb(<a name="index399"></a><a name="index400"></a><i>pitch</i>, <i>index</i> [, <i>dur</i>])</code> [SAL]<br>

<code>(fmfb <i>pitch</i> <i>index</i> [<i>dur</i>])</code> [LISP]</dt>
<dd>Returns
a sound generated by feedback FM synthesis. The <i>pitch</i> parameter
(given in the usual half-step units) 
controls the fundamental frequency. The <i>index</i> is the amount of
feedback, which may be a <code>SOUND</code> or a <code>FLONUM</code>. If <i>index</i> is
a <code>FLONUM</code>, <i>dur</i> must be provided (a <code>FLONUM</code>) to specify
the duration. Otherwise, <i>dur</i> is ignored if present and the duration is
determined by that of <i>index</i>. The sample rate is <code>*sound-srate*</code>.
A sinusoid table is used.
If <i>index</i> is below 1.1, this generates a sawtooth-like waveform.<br><br>
<dt>
<code>buzz(<a name="index401"></a><i>n</i>, <i>pitch</i>, <i>modulation</i>)</code> [SAL]<br>

<code>(buzz <i>n</i> <i>pitch</i> <i>modulation</i>)</code> [LISP]</dt>
<dd>Returns a
sound with <i>n</i> harmonics of equal amplitude and a total amplitude
of 1.0, using a well-known function of two cosines. If <i>n</i> (an integer)
is less than 1, it is set to 1. Aliasing will occur if <i>n</i> is too large.
The <i>pitch</i>specifies the fundamental frequency (a number, in steps)
assuming no modulation.
The duration is
determined by the duration of the sound <i>modulation</i>, which is a
frequency modulation term expressed in Hz (see Section <a href = "#91">Oscillators</a>).
Negative frequencies are correctly handled.
The sample rate is <code>*sound-srate*</code>.<br><br>
<dt>
<code>pluck(<a name="index402"></a><a name="index403"></a><a name="index404"></a><a name="index405"></a><i>pitch</i> [, <i>duration</i>, <i>final-amplitude</i>])</code> [SAL]<br>

<code>(pluck <i>pitch</i> [<i>duration</i> <i>final-amplitude</i>])</code> [LISP]</dt>
<dd>Returns a sound at the 
given <i>pitch</i> created using a modified Karplus-Strong plucked string
algorithm. The tone decays from an amplitude of about 1.0 to about
<i>final-amplitude</i> in <i>duration</i> seconds. The default values are to
decay to 0.001 (-60dB) in 1 second. The sample rate is <code>*sound-srate*</code>.<br><br>
<dt>
<code>siosc(<a name="index406"></a><a name="index407"></a><i>pitch</i>,
<i>modulation</i>, <i>tables</i>)</code> [SAL]<br>

<code>(siosc <i>pitch</i> <i>modulation</i> <i>tables</i>)</code> [LISP]</dt>
<dd>Returns a sound constructed by
interpolating through a succession of periodic waveforms. The frequency is
given (in half steps) by <i>pitch</i> to which a <i>modulation</i> signal (in hz)
is added, exactly as in <code>fmosc</code>. The <i>tables</i> specify a list of
waveforms as follows: (<i>table0</i> <i>time1</i> <i>table2</i> ... <i>timeN</i>
<i>tableN</i>), where each <i>table</i> is a sound representing one period. Each
<i>time</i> is a time interval measured from the starting time. The time is
scaled by the nominal duration (computed using <code>(local-to-global
(get-sustain))</code>) to get the actual time. Note that this implies linear
stretching rather than continuous timewarping of the interpolation or the
breakpoints. The waveform is <i>table0</i> at the starting time, <i>table1</i>
after <i>time1</i> (scaled as described), and so on. The duration and logical
stop time is given by <i>modulation</i>. If <i>modulation</i> is shorter than
<i>timeN</i>, then the full sequence of waveforms is not used.  If
<i>modulation</i> is longer than <i>timeN</i>, <i>tableN</i> is used after <i>timeN</i>
without further interpolation.<br><br>
<dt>
<code>sampler(<a name="index408"></a><i>pitch</i>, <i>modulation</i>
 [, <i>sample</i>, <i>npoints</i>])</code> [SAL]<br>

<code>(sampler <i>pitch</i> <i>modulation</i> [<i>sample</i> <i>npoints</i>])</code> [LISP]</dt>
<dd>Returns a sound constructed by reading a sample from 
beginning to end and then splicing on copies of the same sound from 
a loop point to the end.  
The <i>pitch</i> and <i>modulation</i> parameters are used as in <code>fmosc</code>
described above.  The optional <i>sample</i> (which defaults to 2048-point
sinusoid) is a list of the form
<blockquote>
(<i>sound</i> <i>pitch-number</i> <i>loop-start</i>)</blockquote> where the first element is a sound containing the sample, the second is the
pitch of the sample, and the third element is the time of the loop point. If
the loop point is not in the bounds of the sound, it is set to zero.
The optional <i>npoints</i> specifies how many points should be used for sample
interpolation.  Currently this parameter defaults to 2 and only 2-point
(linear) interpolation is implemented.  It is an error to modulate such that the frequency
is negative. Note also that the loop point may be fractional.
The sample rate is <code>*sound-srate*</code>.  
</dd></dl>
<a name = "92"><h5>Piece-wise Approximations</h5></a><a name="index409"></a><a name="index410"></a><a name="index411"></a> There are a number of related behaviors for piece-wise approximations to functions.  The simplest of these, <code>pwl</code> was mentioned earlier in the manual.  It takes a list of breakpoints, assuming an initial point at (0, 0), and a final value of 0.  An analogous piece-wise exponential function, <code>pwe</code>, is provided. Its implicit starting and stopping values are 1 rather than 0 because exponential decays never reach zero.  This inability to reach zero can be addressed by a pseudo-exponential function, <code>pwz</code>, whose design was borrowed from the ZynAddSubFx software synthesizer, where we add a small bias (0.01) to breakpoints, compute the exponential envelope between these new breakpoints, then subtract 0.01 so that the envelope can actually decay all the way to zero. These curves are very close to exponential (within 0.01) until they approach zero, where they become essentially linear. Like <code>pwl</code> (linear), the <code>pwz</code> envelopes assume an initial point at (0, 0) and a final value of 0. For amplitude envelopes, the <code>linear-attack</code> option for the <code>pwz</code> variants is suggested for a more natural-sounding envelope.
<p>Each of these three forms has variants.
You can specify the initial and final values (instead of taking the
default).  You can specify time in intervals rather than cummulative
time.  Finally, you can pass a list rather than an argument list.  This leads to 24 versions:
<pre><b>Piece-wise Linear Functions:</b>
	<i>Cummulative Time:</i>
		<i>Default initial point at (0, 0), final value at 0:</i>
			pwl
			pwl-list
		<i>Explicit initial value:</i>
			pwlv
			pwlv-list
	<i>Relative Time:</i>
		<i>Default initial point at (0, 0), final value at 0:</i>
			pwlr
			pwlr-list
		<i>Explicit initial value:</i>
			pwlvr
			pwlvr-list

<b>Piece-wise Exponential Functions:</b>
	<i>Cummulative Time:</i>
		<i>Default initial point at (0, 1), final value at 1:</i>
			pwe
			pwe-list
		<i>Explicit initial value:</i>
			pwev
			pwev-list
	<i>Relative Time:</i>
		<i>Default initial point at (0, 1), final value at 1:</i>
			pwer
			pwer-list
		<i>Explicit initial value:</i>
			pwevr
			pwevr-list
<b>Piece-wise Pseudo-Exponential Functions with Bias:</b>
	<i>Cummulative Time:</i>
		<i>Default initial point at (0, 0), final value at 0:</i>
			pwz
			pwz-list
		<i>Explicit initial value:</i>
			pwzv
			pwzv-list
	<i>Relative Time:</i>
		<i>Default initial point at (0, 0), final value at 0:</i>
			pwzr
			pwzr-list
		<i>Explicit initial value:</i>
			pwzvr
			pwzvr-list
</pre> </p>

<p></p>

<p></p>

<p></p>
 All of these functions are implemented in terms of <code>pwl</code> (see <code>nyquist.lsp</code> for the implementations.  There are infinite opportunities for errors in these functions: if you leave off a data point, try to specify points in reverse order, try to create an exponential that goes to zero or negative values, or many other bad things, the behavior is not well-defined.  Nyquist should not crash, but Nyquist does not necessarily attempt to report errors at this time.<dl>
<dt>

<code>pwl(<a name="index412"></a><i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwl <i>t<sub>1</sub></i> <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise linear envelope with breakpoints at (0, 0), (<i>t<sub>1</sub></i>,
<i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>, 0).  The breakpoint
times are scaled linearly by the value of <code>*sustain*</code> (if
<code>*sustain*</code> is a <code>SOUND</code>, it is evaluated once at the starting
time of the envelope).  Each breakpoint time is then mapped according to
<code>*warp*</code>.  The result is a linear interpolation (unwarped) between 
the breakpoints.  The sample rate is <code>*control-srate*</code>.  Breakpoint
times are quantized to the nearest sample time.  If you specify one or more
breakpoints withing one sample period, <code>pwl</code> attempts to give a good
approximation to the specified function.  In particular, if two breakpoints
are simultaneous, <code>pwl</code> will move one of them to an adjacent sample,
producing a steepest possible step in the signal.  The exact details of this
&ldquo;breakpoint munging&rdquo; is subject to change in future versions.  Please report
any cases where breakpoint lists give unexpected behaviors.  The author will
try to apply the &ldquo;principle of least surprise&rdquo; to the design.  Note that
the times are relative to 0; they are not durations of each envelope
segment.<br><br>
<dt><code>pwl-list(<a name="index413"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwl-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>If you have a list of
breakpoints, you can use <code>apply</code> to apply the <code>pwl</code> function to
the breakpoints, but if the list is very long (hundreds or thousands of
points), you might get a stack overflow because XLISP has a fixed-size
argument stack.  Instead, call <code>pwl-list</code>, passing one argument, the
list of breakpoints.<br><br>
<dt><code>pwlv(<a name="index414"></a><i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>t<sub>3</sub></i>, <i>t<sub>3</sub></i>, ... <i>t<sub>n</sub></i>, <i>l<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwlv <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <i>t<sub>3</sub></i> <i>l<sub>3</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i> <i>l<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise linear envelope with breakpoints at (0, l<sub>1</sub>),
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub>, <i>l<sub>n</sub></i></i>.
Otherwise, the behavior is like that of <code>pwl</code>.<br><br>
<dt><code>pwlv-list(<a name="index415"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwlv-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwlv</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwlr(<a name="index416"></a><i>i<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, ... <i>i<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwlr <i>i<sub>1</sub></i> <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise linear envelope with breakpoints at (0, 0), (<i>t<sub>1</sub></i>,
<i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>, 0), where
<i>t<sub>j</sub></i> is the sum of <i>i<sub>1</sub></i> through <i>i<sub>j</sub></i>.  In other
words, the breakpoint times are specified in terms of intervals rather
than cummulative time.  Otherwise, the behavior is like that of
<code>pwl</code>.<br><br>
<dt><code>pwlr-list(<a name="index417"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwlr-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwlr</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwlvr(<a name="index418"></a><i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>i<sub>3</sub></i>, <i>i<sub>3</sub></i>, ... <i>i<sub>n</sub></i>, <i>l<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwlvr <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <i>i<sub>3</sub></i> <i>i<sub>3</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i> <i>l<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise linear envelope with breakpoints at (0, l<sub>1</sub>),
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub>, <i>l<sub>n</sub></i></i>,
where <i>t<sub>j</sub></i> is the sum of <i>i<sub>2</sub></i> through <i>i<sub>j</sub></i>.  In
other words, the breakpoint times are specified in terms of intervals
rather than cummulative time.  Otherwise, the behavior is like that of
<code>pwlv</code>.<br><br>
<dt><code>pwlvr-list(<a name="index419"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwlvr-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwlvr</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwe(<a name="index420"></a><i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwe <i>t<sub>1</sub></i> <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise exponential envelope with breakpoints at (0, 1),
(<i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>,
1).  Exponential segments means that the ratio of values from sample
to sample is constant within the segment.  (The current implementation
actually takes the log of each value, computes a piece-wise
exponential from the points using <code>pwl</code>, then exponentiates each
resulting sample.  A faster implementation is certainly possible!)
Breakpoint values (<i>l<sub>j</sub></i>) must be greater than zero.  Otherwise,
this function is similar to <code>pwl</code>, including stretch by
<code>*sustain*</code>, mapping according to <code>*warp*</code>, sample rate
based on <code>*control-srate*</code>, and "breakpoint munging" (see
<code>pwl</code> described above).  <i>Default initial and final values are
of dubious value with exponentials.  See the <code>pwz</code> functions
which allow decay to zero, and <code>pwev</code> which has explicit initial
and final values.</i><br><br>
<dt><code>pwe-list(<a name="index421"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwe-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwe</code> that takes a single list of breakpoints as its argument.
See <code>pwl-list</code> above for the rationale.<br><br>
<dt>
<code>pwev(<a name="index422"></a><i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>t<sub>3</sub></i>, <i>t<sub>3</sub></i>, <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>, <i>l<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwev <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <i>t<sub>3</sub></i> <i>t<sub>3</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i> <i>l<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise exponential envelope with breakpoints at (0, <i>l<sub>1</sub></i>),
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub></i>, <i>l<sub>n</sub></i>).
Otherwise, the behavior is like that of <code>pwe</code>.<br><br>
<dt><code>pwev-list(<a name="index423"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwev-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwev</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwer(<a name="index424"></a><i>i<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwer <i>i<sub>1</sub></i> <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise exponential envelope with breakpoints at (0, 1),
(<i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>,
1), where <i>t<sub>j</sub></i> is the sum of <i>i<sub>1</sub></i> through <i>i<sub>j</sub></i>.  In
other words, the breakpoint times are specified in terms of intervals
rather than cummulative time.  Otherwise, the behavior is like that of
<code>pwe</code>.  Consider using <code>pwerv</code> instead of this one.<br><br>
<dt><code>pwer-list(<a name="index425"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwer-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwer</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwevr(<a name="index426"></a><a name="index427"></a><i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>i<sub>3</sub></i>, <i>i<sub>3</sub></i>, <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>, <i>l<sub>n</sub></i>)</code> [SAL]<br>

<code>(pwevr <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <i>i<sub>3</sub></i> <i>i<sub>3</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i> <i>l<sub>n</sub></i>)</code> [LISP]</dt>
<dd>Creates
a piece-wise exponential envelope with breakpoints at (0, l<sub>1</sub>),
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub>, <i>l<sub>n</sub></i></i>,
where <i>t<sub>j</sub></i> is the sum of <i>i<sub>2</sub></i> through <i>i<sub>j</sub></i>.  In
other words, the breakpoint times are specified in terms of intervals
rather than cummulative time.  Otherwise, the behavior is like that of
<code>pwev</code>.  Note that this is similar to the csound GEN05 generator.
Which is uglier, <i>GEN05</i> or <i>pwevr</i>?<br><br>
<dt><code>pwevr-list(<a name="index428"></a><i>breakpoints</i>)</code> [SAL]<br>

<code>(pwevr-list <i>breakpoints</i>)</code> [LISP]</dt>
<dd>A version
of <code>pwevr</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the rationale.<br><br>
<dt><code>pwz(<a name="index429"></a><i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwz <i>t<sub>1</sub></i> <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>Creates
a piece-wise pseudo-exponential envelope with breakpoints at (0, 0),
(<i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>,
0).  Each breakpoint value is first incremented by <i>bias</i>, then 
interpolated with exponentials as in <code>pwe</code> (see above), then
<i>bias</i> is subtracted from all samples so that the envelope passes 
through the original breakpoints as specified, including decay to zero.
Breakpoint values (<i>l<sub>j</sub></i>) must be non-negative.  Otherwise,
this function is similar to <code>pwl</code>, including stretch by
<code>*sustain*</code>, mapping according to <code>*warp*</code>, sample rate
based on <code>*control-srate*</code>, and "breakpoint munging" (see
<code>pwl</code> described above). 
The <code>linear-attack</code> keyword parameter,
if true (default is false), causes a linear interpolation from (0, 0) to
(<i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>) rather than exponential.
The <code>bias</code> keyword parameter
is optional, and defaults
to 0.01 (about -40dB).  As bias grows large, the &ldquo;half-life&rdquo; of the
decay becomes large, so the decay is more linear. Even large values
such as 1 are possible. As bias grows small, the &ldquo;half-life&rdquo; of
the decay becomes small, so the decay is more rapid.
Example: If bias is 0.01 (default), a decay from 1 to 0 in 1 second
will decay to about -20dB in 0.5 seconds. If bias is 0.0001 (-80dB),
the envelope will decay to about -20dB in only 0.25 seconds.
You can think of bias as approximately how much attenuation you
want to occur exponentially before the final decay to zero where the
envelope becomes more linear. With bias values at or below 0.01, the
&ldquo;linear part&rdquo; occurs when the signal is barely audible anyway.<br><br>
<dt><code>pwz-list(<a name="index430"></a><i>breakpoints</i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwz-list <i>breakpoints</i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>A 
version of <code>pwz</code> that takes a single list of breakpoints as its argument.
See <code>pwl-list</code> above for the rational for
this &ldquo;-list&rdquo; form of <code>pwz</code> and for an explanation of
the <code>linear-attack</code> keyword parameter.<br><br>
<dt>
<code>pwzv(<a name="index431"></a><i>l<sub>1</sub></i>, <i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>t<sub>3</sub></i>, <i>t<sub>3</sub></i>, <span style="font-style:normal">...</span> <i>t<sub>n</sub></i>, <i>l<sub>n</sub></i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzv <i>l<sub>1</sub></i> <i>t<sub>2</sub></i> <i>l<sub>2</sub></i> <i>t<sub>3</sub></i> <i>t<sub>3</sub></i> <span style="font-style:normal">...</span> <i>t<sub>n</sub></i> <i>l<sub>n</sub></i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>Creates
a piece-wise pseudo-exponential envelope with breakpoints at (0, <i>l<sub>1</sub></i>), 
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub></i>, <i>l<sub>n</sub></i>). If the 
<code>linear-attack</code> parameter is true (default is false), linear interpolation is used
from (0, <i>l<sub>1</sub></i>) to (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>). 
Otherwise, the behavior is like that of <code>pwz</code>.<br><br>
<dt><code>pwzv-list(<a name="index432"></a><i>breakpoints</i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzv-list <i>breakpoints</i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>A
version of <code>pwzv</code> that takes a single list of breakpoints as its
argument. See <code>pwl-list</code> above for the
rational for this &ldquo;-list&rdquo; form of <code>pwzv</code>.<br><br>
<dt><code>pwzr(<a name="index433"></a><i>i<sub>1</sub></i>, <i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzr <i>i<sub>1</sub></i> <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>Creates
a piece-wise pseudo-exponential envelope with breakpoints at (0, 0),
(<i>t<sub>1</sub></i>, <i>l<sub>1</sub></i>), (<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), ... (<i>t<sub>n</sub></i>,
0), where <i>t<sub>j</sub></i> is the sum of <i>i<sub>1</sub></i> through <i>i<sub>j</sub></i>.  In
other words, the breakpoint times are specified in terms of intervals
rather than cummulative time.  Otherwise, the behavior is like that of
<code>pwz</code>.<br><br>
<dt><code>pwzr-list(<a name="index434"></a><i>breakpoints</i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzr-list <i>breakpoints</i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>A
version of <code>pwzr</code> that takes a single list of breakpoints as its
argument. See <code>pwl-list</code> above for the
rational for this &ldquo;-list&rdquo; form of <code>pwzr</code>.<br><br>
<dt><code>pwzvr(<a name="index435"></a><a name="index436"></a><i>l<sub>1</sub></i>, <i>i<sub>2</sub></i>, <i>l<sub>2</sub></i>, <i>i<sub>3</sub></i>, <i>i<sub>3</sub></i>, <span style="font-style:normal">...</span> <i>i<sub>n</sub></i>, <i>l<sub>n</sub></i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzvr <i>l<sub>1</sub></i> <i>i<sub>2</sub></i> <i>l<sub>2</sub></i> <i>i<sub>3</sub></i> <i>i<sub>3</sub></i> <span style="font-style:normal">...</span> <i>i<sub>n</sub></i> <i>l<sub>n</sub></i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>Creates
a piece-wise exponential envelope with breakpoints at (0, l<sub>1</sub>),
(<i>t<sub>2</sub></i>, <i>l<sub>2</sub></i>), etc., ending with (<i>t<sub>n</sub>, <i>l<sub>n</sub></i></i>,
where <i>t<sub>j</sub></i> is the sum of <i>i<sub>2</sub></i> through <i>i<sub>j</sub></i>.  In
other words, the breakpoint times are specified in terms of intervals
rather than cummulative time.  Otherwise, the behavior is like that of
<code>pwzv</code>. See <code>pwz</code> (above) for an explanation of <i>bias</i> and <i>linatk</i>.<br><br>
<dt><code>pwzvr-list(<a name="index437"></a><i>breakpoints</i>, [bias: <i>bias</i>], [linear-attack: <i>linatk</i>])</code> [SAL]<br>

<code>(pwzvr-list <i>breakpoints</i> [:bias <i>bias</i>] [:linear-attack <i>linatk</i>])</code> [LISP]</dt>
<dd>A
version of <code>pwzvr</code> that takes a single list of breakpoints as its
argument.  See <code>pwl-list</code> above for the
rational for this &ldquo;-list&rdquo; form of <code>pwzvr</code>.
</dd></dl>
<a name = "93"><h5>Filter Behaviors</h5></a><dl>
<dt>

<code>alpass(<a name="index438"></a><a name="index439"></a><a name="index440"></a><i>sound</i>, <i>decay</i>, <i>hz</i> [, <i>minhz</i>])</code> [SAL]<br>

<code>(alpass <i>sound</i> <i>decay</i> <i>hz</i> [<i>minhz</i>])</code> [LISP]</dt>
<dd>Applies an all-pass filter to <i>sound</i>.  This all-pass filter creates a delay effect without the resonances of a comb filter. The decay time of the filter is given by <i>decay</i>.  The <i>hz</i> parameter must be a number or sound greater than zero.  It is used to compute delay, which is then rounded to the nearest integer number of samples (so the frequency is not always exact.  Higher sampling rates yield better delay resolution.)  The <i>decay</i> may be a sound or a number.  In either case, it must also be positive.  (Implementation note: an exponentiation is needed to convert <i>decay</i> into the <i>feedback</i> parameter, and exponentiation is typically more time-consuming than the filter operation itself.  To get high performance, provide <i>decay</i> at a low sample rate.)  The resulting sound will have the start time, sample rate, etc. of <i>sound</i>. If <i>hz</i> is of type <code>SOUND</code>, the delay may be time-varying. Linear interpolation is then used for fractional sample delay, but it should be noted that linear interpolation implies a low-pass transfer function. Thus, this filter may behave differently with a constant <code>SOUND</code> than it does with a <code>FLONUM</code> value for <i>hz</i>. In addition, if <i>hz</i> is of type <code>SOUND</code>, then <i>minhz</i> is required. The <i>hz</i> parameter will be clipped to be greater than <i>minhz</i>, placing an upper bound on the delay buffer length.<br><br>
<dt>
<code>comb(<a name="index441"></a><a name="index442"></a><i>sound</i>, <i>decay</i>, <i>hz</i>)</code> [SAL]<br>

<code>(comb <i>sound</i> <i>decay</i> <i>hz</i>)</code> [LISP]</dt>
<dd>Applies a comb filter to <i>sound</i>.  A comb filter emphasizes (resonates at) frequencies that are multiples of a <i>hz</i>. The decay time of the resonance is given by <i>decay</i>.  This is a variation on <code>feedback-delay</code> (see below).  The <i>hz</i> parameter must be a number greater than zero.  It is used to compute delay, which is then rounded to the nearest integer number of samples (so the frequency is not always exact.  Higher sampling rates yield better delay resolution.)  The <i>decay</i> may be a sound or a number.  In either case, it must also be positive.  (Implementation note: an exponentiation is needed to convert <i>decay</i> into the <i>feedback</i> parameter for <code>feedback-delay</code>, and exponentiation is typically more time-consuming than the filter operation itself.  To get high performance, provide <i>decay</i> at a low sample rate.)  The resulting sound will have the start time, sample rate, etc. of <i>sound</i>.<br><br>
<dt>
<code>congen(<a name="index443"></a><a name="index444"></a><a name="index445"></a><i>gate</i>, <i>risetime</i>, <i>falltime</i>)</code> [SAL]<br>

<code>(congen <i>gate</i> <i>risetime</i> <i>falltime</i>)</code> [LISP]</dt>
<dd>Implements an analog synthesizer-style contour generator. The input <i>gate</i> normally goes from 0.0 to 1.0 to create an attack and from 1.0 to 0.0 to start a release.  During the attack (output is increasing), the output converges half-way to <i>gate</i> in <i>risetime</i> (a <code>FLONUM</code>) seconds. During the decay, the half-time is <i>falltime</i> seconds. The sample rate, start time, logical stop, and terminate time all come from <i>gate</i>. If you want a nice decay, be sure that the <i>gate</i> goes to zero and stays there for awhile before <i>gate</i> terminates, because <code>congen</code> (and all Nyquist sounds) go immediately to zero at termination time.  For example, you can use <code>pwl</code> to build a pulse followed by some zero time:

<p></p>
<pre>
(pwl 0 1 duty 1 duty 0 1)
</pre>

<p>
Assuming <i>duty</i> is less than 1.0, this will be a pulse of duration <i>duty</i> followed by zero for a total duration of 1.0.
</p>
<pre>
(congen (pwl 0 1 duty 1 duty 0 1) 0.01 0.05)
</pre>

<p>
will have a duration of 1.0 because that is the termination time of the <code>pwl</code> input. The decaying release of the resulting envelope will be truncated to zero at time 1.0. (Since the decay is theoretically infinite, there is no way to avoid truncation, although you could multiply by another envelope that smoothly truncates to zero in the last millisecond or two to get both an exponential decay and a smooth final transition to zero.)</p>
<dt>
<code>convolve(<a name="index446"></a><a name="index447"></a><a name="index448"></a><i>sound</i>,
<i>response</i>)</code> [SAL]<br>

<code>(convolve <i>sound</i> <i>response</i>)</code> [LISP]</dt>
<dd>Convolves two signals. The first can be any length, but the total space required is proportional to
the length of <i>response</i>. The start time, logical stop time, and sample 
rate of the output match those of the input <i>sound</i>. The physical stop 
time of the result is the physical stop time of <i>sound</i> plus the duration 
of the <i>response</i> so that the result sound includes the &ldquo;tail&rdquo; of the 
filter response. The response is linearly interpolated if necessary to have same sample rate as <i>sound</i>. The current implementation uses a &ldquo;fast convolution&rdquo; algorithm with a maximum FFT size of 64K, which after zero padding allows up to 32K point convolutions. If the impulse response is longer, it is broken into multiple blocks of 32K samples. There is no limit on the length of the impulse response. This is an Order(N x M) algorithm where N and M are the number of 32K sample blocks in the <i>sound</i> and <i>response</i>, respectively.
Further discussion and examples can be found in 
<code>nyquist/lib/convolve/convolution.html</code><a name="index449"></a><a name="index450"></a>. <br><br>
<dt>
<code>feedback-delay(<a name="index451"></a><a name="index452"></a><a name="index453"></a><i>sound</i>, <i>delay</i>, <i>feedback</i>)</code> [SAL]<br>

<code>(feedback-delay <i>sound</i> <i>delay</i> <i>feedback</i>)</code> [LISP]</dt>
<dd>Applies feedback delay to <i>sound</i>.  The <i>delay</i> must be a number (in seconds).  It is rounded to the nearest sample to determine the length of the delay.  The sample rate is the maximum from <i>sound</i> and <i>feedback</i> (if feedback is also a sound).  The amound of <i>feedback</i> should be less than one to avoid an exponential increase in amplitude.  The start time and stop time, and logical stop time are taken from <i>sound</i>.  Since output is truncated at the stop time of <i>sound</i>, you may want to append some silence to <i>sound</i> to give the filter time to decay.<br><br>
<dt>
<code>lp(<a name="index454"></a><a name="index455"></a><i>sound</i>, <i>cutoff</i>)</code> [SAL]<br>

<code>(lp <i>sound</i> <i>cutoff</i>)</code> [LISP]</dt>
<dd>Filters <i>sound</i>
using a first-order Butterworth low-pass filter.  <i>Cutoff</i> may be a float
or a signal (for time-varying filtering) and expresses hertz.  Filter
coefficients (requiring trig functions) are recomputed at the sample rate of
<i>cutoff</i>.  The resulting sample rate, start time, etc. are taken from <i>sound</i>.<br><br>
<dt><code>tone(<a name="index456"></a><i>sound</i>, <i>cutoff</i>)</code> [SAL]<br>

<code>(tone <i>sound</i> <i>cutoff</i>)</code> [LISP]</dt>
<dd>No longer defined; use <code>lp</code> instead, or define it by adding <code>(setfn tone lp)</code> to your program.<br><br>
<dt>
<code>hp(<a name="index457"></a><a name="index458"></a><i>sound</i>, <i>cutoff</i>)</code> [SAL]<br>

<code>(hp <i>sound</i> <i>cutoff</i>)</code> [LISP]</dt>
<dd>Filters <i>sound</i>
using a first-order Butterworth high-pass filter.  <i>Cutoff</i> may be a
float or a signal (for time-varying filtering) and expresses hertz.  Filter
coefficients (requiring trig functions) are recomputed at the sample rate of
<i>cutoff</i>.  This filter is an exact complement of <code>lp</code>.<br><br>
<dt><code>atone(<a name="index459"></a><i>sound</i>, <i>cutoff</i>)</code> [SAL]<br>

<code>(atone <i>sound</i> <i>cutoff</i>)</code> [LISP]</dt>
<dd>No longer defined; use <code>hp</code> instead, or define it by adding <code>(setfn atone hp)</code> to your program.<br><br>
<dt>
<code>reson(<a name="index460"></a><a name="index461"></a><i>sound</i>, <i>center</i>, <i>bandwidth</i> [, <i>n</i>])</code> [SAL]<br>

<code>(reson <i>sound</i> <i>center</i> <i>bandwidth</i> [<i>n</i>])</code> [LISP]</dt>
<dd>Apply
a resonating filter to <i>sound</i> with center frequency <i>center</i> (in hertz),
which may be a float or a signal.  <i>Bandwidth</i> is the filter bandwidth (in
hertz), which may also be a signal.  Filter coefficients (requiring trig
functions) are recomputed at each new sample of either <i>center</i> or
<i>bandwidth</i>, and coefficients are <i>not</i> interpolated.  The last
parameter <i>n</i> specifies the type of normalization as in Csound: A value of 1 specifies a peak amplitude
response of 1.0; all frequencies other than <i>hz</i> are attenuated.  A
value of 2 specifies the overall RMS value of the amplitude response
is 1.0; thus filtered white noise would retain the same power.  A value of
zero specifies no scaling.  The resulting sample rate, start time, etc. are taken from <i>sound</i>.<br><br>
<dt>One application of <code>reson</code> is to simulate resonances in the human vocal tract.
See <code>nyquist/lib/voice/voice_synthesis.html</code><a name="index462"></a><a name="index463"></a>
for sample code and documentation.<br><br>
<dt>
<code>areson(<a name="index464"></a><a name="index465"></a><i>sound</i>, <i>center</i>, <i>bandwidth</i> [, <i>n</i>])</code> [SAL]<br>

<code>(areson <i>sound</i> <i>center</i> <i>bandwidth</i> [<i>n</i>])</code> [LISP]</dt>
<dd>The <code>areson</code> filter is an exact
complement of <code>reson</code> such that if both are applied to the
same signal with the same parameters, the sum of the results yeilds
the original signal.<br><br>
<dt>
<code>shape(<a name="index466"></a><a name="index467"></a><a name="index468"></a><i>signal</i>, <i>table</i>, <i>origin</i>)</code> [SAL]<br>

<code>(shape <i>signal</i> <i>table</i> <i>origin</i>)</code> [LISP]</dt>
<dd>A waveshaping function.  Use <i>table</i> as a function; apply the function to each sample of <i>signal</i> to yield a new sound.  <i>Signal</i> should range from -1 to +1.  Anything beyond these bounds is clipped.  <i>Table</i> is also a sound, but it is converted into a lookup table (similar to table-lookup oscillators).  The <i>origin</i> is a <code>FLONUM</code> and gives the time which should be considered the origin of <i>table</i>.  (This is important because <i>table</i> cannot have values at negative times, but <i>signal</i> will often have negative values.  The <i>origin</i> gives an offset so that you can produce suitable tables.)  The output at time <i>t</i> is:
<blockquote>
<i>table</i>(<i>origin</i> + clip(<i>signal</i>(<i>t</i>))</blockquote> where clip(<i>x</i>) = <i>max</i>(1, <i>min</i>(-1, <i>x</i>)).
(E.g. if <i>table</i> is a signal defined over the interval [0, 2], then <i>origin</i> should be 1.0.  The value of <i>table</i> at time 1.0 will be output when the input signal is zero.)  The output has the same start time, sample rate, etc. as <i>signal</i>.  The <code>shape</code> function will also accept multichannel <i>signal</i>s and <i>table</i>s.

Further discussion and examples can be found by installing the
&ldquo;distortion&rdquo; extension with the NyquistIDE Extension Manager.
The code will appear in
<code>nyquist/lib/distortion/distortion.html</code><a name="index469"></a><a name="index470"></a>.  The <code>shape</code> function is also
used to map frequency to amplitude to achieve a spectral envelope for
Shepard tones (install the &ldquo;shepard&rdquo; extension)
in  <code>nyquist/lib/shepard/shepard.lsp</code>.<a name="index471"></a><a name="index472"></a><br><br>
<dt>
<code>biquad(<a name="index473"></a><i>signal</i>, <i>b0</i>, <i>b1</i>, <i>b2</i>, <i>a0</i>, <i>a1</i>, <i>a2</i>)</code> [SAL]<br>

<code>(biquad <i>signal</i> <i>b0</i> <i>b1</i> <i>b2</i> <i>a0</i> <i>a1</i> <i>a2</i>)</code> [LISP]</dt>
<dd>A fixed-parameter biquad filter. All filter coefficients are <code>FLONUM</code>s. See also <code>lowpass2</code>, <code>highpass2</code>, <code>bandpass2</code>, <code>notch2</code>, <code>allpass2</code>, <code>eq-lowshelf</code>, <code>eq-highshelf</code>, <code>eq-band</code>, <code>lowpass4</code>, <code>lowpass6</code>, <code>highpass4</code>, and <code>highpass8</code> in this section for convenient variations based on the same filter. The equations for the filter are: z<sub>n</sub> = s<sub>n</sub> + a1 * z<sub>n-1</sub> + a2 * z<sub>n-2</sub>, and y<sub>n</sub> = z<sub>n</sub> * b0 + z<sub>n-1</sub> * b1 + z<sub>n-2</sub> * b2.<br><br>
<dt>
<code>biquad-m(<a name="index474"></a><i>signal</i>, <i>b0</i>, <i>b1</i>, <i>b2</i>, <i>a0</i>, <i>a1</i>, <i>a2</i>)</code> [SAL]<br>

<code>(biquad-m <i>signal</i> <i>b0</i> <i>b1</i> <i>b2</i> <i>a0</i> <i>a1</i> <i>a2</i>)</code> [LISP]</dt>
<dd>A fixed-parameter biquad filter with Matlab sign conventions for <i>a0</i>, <i>a1</i>, and <i>a2</i>. All filter coefficients are <code>FLONUM</code>s.<br><br>
<dt>
<code>lowpass2(<a name="index475"></a><i>signal</i>, <i>hz</i> [, <i>q</i>])</code> [SAL]<br>

<code>(lowpass2 <i>signal</i> <i>hz</i> [<i>q</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order lowpass filter based on <code>snd-biquad</code>. The cutoff frequency is given by <i>hz</i> (a <code>FLONUM</code>) and an optional Q factor is given by <i>q</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>highpass2(<a name="index476"></a><i>signal</i>, <i>hz</i> [, <i>q</i>])</code> [SAL]<br>

<code>(highpass2 <i>signal</i> <i>hz</i> [<i>q</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order highpass filter based on <code>snd-biquad</code>. The cutoff frequency is given by <i>hz</i> (a <code>FLONUM</code>) and an optional Q factor is given by <i>q</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>bandpass2(<a name="index477"></a><i>signal</i>, <i>hz</i> [, <i>q</i>])</code> [SAL]<br>

<code>(bandpass2 <i>signal</i> <i>hz</i> [<i>q</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order bandpass filter based on <code>snd-biquad</code>. The center frequency is given by <i>hz</i> (a <code>FLONUM</code>) and an optional Q factor is given by <i>q</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>notch2(<a name="index478"></a><i>signal</i>, <i>hz</i> [, <i>q</i>])</code> [SAL]<br>

<code>(notch2 <i>signal</i> <i>hz</i> [<i>q</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order notch filter based on <code>snd-biquad</code>. The center frequency is given by <i>hz</i> (a <code>FLONUM</code>) and an optional Q factor is given by <i>q</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>allpass2(<a name="index479"></a><i>signal</i>, <i>hz</i> [, <i>q</i>])</code> [SAL]<br>

<code>(allpass2 <i>signal</i> <i>hz</i> [<i>q</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order allpass filter based on <code>snd-biquad</code>. The frequency is given by <i>hz</i> (a <code>FLONUM</code>) and an optional Q factor is given by <i>q</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>eq-lowshelf(<a name="index480"></a><a name="index481"></a><i>signal</i>, <i>hz</i>, <i>gain</i> [, <i>slope</i>])</code> [SAL]<br>

<code>(eq-lowshelf <i>signal</i> <i>hz</i> <i>gain</i> [<i>slope</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order bass shelving equalization (EQ) filter based on <code>snd-biquad</code>. The <i>hz</i> parameter (a <code>FLONUM</code>)is the halfway point in the transition, and <i>gain</i> (a <code>FLONUM</code>) is the bass boost (or cut) in dB. The optional <i>slope</i> (a <code>FLONUM</code>) is 1.0 by default, and response becomes peaky at values greater than 1.0.<br><br>
<dt>
<code>eq-highshelf(<a name="index482"></a><a name="index483"></a><i>signal</i>, <i>hz</i>, <i>gain</i> [, <i>slope</i>])</code> [SAL]<br>

<code>(eq-highshelf <i>signal</i> <i>hz</i> <i>gain</i> [<i>slope</i>])</code> [LISP]</dt>
<dd>A fixed-parameter, second-order treble shelving equalization (EQ) filter based on <code>snd-biquad</code>. The <i>hz</i> parameter (a <code>FLONUM</code>)is the halfway point in the transition, and <i>gain</i> (a <code>FLONUM</code>) is the treble boost (or cut) in dB. The optional <i>slope</i> (a <code>FLONUM</code>) is 1.0 by default, and response becomes peaky at values greater than 1.0.<br><br>
<dt>
<code>eq-band(<a name="index484"></a><a name="index485"></a><i>signal</i>, <i>hz</i>, <i>gain</i>, <i>width</i>)</code> [SAL]<br>

<code>(eq-band <i>signal</i> <i>hz</i> <i>gain</i> <i>width</i>)</code> [LISP]</dt>
<dd>A fixed- or variable-parameter, second-order midrange equalization (EQ) filter based on <code>snd-biquad</code>, <code>eq-band-ccc</code> and <code>eq-band-vvv</code>. The <i>hz</i> parameter (a <code>FLONUM</code>) is the center frequency, <i>gain</i> (a <code>FLONUM</code>) is the boost (or cut) in dB, and <i>width</i> (a <code>FLONUM</code>) is the half-gain width in octaves. Alternatively, <i>hz</i>, <i>gain</i>, and <i>width</i> may be <code>SOUND</code>s, but they must all have the same sample rate, e.g. they should all run at the control rate or at the sample rate.<br><br>
<dt>
<code>lowpass4(<a name="index486"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(lowpass4 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A four-pole Butterworth lowpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>lowpass6(<a name="index487"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(lowpass6 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A six-pole Butterworth lowpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>lowpass8(<a name="index488"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(lowpass8 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>An eight-pole Butterworth lowpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>highpass4(<a name="index489"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(highpass4 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A four-pole Butterworth highpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>highpass6(<a name="index490"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(highpass6 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A six-pole Butterworth highpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>highpass8(<a name="index491"></a><i>signal</i>, <i>hz</i>)</code> [SAL]<br>

<code>(highpass8 <i>signal</i> <i>hz</i>)</code> [LISP]</dt>
<dd>An eight-pole Butterworth highpass filter. The cutoff frequency is <i>hz</i> (a <code>FLONUM</code>).<br><br>
<dt>
<code>tapv(<a name="index492"></a><a name="index493"></a><a name="index494"></a><i>sound</i>, <i>offset</i>, 
<i>vardelay</i>, <i>maxdelay</i>)</code> [SAL]<br>

<code>(tapv <i>sound</i> <i>offset</i> <i>vardelay</i> <i>maxdelay</i>)</code> [LISP]</dt>
<dd>A delay line with a variable position tap. 
Identical to <code>snd-tapv</code>. See it for details (page <a href = "#103">Signal Operations</a>).
</dd></dl>
<a name = "94"><h5>Effects</h5></a><dl>
<dt>

<code>nrev(<a name="index495"></a><a name="index496"></a><a name="index497"></a><a name="index498"></a><i>sound</i>, <i>decay</i>, <i>mix</i>)</code> [SAL]<br>

<code>(nrev <i>sound</i> <i>decay</i> <i>mix</i>)</code> [LISP]<br><br>
<dt><code>jcrev(<a name="index499"></a><a name="index500"></a><a name="index501"></a><a name="index502"></a><i>sound</i>, <i>decay</i>, <i>mix</i>)</code> [SAL]<br>

<code>(jcrev <i>sound</i> <i>decay</i> <i>mix</i>)</code> [LISP]<br><br>
<dt><code>prcrev(<a name="index503"></a><a name="index504"></a><a name="index505"></a><a name="index506"></a><i>sound</i>, <i>decay</i>, <i>mix</i>)</code> [SAL]<br>

<code>(prcrev <i>sound</i> <i>decay</i> <i>mix</i>)</code> [LISP]</dt>
<dd>These reverbs (<code>nrev</code>, <code>jcrev</code>, and <code>prcrev</code>) are implemented 
in STK (running within Nyquist). <code>nrev</code> derives from Common Music's 
NRev,  which consists of 6 comb filters followed by 3 allpass filters, a
 lowpass filter, and another allpass in series followed by two allpass 
filters in parallel. <code>jcrev</code> is the John Chowning 
reverberator which is based on the use of networks of simple allpass 
and comb delay filters. This reverb implements three series allpass units, 
followed by four parallel comb filters, and two decorrelation delay 
lines in parallel at the output. <code>prcrev</code> is a Perry Cook's 
reverberator which is based on the Chowning/Moorer/Schroeder 
reverberators using networks of simple allpass and comb delay filters. 
This one implements two series allpass units and two parallel comb filters.
The <i>sound</i> input may be single or multichannel. The <i>decay</i> time is
in seconds, and <i>mix</i> sets the mixture of input sound reverb sound, 
where 0.0 means input only (dry) and 1.0 means reverb only (wet).<br><br>
<dt>
<code>stkchorus(<a name="index507"></a><a name="index508"></a><a name="index509"></a><a name="index510"></a><i>sound</i>, <i>depth</i>, <i>freq</i>, <i>mix</i> [, <i>delay</i>])</code> [SAL]<br>

<code>(stkchorus <i>sound</i> <i>depth</i> <i>freq</i> <i>mix</i> [<i>delay</i>])</code> [LISP]</dt>
<dd>Chorus 
implemented in STK. The input <i>sound</i> can be single or multichannel.
The <code>FLONUM</code> parameters <i>depth</i> and <i>freq</i> set 
the modulation 
depth from 0 to 1 
and modulation frequency (in Hz), and <i>mix</i> sets the mixture
of input sound and chorused sound, where 0.0 means input sound only (dry)
and 1.0 means chorused sound only (wet). The parameter <i>delay</i> is a
<code>FIXNUM</code> representing the median desired delay length in samples. <br><br>
<dt>
<code>pitshift(<a name="index511"></a><a name="index512"></a><a name="index513"></a><a name="index514"></a><i>sound</i>, <i>shift</i>, <i>mix</i>)</code> [SAL]<br>

<code>(pitshift <i>sound</i> <i>shift</i> <i>mix</i>)</code> [LISP]</dt>
<dd>A pitch
 shifter implemented in STK. The input <i>sound</i>, a single-channel
 or multichannel <code>SOUND</code> is pitch-shifted by <i>shift</i>, 
a <code>FLONUM</code> ratio. A value of 1.0 means no shift.  The parameter <i>mix</i>
 sets the mixture of input and shifted sounds. A value of 0.0 
means input only (dry) 
and a value of 1.0 means shifted sound only (wet).
</dd></dl><a name = "95"><h5>Physical Models</h5></a><a name="index515"></a><dl>
<dt>

<code>clarinet(<a name="index516"></a><a name="index517"></a><i>step</i>, <i>breath-env</i>)</code> [SAL]<br>

<code>(clarinet <i>step</i> <i>breath-env</i>)</code> [LISP]</dt>
<dd>A 
physical model of a clarinet from STK. The <i>step</i> parameter is a <code>FLONUM</code> 
that controls the tube length, and the <i>breath-env</i> (a <code>SOUND</code>) 
controls the air pressure
and also determines the length of the resulting sound. The <i>breath-env</i> signal
should range from zero to one.<br><br>
<dt><code>clarinet-freq(<a name="index518"></a><a name="index519"></a><a name="index520"></a><i>step</i>, <i>breath-env</i>, <i>freq-env</i>)</code> [SAL]<br>

<code>(clarinet-freq <i>step</i> <i>breath-env</i> <i>freq-env</i>)</code> [LISP]</dt>
<dd>A variation of <code>clarinet</code>
that includes a variable frequency control, <i>freq-env</i>, which specifies
frequency deviation in Hz. The duration of the resulting sound is the minimum
duration of <i>breath-env</i> and <i>freq-env</i>. These parameters may be of type
<code>FLONUM</code> or <code>SOUND</code>. <code>FLONUM</code>s are coerced into <code>SOUND</code>s
with a nominal duration arbitrarily set to 30.<br><br>
<dt><code>clarinet-all(<a name="index521"></a><a name="index522"></a><a name="index523"></a><i>step</i>, <i>breath-env</i>, <i>freq-env</i>, <i>vibrato-freq</i>, <i>vibrato-gain</i>, <i>reed-stiffness</i>, <i>noise</i>)</code> [SAL]<br>

<code>(clarinet-all <i>step</i> <i>breath-env</i> <i>freq-env</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>reed-stiffness</i> <i>noise</i>)</code> [LISP]</dt>
<dd>A variation of <code>clarinet-freq</code>
that includes controls <i>vibrato-freq</i> (a <code>FLONUM</code> for vibrato frequency in Hertz), 
<i>vibrato-gain</i> (a <code>FLONUM</code> for the amount of amplitude vibrato),
<i>reed-stiffness</i> (a <code>FLONUM</code> or <code>SOUND</code> controlling reed stiffness in the clarinet
model), and <i>noise</i> (a <code>FLONUM</code> or <code>SOUND</code> controlling noise amplitude in the input
air pressure). The <i>vibrato-gain</i> is a number from zero to one, where zero
indicates no vibrato, and one indicates a plus/minus 50% change in breath
envelope values. Similarly, the <i>noise</i> parameter ranges from zero to one where 
zero means no noise and one means white noise with a peak amplitude of
plus/minus 40% of the <i>breath-env</i>. The <i>reed-stiffness</i> parameter varies
from zero to one.
The duration of the resulting sound is the minimum duration of
<i>breath-env</i>, <i>freq-env</i>, <i>reed-stiffness</i>, and <i>noise</i>. As with
<code>clarinet-freq</code>, these parameters may be either <code>FLONUM</code>s or 
<code>SOUND</code>s, and <code>FLONUM</code>s are coerced to sounds with a nominal 
duration of 30.<br><br>
<dt>
<code>sax(<a name="index524"></a><a name="index525"></a><i>step</i>, <i>breath-env</i>)</code> [SAL]<br>

<code>(sax <i>step</i> <i>breath-env</i>)</code> [LISP]</dt>
<dd>A 
physical model of a sax from STK. The <i>step</i> parameter is a <code>FLONUM</code> 
that controls the tube length, and the <i>breath-env</i> controls the air pressure
and also determines the length of the resulting sound. The <i>breath-env</i> signal
should range from zero to one.<br><br>
<dt><code>sax-freq(<a name="index526"></a><a name="index527"></a><a name="index528"></a><i>step</i>, <i>breath-env</i>, <i>freq-env</i>)</code> [SAL]<br>

<code>(sax-freq <i>step</i> <i>breath-env</i> <i>freq-env</i>)</code> [LISP]</dt>
<dd>A variation of <code>sax</code>
that includes a variable frequency control, <i>freq-env</i>, which specifies
frequency deviation in Hz. The duration of the resulting sound is the minimum
duration of <i>breath-env</i> and <i>freq-env</i>. These parameters may be of type
<code>FLONUM</code> or <code>SOUND</code>. <code>FLONUM</code>s are coerced into <code>SOUND</code>s
with a nominal duration arbitrarily set to 30.<br><br>
<dt><code>sax-all(<a name="index529"></a><a name="index530"></a><a name="index531"></a><i>step</i>, <i>breath-env</i>, <i>freq-env</i>, <i>vibrato-freq</i>, <i>vibrato-gain</i>, <i>reed-stiffness</i>, <i>noise</i>, <i>blow-pos</i>, <i>reed-table-offset</i>)</code> [SAL]<br>

<code>(sax-all <i>step</i> <i>breath-env</i> <i>freq-env</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>reed-stiffness</i> <i>noise</i> <i>blow-pos</i> <i>reed-table-offset</i>)</code> [LISP]</dt>
<dd>A variation of
<code>sax-freq</code>
that includes controls <i>vibrato-freq</i> (a <code>FLONUM</code> for vibrato frequency in Hertz), 
<i>vibrato-gain</i> (a <code>FLONUM</code> for the amount of amplitude vibrato),
<i>reed-stiffness</i> (a <code>SOUND</code> controlling reed stiffness in the sax
model), <i>noise</i> (a <code>SOUND</code> controlling noise amplitude in the input
air pressure), <i>blow-pos</i> (a <code>SOUND</code> controlling the point of excitation
of the air column), and <i>reed-table-offset</i> (a <code>SOUND</code> controlling a
parameter of the reed model). The <i>vibrato-gain</i> is a number from zero to one, where zero
indicates no vibrato, and one indicates a plus/minus 50% change in breath
envelope values. Similarly, the <i>noise</i> parameter ranges from zero to one where 
zero means no noise and one means white noise with a peak amplitude of
plus/minus 40% of the <i>breath-env</i>. The <i>reed-stiffness</i>, <i>blow-pos</i>, and
<i>reed-table-offset</i> parameters all vary from zero to one.
The duration of the resulting sound is the minimum duration of
<i>breath-env</i>, <i>freq-env</i>, <i>reed-stiffness</i>, <i>noise</i>, <i>breath-env</i>,
<i>blow-pos</i>, and <i>reed-table-offset</i>. As with
<code>sax-freq</code>, these parameters may be either <code>FLONUM</code>s or 
<code>SOUND</code>s, and <code>FLONUM</code>s are coerced to sounds with a nominal 
duration of 30.<br><br>
<dt>
<code>flute(<a name="index532"></a><a name="index533"></a><i>step</i>, <i>breath-env</i>)</code> [SAL]<br>

<code>(flute <i>step</i> <i>breath-env</i>)</code> [LISP]</dt>
<dd>A physical model of a flute from STK. 
The <i>step</i> parameter is a <code>FLONUM</code> that controls the tube 
length, and the <i>breath-env</i>
controls the air pressure and also determines the starting time and
length of the resulting sound. The <i>breath-env</i> signal should
 range from zero to one.<br><br>
<dt><code>flute-freq(<a name="index534"></a><a name="index535"></a><i>step</i>, <i>breath-env</i>, <i>freq-env</i>)</code> [SAL]<br>

<code>(flute-freq <i>step</i> <i>breath-env</i> <i>freq-env</i>)</code> [LISP]</dt>
<dd>A variation of <code>flute</code>
 that includes a variable frequency control, <i>freq-env</i>, which
 specifies frequency deviation in Hz. The duration of the 
resulting sound is the minimum duration of <i>breath-env</i> and 
<i>freq-env</i>. These parameters may be of type <code>FLONUM</code> or
<code>SOUND</code>. <code>FLONUM</code>s are coerced into SOUNDs with a 
nominal duration arbitrarily set to 30.<br><br>
<dt><code>flute-all(<a name="index536"></a><a name="index537"></a><i>step</i>, 
<i>breath-env</i>, <i>freq-env</i>, <i>vibrato-freq</i>,
<i>vibrato-gain</i>, <i>jet-delay</i>, <i>noise</i>)</code> [SAL]<br>

<code>(flute-all <i>step</i> <i>breath-env</i> <i>freq-env</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>jet-delay</i> <i>noise</i>)</code> [LISP]</dt>
<dd>A variation of 
<code>clarinet-freq</code> that includes controls <i>vibrato-freq</i> (a 
<code>FLONUM</code> for vibrato frequency in Hz), <i>vibrato-gain</i> (a
<code>FLONUM</code> for the amount of amplitude vibrato), <i>jet-delay</i>
 (a <code>FLONUM</code> or <code>SOUND</code> controlling jet delay in the
 flute model), and 
noise (a <code>FLONUM</code> or <code>SOUND</code> controlling noise amplitude
in the input air pressure). The <i>vibrato-gain</i> is a number from zero
 to one where zero means no vibrato, and one indicates a plus/minus 
50% change in breath envelope values. Similarly, the <i>noise</i> parameter
 ranges from zero to one, where zero means no noise and one means white 
noise with a peak amplitude of
 plus/minus 40% of the <i>breath-env</i>. The <i>jet-delay</i> is a ratio
 that controls a delay length from the flute model, and therefore it 
changes the pitch of the resulting sound. A value of 0.5 will maintain 
the pitch indicated by the step parameter. The duration of the 
resulting sound is the minimum duration of <i>breath-env</i>, <i>freq-env</i>, 
<i>jet-delay</i>, and <i>noise</i>. These parameters may be either 
<code>FLONUM</code>s or <code>SOUND</code>s, and <code>FLONUM</code>s are coerced
 to sounds with a nominal duration of 30. <br><br>
<dt>
<code>bowed(<a name="index538"></a><a name="index539"></a><i>step</i>, <i>bowpress-env</i>)</code> [SAL]<br>

<code>(bowed <i>step</i> <i>bowpress-env</i>)</code> [LISP]</dt>
<dd>A physical model of a bowed string
 instrument from STK. The <i>step</i> parameter is a <code>FLONUM</code>
 that controls the string length,
 and the <i>bowpress-env</i> controls the bow pressure and also 
determines the duration of the resulting sound. The <i>bowpress-env</i>
 signal should range from zero to one.<br><br>
<dt><code>bowed-freq(<a name="index540"></a><a name="index541"></a><i>step</i>, <i>bowpress-env</i>, <i>freq-env</i>)</code> [SAL]<br>

<code>(bowed-freq <i>step</i> <i>bowpress-env</i> <i>freq-env</i>)</code> [LISP]</dt>
<dd>A variation of <code>bowed</code>
 that includes a variable frequency control, <i>freq-env</i>, which
 specifies frequency deviation in Hz. The duration of the resulting
 sound is the minimum duration of <i>bowpress-env</i> and <i>freq-env</i>. 
These parameters may be of type <code>FLONUM</code> or <code>SOUND</code>. 
<code>FLONUM</code>s are coerced into <code>SOUND</code>s
 with a nominal duration arbitrarily set to 30s.<br><br>
<dt>
<code>mandolin(<a name="index542"></a><a name="index543"></a><i>step</i>, <i>dur</i>, &amp;optional <i>detune</i>)</code> [SAL]<br>

<code>(mandolin <i>step</i> <i>dur</i> <i>detune</i>)</code> [LISP]</dt>
<dd>A physical model of a
 plucked double-string instrument from STK. The <i>step</i> parameter
 is a <code>FLONUM</code> wich specifies the desired pitch, <i>dur</i>
 means the duration of the resulting sound and detune is a 
<code>FLONUM</code> that controls the relative detune of the two strings. 
A value of 1.0 means unison. The default value is 4.0.
Note: <i>body-size</i> (see <code>snd-mandolin</code> does not seem to
 work correctly, so a default value is always used
 by <code>mandolin</code>.<br><br>
<dt>
<code>wg-uniform-bar(<a name="index544"></a><a name="index545"></a><i>step</i>, <i>bowpress-env</i>)</code> [SAL]<br>

<code>(wg-uniform-bar <i>step</i> <i>bowpress-env</i>)</code> [LISP]<br><br>
<dt><code>wg-tuned-bar(<a name="index546"></a><a name="index547"></a><i>step</i>, <i>bowpress-env</i>)</code> [SAL]<br>

<code>(wg-tuned-bar <i>step</i> <i>bowpress-env</i>)</code> [LISP]<br><br>
<dt><code>wg-glass-harm(<a name="index548"></a><a name="index549"></a><i>step</i>, <i>bowpress-env</i>)</code> [SAL]<br>

<code>(wg-glass-harm <i>step</i> <i>bowpress-env</i>)</code> [LISP]<br><br>
<dt><code>wg-tibetan-bowl(<a name="index550"></a><a name="index551"></a><i>step</i>, <i>bowpress-env</i>)</code> [SAL]<br>

<code>(wg-tibetan-bowl <i>step</i> <i>bowpress-env</i>)</code> [LISP]</dt>
<dd>These 
sounds are presets for a Banded Wave Guide Percussion instrument implemented in STK.
The parameter <i>step</i> is a <code>FLONUM</code>
 that controls the resultant pitch, and <i>bowpress-env</i> is a <code>SOUND</code> ranging 
from zero to one that controls a parameter of the model. In addition, 
<i>bowpress-env</i> determines the duration of the resulting sound.
(Note: The <i>bowpress-env</i> does not seems influence the timbral 
quality of the resulting sound).<br><br>
<dt>
<code>modalbar(<a name="index552"></a><a name="index553"></a><i>preset</i>, <i>step</i>, <i>dur</i>)</code> [SAL]<br>

<code>(modalbar <i>preset</i> <i>step</i> <i>dur</i>)</code> [LISP]</dt>
<dd>A physical model of a struck bar
 instrument implemented in STK. The parameter <i>preset</i> is one of the
symbols
<code>MARIMBA</code>, <code>VIBRAPHONE</code>, <code>AGOGO</code>, <code>WOOD1</code>, 
<code>RESO</code>, <code>WOOD2</code>, <code>BEATS</code>, <code>TWO-FIXED</code>, or
<code>CLUMP</code>. The symbol must be quoted, e.g. for SAL syntax use
<code>quote(marimba)</code>, and for Lisp syntax use <code>'marimba</code>.
The parameter <i>step</i> is a <code>FLONUM</code> that 
sets the pitch (in steps), and <i>dur</i> is the duration in seconds.<br><br>
<dt>
<code>sitar(<a name="index554"></a><a name="index555"></a><i>step</i>, <i>dur</i>)</code> [SAL]<br>

<code>(sitar <i>step</i> <i>dur</i>)</code> [LISP]</dt>
<dd>A sitar physical model implemented in STK. 
The parameter <i>step</i> is a <code>FLONUM</code> that sets the pitch,
and <i>dur</i> is the duration.<br><br>
<dt>
<code>stk-breath-env(<a name="index556"></a><a name="index557"></a><i>dur</i>, <i>note-on</i> <i>note-off</i>)</code> [SAL]<br>

<code>(stk-breath-env <i>dur</i> <i>note-on</i> <i>note-off</i>)</code> [LISP]</dt>
<dd>A simple envelope function
intended for STK instruments such as <code>CLARINET</code>, where <i>dur</i> is the duration, <i>note-on</i> is the
attack time, and <i>note-off</i> is the decay time, all <code>FLONUM</code>s in seconds.
</dd></dl><a name = "96"><h5>Phase Vocoder</h5></a><dl>
<dt>

<code>phasevocoder(<a name="index558"></a><a name="index559"></a><a name="index560"></a><a name="index561"></a><i>s</i>,
       <i>map</i>, [<i>fftsize</i>, <i>hopsize</i>, <i>mode</i>])</code> [SAL]<br>

<code>(phasevocoder <i>s</i> <i>map</i> [<i>fftsize</i> <i>hopsize</i> <i>mode</i>])</code>
       [LISP]</dt>
<dd>Phase vocoder: the input SOUND <i>s</i> is stretched in 
time according to the control signal (a SOUND) <i>map</i>. The <i>map</i> parameter
must be strictly non-decreasing. It specifies the input time for each time
in the output. E.g. if <i>map</i> at time 3 is 4, then the output at time 3 will
sound like the input at time 4, assuming <i>s</i> and <i>map</i> start at time 0.
In the general case, <i>s</i> and <i>map</i> must start at the same time. The phase 
vocoder operation is applied as if <i>s</i> and <i>map</i> started at time 0, and
the result is shifted to start at the same starting time as <i>s</i> and <i>map</i>.
The <i>fftsize</i> is a FIXNUM and power of 2, indicating the size of the 
analysis and synthesis windows in samples. The default is 2048. 
The <i>hopsize</i> is the hop size (in samples, a FIXNUM) of the 
synthesis stage where overlapping windows are added. The <i>hopsize</i> 
should be a power of 2 that is smaller than the <i>fftsize</i>. The default is
the <i>fftsize</i>/8. Note that the analysis hopsize is determined by the <i>map</i>.
If the playback speed (slope of <i>map</i>) is too great, the analysis hopsize
will be large and the sound quality will suffer. You can always make the 
analysis hopsize smaller by making the synthesis hopsize smaller (at the
cost of greater computation). The <i>mode</i> is a FIXNUM that defaults to
0, meaning a standard phase vocoder. A value of 1 invokes a phase computation
that attempts to reduce phase artifacts by preserving the phase relationships
between peaks and nearby bins. A value of 2 invokes a &ldquo;robot voice&rdquo; mode
that assigns fixed phases and creates a constant pitch (controlled
by the hopsize) vocoder-like effect. (Thanks to M.C.Sharma for this idea.) 
A phase vocoder constructs output from overlapped and added windowed
IFFT frames. This presents a special problem at the beginning and
ending of the output sound. To output a sound starting at time <i>t</i>,
the first frame is centered at <i>t</i> + <i>fftsize</i>/2, so the output at
<i>t</i> will smoothly rise from zero because all frames are smoothed by
a windowing function. Considerations are: (1) The output at time <i>t</i>
will rise from zero rather than being the sum of multiple overlapping
windows; (2) if <i>t</i> maps to an input window that begins before
the start time of the input sound, the input window will be padded
with zeros and may include an abrupt onset if one exists at the
start of the input sound.<br><br>
<dt><code>pv-time-pitch(<a name="index562"></a><a name="index563"></a><a name="index564"></a><i>s</i>,
    <i>stretchfn</i>, <i>pitchfn</i>, <i>dur</i>, [<i>fftsize</i>, <i>hopsize</i>, <i>mode</i>])</code> [SAL]<br>

<code>(pv-time-pitch <i>s</i> <i>stretchfn</i> <i>pitchfn</i> <i>dur</i> [<i>fftsize</i> <i>hopsize</i> <i>mode</i>])</code> [LISP]</dt>
<dd>Combines phase vocoder and resampling
to perform simultaneous time stretching and pitch shifting. The input SOUND
<i>s</i> is stretched according to SOUND <i>stretchfn</i> and pitch-shifted according
to SOUND <i>pitchfn</i>. The approximate output duration should be specified by
<i>dur</i> (which is used to optimize the sample rate of computed control
functions), and the remaining parameters <i>fftsize</i>, <i>hopsize</i> and
<i>mode</i> are passed to the phase vocoder (see <code>phasevocoder</code> above). The
<i>stretchfn</i> gives the factor by which the input should be stretched at each
point in time; thus, the total duration is the <i>integral</i> of this function. The <i>pitchfn</i> specifies the amount by which pitch should be shifted at each
point in time. For example, where <i>pitchfn</i> is 2, the sample rate will be
doubled, increasing pitch and frequencies by an octave. The phase vocoder is
used to compensate for time stretching caused by resampling,
so <i>stretchfn</i> and <i>pitchfn</i> operate independently.
</dd></dl><a name = "97"><h5>More Behaviors</h5></a><dl>
<dt>

<code>clip(<a name="index565"></a><a name="index566"></a><i>sound</i>, <i>peak</i>)</code> [SAL]<br>

<code>(clip <i>sound</i> <i>peak</i>)</code> [LISP]</dt>
<dd>Hard limit <i>sound</i> 
to the given <i>peak</i>, a positive number. The samples of <i>sound</i> are constrained between an upper value
of <i>peak</i> and a lower value of -<i>peak</i>. If <i>sound</i> is a number, <code>clip</code> will return <i>sound</i> limited by <i>peak</i>.  If <i>sound</i> is a multichannel sound, <code>clip</code> returns a multichannel sound where each channel is clipped.  The result has the type, sample rate, starting time, etc. of <i>sound</i>.
<b><i>Note:</i></b> Many systems clip output when converting to fixed-point audio, e.g. 16-bit samples. Instead Nyquist simply takes the low-order 16 bits, allowing
samples to &ldquo;wrap around.&rdquo; This sounds <i>terrible</i>, but that is the point:
It is hard to miss when your samples go out of range. One use of this function
is to clip rather than wrap output. <b><i>Warning:</i></b> A floating point sample 
value of 1.0 maps to 
2<sup>15</sup>
in 16-bit audio, but the maximum 16-bit sample 
value is
2<sup>15</sup>-1!
If your goal is to clip to the 16-bit range, you should
set <i>peak</i> to the ratio 32767.0/32768.0. For 24-bit audio, use
(2<sup>23</sup>-1)/2<sup>23</sup>, etc.<br><br>
<dt>
<code>s-abs(<a name="index567"></a><a name="index568"></a><i>sound</i>)</code> [SAL]<br>

<code>(s-abs <i>sound</i>)</code> [LISP]</dt>
<dd>A generalized absolute value
function. If <i>sound</i> is a <code>SOUND</code>, compute the absolute value
of each sample. If <i>sound</i> is a number, just compute the absolute
value. If <i>sound</i> is a multichannel sound, return a multichannel
sound with <code>s-abs</code> applied to each element. The result has the
type, sample rate, starting time, etc. of <i>sound</i>.<br><br>
<dt>
<code>s-avg(<a name="index569"></a><a name="index570"></a><a name="index571"></a><a name="index572"></a><a name="index573"></a><i>sound</i>, <i>blocksize</i>, <i>stepsize</i>, <i>operation</i>)</code> [SAL]<br>

<code>(s-avg <i>sound</i> <i>blocksize</i> <i>stepsize</i> <i>operation</i>)</code> [LISP]</dt>
<dd>Computes the averages 
or peak values of blocks of samples. Each output sample is an average or 
peak of <i>blocksize</i> (a fixnum) adjacent samples from the input <i>sound</i>. 
After each average or peak is taken, the input is advanced by <i>stepsize</i>, 
a fixnum which may be greater or less than <i>blocksize</i>.  The output 
sample rate is the <i>sound</i> (input) sample rate divided by
<i>stepsize</i>. The duration of the output is the same (approximately,
due to rounding) as that of <i>sound</i>. Notice however, that the
features of the input will appear earlier in the output by half the
window size. For example, a sharp peak in the input will result in a
smoothed peak (using <code>OP-AVERAGE</code>) one half <i>blocksize</i>
earlier. You can correct for this shift by inserting one half
<i>blocksize</i> of silence before <i>sound</i>,
e.g. if <code>s</code> has a sample rate of 44100 Hz, then
<code>snd-avg(seq(s-rest(0.01), cue(s)), 882, 441, OP-AVERAGE)</code> will
shift <code>s</code> by 0.01 s to compensate for the shift introduced by a
smoothing window of size 0.02 s (882/44100).
If <i>sound</i> is a multichannel sound, return a multichannel
sound with <code>s-avg</code> applied to each element.
This function is useful for computing low-sample-rate rms or peak 
amplitude signals for input to <code>snd-gate</code> or <code>snd-follow</code>.  
To select the operation, <i>operation</i> should be one of <code>OP-AVERAGE</code> 
or <code>OP-PEAK</code>.  (These are global lisp variables; the actual 
<i>operation</i> parameter is an integer.) For RMS computation, see 
<code>rms</code> in Section <a href = "#97">More Behaviors</a>.<br><br>
<dt>
<code>s-sqrt(<a name="index574"></a><a name="index575"></a><i>sound</i>)</code> [SAL]<br>

<code>(s-sqrt <i>sound</i>)</code> [LISP]</dt>
<dd>A generalized square root function. If <i>sound</i> is a <code>SOUND</code>, compute the square root of each sample. If <i>sound</i> is a number, just compute the square root. If <i>sound</i> is a multichannel sound, return a multichannel sound with <code>s-sqrt</code> applied to each element. The result has the type, sample rate, starting time, etc. of <i>sound</i>. In taking square roots, if an input sample is less than zero, the corresponding output sample is zero. This is done because the square root of a negative number is undefined.<br><br>
<dt>
<code>s-exp(<a name="index576"></a><a name="index577"></a><i>sound</i>)</code> [SAL]<br>

<code>(s-exp <i>sound</i>)</code> [LISP]</dt>
<dd>A generalized exponential function.  If <i>sound</i> is a <code>SOUND</code>, compute <i>e</i><sup T><i>x</i></sup> for each sample <i>x</i>.  If <i>sound</i> is a number <i>x</i>, just compute <i>e</i><sup T><i>x</i></sup>.  If <i>sound</i> is a multichannel sound, return a multichannel sound with <code>s-exp</code> applied to each element.  The result has the type, sample rate, starting time, etc. of <i>sound</i>.<br><br>
<dt>
<code>s-log(<a name="index578"></a><a name="index579"></a><a name="index580"></a><i>sound</i>)</code> [SAL]<br>

<code>(s-log <i>sound</i>)</code> [LISP]</dt>
<dd>A generalized natural log function.  If <i>sound</i> is a <code>SOUND</code>, compute <i>ln</i>(<i>x</i>) for each sample <i>x</i>.  If <i>sound</i> is a number <i>x</i>, just compute <i>ln</i>(<i>x</i>).  If <i>sound</i> is a multichannel sound, return a multichannel sound with <code>s-log</code> applied to each element.  The result has the type, sample rate, starting time, etc. of <i>sound</i>.  Note that the <i>ln</i> of 0 is undefined (some implementations return negative infinity), so use this function with care.<br><br>
<dt>
<code>s-max(<a name="index581"></a><a name="index582"></a><i>sound1</i>, <i>sound2</i>)</code> [SAL]<br>

<code>(s-max <i>sound1</i> <i>sound2</i>)</code> [LISP]</dt>
<dd>Compute
the maximum of two functions, <i>sound1</i> and <i>sound2</i>. This function
also accepts numbers and multichannel sounds and returns the
corresponding data type. The start time of the result is the maximum
of the start times of <i>sound1</i> and <i>sound2</i>. The logical stop time
and physical stop time of the result is the minimum of the logical
stop and physical stop times respectively of <i>sound1</i> and
<i>sound2</i>. Note, therefore, that the result value is zero except
within the bounds of <i>both</i> input sounds.<br><br>
<dt><code>s-min(<a name="index583"></a><a name="index584"></a><i>sound1</i>, <i>sound2</i>)</code> [SAL]<br>

<code>(s-min <i>sound1</i> <i>sound2</i>)</code> [LISP]</dt>
<dd>Compute the minimum of two functions, <i>sound1</i> and <i>sound2</i>. This function also accepts numbers and multichannel sounds and returns the corresponding data type. The start time of the result is the maximum of the start times of <i>sound1</i> and <i>sound2</i>. The logical stop time and physical stop time of the result is the minimum of the logical stop and physical stop times respectively of <i>sound1</i> and <i>sound2</i>. Note, therefore, that the result value is zero except within the bounds of <i>both</i> input sounds.<br><br>
<dt><code>osc-note(<a name="index585"></a><i>pitch</i> [, <i>duration</i>, <i>env</i>, <i>loud</i>, 
<i>table</i>])</code> [SAL]<br>

<code>(osc-note <i>pitch</i> [<i>duration</i> <i>env</i> <i>loud</i> <i>table</i>])</code> [LISP]</dt>
<dd>Same as <code>osc</code>, but <code>osc-note</code>
multiplies the result by <i>env</i>.  The <i>env</i> may be a sound, 
or a list supplying (<i>t<sub>1</sub></i> <i>t<sub>2</sub></i> 
<i>t<sub>4</sub></i> <i>l<sub>1</sub></i> <i>l<sub>2</sub></i> <i>l<sub>3</sub></i>).  The result has a sample rate of <code>*sound-srate*</code>.<br><br>
<dt>
<code>quantize(<a name="index586"></a><i>sound</i>, <i>steps</i>)</code> [SAL]<br>

<code>(quantize <i>sound</i> <i>steps</i>)</code> [LISP]</dt>
<dd>Quantizes <i>sound</i> as follows: <i>sound</i> is multiplied by <i>steps</i> and rounded to the nearest integer. The result is then divided by <i>steps</i>. For example, if <i>steps</i> is 127, then a signal that ranges from -1 to +1 will be quantized to 255 levels (127 less than zero, 127 greater than zero, and zero itself). This would match the quantization Nyquist performs when writing a signal to an 8-bit audio file. The <i>sound</i> may be multichannel.<br><br>
<dt><code>ramp(<a name="index587"></a>[<i>duration</i>])</code> [SAL]<br>

<code>(ramp [<i>duration</i>])</code> [LISP]</dt>
<dd>Returns a
linear ramp from 0 to 1
over <i>duration</i> (default is 1).  The function actually reaches 1 at
<i>duration</i>, and therefore has one extra sample, making the total duration
be <i>duration</i> + 1/<code>*Control-srate*</code>.  See Figure <a href = "#97">6</a> for
more detail.  Ramp is unaffected by the <code>sustain</code> transformation.  The
effect of time warping is to warp the starting and ending times only.  The
ramp itself is unwarped (linear).  The sample rate is <code>*control-srate*</code>.<br><br>
<dt>
<code>rms(<a name="index588"></a><i>sound</i> [, <i>rate</i>, <i>window-size</i>])</code> [SAL]<br>

<code>(rms <i>sound</i> [<i>rate</i> <i>window-size</i>])</code> [LISP]</dt>
<dd>Computes
the RMS of <i>sound</i> using a square window of size
<i>window-size</i>. The result has a sample rate of <i>rate</i>. The default
value of <i>rate</i> is 100 Hz, and the default window size is 1/rate
seconds (converted to samples). The <i>sound</i> is a SOUND or a multichannel
sound (in which case the result is a multichannel sound). 
The <i>rate</i> is a <code>FLONUM</code> and <i>window-size</i> is a <code>FIXNUM</code>.<br><br>
<dt>
<code>recip(<a name="index589"></a><a name="index590"></a><a name="index591"></a><i>sound</i>)</code> [SAL]<br>

<code>(recip <i>sound</i>)</code> [LISP]</dt>
<dd>A generalized reciprocal function.  
If <i>sound</i> is a <code>SOUND</code>, compute 1/<i>x</i> for each sample <i>x</i>.  If <i>sound</i> is a number <i>x</i>, just compute 1/<i>x</i>.  If <i>sound</i> is a multichannel sound, return a multichannel sound with <code>recip</code> applied to each element.  The result has the type, sample rate, starting time, etc. of <i>sound</i>.  Note that the reciprocal of 0 is undefined (some implementations return  infinity), so use this function with care on sounds.  Division of sounds is accomplished by multiplying by the reciprocal.  Again, be careful not to divide by zero.
</dd></dl>
<hr>
<blockquote>
</blockquote>
<img src="fig6.gif"><br><br>

<p><b>Figure 6: </b>Ramps generated by <code>pwl</code> and <code>ramp</code> functions.  The
<code>pwl</code> version ramps toward the breakpoint (1, 1), but in order to ramp
back to zero at breakpoint (1, 0), the function never reaches an amplitude
of 1.  If used at the beginning of a <code>seq</code> construct, the next sound
will begin at time 1.  The <code>ramp</code> version actually reaches breakpoint
(1, 1); notice that it is one sample longer than the <code>pwl</code> version.  If
used in a sequence, the next sound after <code>ramp</code> would start at time 1 +
<i>P</i>, where <i>P</i> is the sample period.

</p>
<hr>
<dl>
<dt>
<code>s-rest(<a name="index592"></a><a name="index593"></a>[<i>duration</i>])</code> [SAL]<br>

<code>(s-rest [<i>duration</i>])</code> [LISP]</dt>
<dd>Create silence (zero samples)
for the given 
<i>duration</i> at the sample rate <code>*sound-srate*</code>.  
Default duration is 1.0 sec, and the sound is transformed in time according
to <code>*warp*</code>.  <b><i>Note:</i></b> <code>rest</code> is a Lisp function that is equivalent to <code>cdr</code>.  Be careful to use <code>s-rest</code> when you need a sound!<br><br>
<dt>
<code>noise(<a name="index594"></a>[<i>duration</i>])</code> [SAL]<br>

<code>(noise <i>duration</i>)</code> [LISP]</dt>
<dd>Generate noise with the given 
<i>duration</i>.  Duration (default is 1.0) 
is transformed according to <code>*warp*</code>.  The
sample rate is <code>*sound-srate*</code> and the amplitude is +/- <code>*loud*</code>.<br><br>
<dt>
<code>yin(<a name="index595"></a><a name="index596"></a><a name="index597"></a><a name="index598"></a><a name="index599"></a><a name="index600"></a><i>sound</i>, <i>minstep</i>, <i>maxstep</i>, <i>stepsize</i>)</code> [SAL]<br>

<code>(yin <i>sound</i> <i>minstep</i> <i>maxstep</i> <i>stepsize</i>)</code> [LISP]</dt>
<dd>Fundamental 
frequency estimation (pitch detection. Use the YIN algorithm to estimate
the fundamental frequency of <i>sound</i>, which must be a <code>SOUND</code>. 
The <i>minstep</i>, a <code>FLONUM</code>, is the minimum frequency considered (in steps), 
<i>maxstep</i>, a <code>FLONUM</code>, is the maximum frequency considered (in steps), and 
<i>stepsize</i>, a <code>FIXNUM</code>, is the desired hop size.  The result is 
a &ldquo;stereo&rdquo; signal,
i.e. an array of two <code>SOUND</code>s, both at the same sample rate, which is 
approximately the sample rate of <i>sound</i> divided by <i>stepsize</i>. 
The first <code>SOUND</code> consists of frequency estimates (in units of
steps, i.e. middle C = 60). The second sound consists
of values that measure the confidence or reliability of the frequency estimate.
A small value (less than 0.1) indicates fairly high confidence. A larger value
indicates lower confidence. This number can also be thought of as a ratio of 
non-periodic power to periodic power. When the number is low, it means the signal
is highly periodic at that point in time, so the period estimate will be 
reliable.
Hint #1: See 
Alain de Cheveigne and Hideki Kawahara's article "YIN, a Fundamental Frequency
Estimator for Speech and Music" in the Journal of the 
Acoustic Society of America, April 2002 for details on the yin algorithm.  
Hint #2: Typically, the <i>stepsize</i> should be at least the expected number
of samples in one period so that the 
fundamental frequency estimates are calculated at a rate far below
the sample rate of the signal. Frequency does not change rapidly and
the yin algorithm is fairly slow. To optimize speed, 
you may want to use less than 44.1 kHz sample rates for input sounds.Yin
uses interpolation to achieve potentially fractional-sample-accurate estimates, 
so higher sample rates do not necessarily help the algorithm and definitely
slow it down. The computation time is O(<i>n</i><sup T>2</sup>) per estimate, 
where <i>n</i> is the number
of samples in the longest period considered. Therefore, each increase
of <i>minstep</i> by 12 (an octave) gives you a factor of 4 speedup, and 
each decrease of the sample rate of <i>sound</i> by a factor of
two gives you another factor of 4 speedup. Finally, the number of estimates is
inversely proportional to <i>stepsize</i>.
Hint #3: Use <code>snd-srate</code> (see Section <a href = "#86">Accessing and Creating Sound</a>) to get
the exact sample rate of the result, which will be the sample rate of
<i>sound</i> divided by <i>stepsize</i>. 
E.g. <code>(snd-srate (aref yin-output 0))</code>,
where <code>yin-output</code> is a result returned by <code>yin</code>, will be the 
sample rate of the estimates. 
</dd></dl><a name = "98"><h3>Transformations</h3></a><a name="index601"></a>
<p>These functions change the environment that is seen by other high-level
functions.  Note that these changes are usually relative to the
current environment.  There are also &ldquo;absolute&rdquo; versions of each
transformation function, with the exception of <code>seq</code>,
<code>seqrep</code>, <code>sim</code>, and <code>simrep</code>.  The
&ldquo;absolute&rdquo; versions (starting or ending with &ldquo;abs&rdquo;) do not look at the
current environment, but rather set an environment variable to a specific value.
In this way, sections of code can be insulated from external
transformations.</p>
<dl>
<dt>
<code>abs-env(<a name="index602"></a><i>beh</i>)</code> [SAL]<br>

<code>(abs-env <i>beh</i>)</code> [LISP]</dt>
<dd>Compute <i>beh</i> in the default environment.  
This is useful for computing waveform tables and signals that are 
&ldquo;outside&rdquo; of
time.  For example, <code>(at 10.0 (abs-env (my-beh)))</code> is equivalent to
<code>(abs-env (my-beh))</code> because <code>abs-env</code> forces the default environment. Or in SAL, we would say <code>abs-env(my-beh()) @ 10</code> is equivalent to <code>abs-env(my-beh())</code>.<br><br>
<dt><code>at(<a name="index603"></a><i>time</i>, <i>beh</i>)</code> [SAL]<br>

<code>(at <i>time</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluate <i>beh</i> with
<code>*warp*<a name="index604"></a></code> shifted by <i>time</i>. In SAL, you can use the infix
operator <code>@</code> as in <code><i>beh</i> @ <i>time</i></code>. To discover how the
environment is shifting time, use <code>local-to-global(<i>time</i>)</code>. Most
commonly, you call <code>local-to-global(0)</code> to find when a sound created
in the current environment will start, expressed in absolute (global) terms.  
This can be regarded as the &ldquo;current time.&rdquo;<br><br>
<dt><code>at-abs(<a name="index605"></a><i>time</i>, <i>beh</i>)</code> [SAL]<br>

<code>(at-abs <i>time</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluate <i>beh</i> with
<code>*warp*<a name="index606"></a></code> shifted so that local time 0 maps to <i>time</i>. In SAL, you can use the infix operator <code>@@</code> as in <code><i>beh</i> @@ <i>time</i></code>.<br><br>
<dt>
<code>continuous-control-warp(<a name="index607"></a><i>beh</i>)</code> [SAL]<br>

<code>(continuous-control-warp <i>beh</i>)</code> [LISP]</dt>
<dd>Applies the current warp environment to the signal returned by <i>beh</i>. The result has the default control sample rate <code>*control-srate*</code>. Linear interpolation is currently used. Implementation: <i>beh</i> is first evaluated without any shifting, stretching, or warping. The result is functionally composed with the inverse of the environment's warp function.<br><br>
<dt>
<code>continuous-sound-warp(<a name="index608"></a><i>beh</i>)</code> [SAL]<br>

<code>(continuous-sound-warp <i>beh</i>)</code> [LISP]</dt>
<dd>Applies the current warp environment to the signal returned by <i>beh</i>. The result has the default sound sample rate <code>*sound-srate*</code>. Linear interpolation is currently used. See <code>continuous-control-warp</code> for implementation notes.<br><br>
<dt>
<code>control-srate-abs(<a name="index609"></a><i>srate</i>, 
<i>beh</i>)</code> [SAL]<br>

<code>(control-srate-abs <i>srate</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluate <i>beh</i> with <code>*control-srate*<a name="index610"></a></code>
set to sample rate <i>srate</i>.  <b><i>Note:</i></b> there is no &ldquo;relative&rdquo; version of 
this function.<br><br>
<dt><code>extract(<a name="index611"></a><i>start</i>, <i>stop</i>, <i>beh</i>)</code> [SAL]<br>

<code>(extract <i>start</i> <i>stop</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Returns a sound 
which is the portion of
<i>beh</i> between <i>start</i> and <i>stop</i>.  Note that this is done 
relative to the current <code>*warp*</code>.  The result is shifted
to start according to <code>*warp*</code>, so normally the result will start without a delay of <i>start</i>.<br><br>
<dt><code>extract-abs(<a name="index612"></a><i>start</i>, <i>stop</i>, <i>beh</i>)</code> [SAL]<br>

<code>(extract-abs <i>start</i> <i>stop</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Returns a sound which
is the portion of
<i>beh</i> between <i>start</i> and <i>stop</i>, independent of the 
current <code>*warp*</code>.  The result is shifted to start at time zero.
Wrapping a call to <code>extract-abs</code> in <code>cue</code> will shift the result to
start at the current time, which is <code>local-to-global(0</code>).<br><br>
<dt><code>loud(<a name="index613"></a><i>volume</i>, <i>beh</i>)</code> [SAL]<br>

<code>(loud <i>volume</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*loud*</code>
incremented by <i>volume</i>. (Recall that <code>*loud*</code> is in decibels, so increment is the proper operation.)<br><br>
<dt><code>loud-abs(<a name="index614"></a><i>volume</i>, <i>beh</i>)</code> [SAL]<br>

<code>(loud-abs <i>volume</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*loud*</code>
set to <i>volume</i>.<br><br>
<dt>
<code>sound-srate-abs(<a name="index615"></a><i>srate</i>, <i>beh</i>)</code> [SAL]<br>

<code>(sound-srate-abs <i>srate</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluate <i>beh</i> with <code>*sound-srate*<a name="index616"></a></code> set to sample rate <i>srate</i>.  <b><i>Note:</i></b> there is no &ldquo;relative&rdquo; version of this function.  <br><br>
<dt><code>stretch(<a name="index617"></a><i>factor</i>, <i>beh</i>)</code> [SAL]<br>

<code>(stretch <i>factor</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with
<code>*warp*</code> scaled by <i>factor</i>.  The effect is to &ldquo;stretch&rdquo; the result
of <i>beh</i> (under the current environment) by <i>factor</i>.  See Chapter
<a href = "part5.html#38">Continuous Transformations and Time Warps</a> for more information. Use <code>get-duration(<i>dur</i>)</code> to 
get the nominal actual duration of a behavior that locally has a duration
of <i>dur</i>. Here, &ldquo;nominal&rdquo; means what would be expected if the behavior
obeys the shift, stretch, and warp components of the environment. (Any 
behavior is free to deviate from the nominal timing. For example, a percussion
sound might have a fixed duration independent of the stretch factor.) Also,
&ldquo;actual&rdquo; means global or absolute time, and &ldquo;locally&rdquo; means within the
environment where <code>get-duration</code> is called. <code>get-duration</code> works
by mapping the current time (local time 0) using <code>local-to-global</code> to
obtain an actual start time, and mapping <i>dur</i> to obtain an actual end time.
The difference is returned.<br><br>
<dt><code>stretch-abs(<a name="index618"></a><i>factor</i>, <i>beh</i>)</code> [SAL]<br>

<code>(stretch-abs <i>factor</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*warp*</code> set to a linear time transformation where each unit of logical time maps to <i>factor</i> units of real time.  The effect is to stretch the nominal behavior of <i>beh</i> (under the default global environment) by <i>factor</i>.  See Chapter <a href = "part5.html#38">Continuous Transformations and Time Warps</a> for more information.<br><br>
<dt><code>sustain(<a name="index619"></a><a name="index620"></a><a name="index621"></a><a name="index622"></a><i>factor</i>, <i>beh</i>)</code> [SAL]<br>

<code>(sustain <i>factor</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*sustain*</code> scaled by <i>factor</i>. The effect is to &ldquo;stretch&rdquo; the result of <i>beh</i> (under the current environment) by <i>factor</i>; however, the logical stop times are not stretched. Therefore, the overall duration of a sequence is not changed, and sounds will tend to overlap if <code>*sustain*</code> is greater than one (legato) and be separated by silence if <code>*sustain*</code> is less than one.<br><br>
<dt><code>sustain-abs(<a name="index623"></a><i>factor</i>, <i>beh</i>)</code> [SAL]<br>

<code>(sustain-abs <i>factor</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*sustain*</code> set to <i>factor</i>. (See <code>sustain</code>, above.)<br><br>
<dt><code>transpose(<a name="index624"></a><i>amount</i>, <i>beh</i>)</code> [SAL]<br>

<code>(transpose <i>amount</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with 
<code>*transpose*</code> shifted by <i>amount</i>.  The effect is relative transposition by <i>amount</i> semitones.<br><br>
<dt><code>transpose-abs(<a name="index625"></a><i>amount</i>, <i>beh</i>)</code> [SAL]<br>

<code>(transpose-abs <i>amount</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with 
<code>*transpose*</code> set to <i>amount</i>.  The effect is the transposition of the nominal pitches in <i>beh</i> (under the default global environment) by <i>amount</i>.<br><br>
<dt><code>warp(<a name="index626"></a><i>fn</i>, <i>beh</i>)</code> [SAL]<br>

<code>(warp <i>fn</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*warp*</code> modified by <i>fn</i>.  The idea is that <i>beh</i> and <i>fn</i> are written in the same time system, and <i>fn</i> warps that time system to local time.  The current environment already contains a mapping from local time to global (real) time.  The value of <code>*warp*</code> in effect when <i>beh</i> is evaluated is the functional composition of the initial <code>*warp*</code> with <i>fn</i>.<br><br>
<dt><code>warp-abs(<a name="index627"></a><i>fn</i>, <i>beh</i>)</code> [SAL]<br>

<code>(warp-abs <i>fn</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Evaluates <i>beh</i> with <code>*warp*</code> set to <i>fn</i>.  In other words, the current <code>*warp*</code> is ignored and not composed with <i>fn</i> to form the new <code>*warp*</code>.
</dd></dl><a name = "99"><h3>Combination and Time Structure</h3></a><a name="index628"></a><a name="index629"></a>
<p>These behaviors combine component behaviors into structures, including
sequences (melodies), simultaneous sounds (chords), and structures based
on iteration. See also the <code>trigger</code> function, described in
Section <a href = "part10.html#115">Starting and Stopping Sounds</a>, which uses a SOUND to trigger instances of a behavior.</p>
<dl>
<dt>

<code>seq(<a name="index630"></a><i>beh<sub>1</sub></i> [, <i>beh<sub>2</sub></i>, <span style="font-style:normal">...</span>])</code> [SAL]<br>

<code>(seq <i>beh<sub>1</sub></i> [<i>beh<sub>2</sub></i> <span style="font-style:normal">...</span>])</code> [LISP]</dt>
<dd>Evaluates the first behavior
<i>beh<sub>1</sub></i> according to the current time in the environment
 and each successive behavior at the
<code>logical-stop</code> time of the previous one.  The results are summed to form a
sound whose <code>logical-stop</code> is
the <code>logical-stop</code> of the last behavior in the sequence.  Each behavior
can result in a multichannel sound, in which case, the logical stop time is
considered to be the maximum logical stop time of any channel.  The number
of channels in the result is the number of channels of the first behavior.
If other behaviors return fewer channels, new channels are created containing
constant zero signals until the required number of channels is obtained.  If
other behaviors return a simple sound rather than multichannel sounds, the
sound is automatically assigned to the first channel of a multichannel sound
that is then filled out with zero signals.  If another behavior returns more
channels than the first behavior, the error is reported and the computation
is stopped.  Sample rates are converted up or down to match the sample rate of the first sound in a sequence.

Nyquist programs should generally avoid storing sounds in global variables
because that tends to cause sound samples to be retained in memory. A 
related problem can occur with <code>seq</code> and <code>seqrep</code>. With these
functions, behaviors are not evaluated until needed, but what if the behaviors
depend on local variables as parameters? Ordinarily, the variables would
be long gone and garbage collected by the time the behavior is evaluated.
So, <code>seq</code> and <code>seqrep</code> capture all local variables and their 
bindings (values) in <i>closures</i>. This solves the problem of retaining
local variables and values until they are needed by the behaviors, but it
has a problem similar to global variables in that <i>any sounds captured in 
the closure cannot be released until the last behavior in the sequence is
evaluated.</i>

Here is an example:

<p></p>
<pre>
load "reverb"

function long-tone() return buzz(15, c4, lfo(5, 10))

function rev-with-tail(s, rt)
  return reverb(seq(s, s-rest(rt * 2)), rt)

play rev-with-tail(pluck(c4), 10)
</pre>

<p> This SAL function uses <code>seq</code> to append
<code>rt * 2</code> seconds of silence to sound <code>s</code> before passing it
to <code>reverb</code> ensuring that the reverb tail will not be cut off
immediately at the end of <code>s</code>.  Behavior 2, <code>s-rest(rt * 2)</code>, is
wrapped in a closure which also captures the binding of <code>s</code> to
the input sound (returned from <code>long-tone()</code>) and that of <code>rt</code> to 10.
If there were no closure, then
when <code>rev-with-tail</code> returns a sound to <code>play</code>, the variable
<code>s</code> would be freed by garbage collection, and the only remaining
reference to <code>long-tone()</code> would be internal to the <code>reverb</code>
sound computation. <code>reverb</code> disposes of samples as soon as they
are computed and used, so the total memory requirements would be minimal.
In this case, however, since <code>s</code> is captured in a closure,
as <code>reverb</code> demands computation of samples from
<code>long-tone()</code>, <code>reverb</code> releases its claim on the samples,
but <code>s</code> does not, so all the samples are retained in memory 
until <code>s-rest(rt * 2)</code> is evaluated and the closure (and <code>s</code>)
are freed.

For 10 seconds of sound (such as <code>long-tone(</code>)), this is not a big
problem. In fact, if you use the default settings for autonorm, Nyquist
will store about 20 seconds of sound in memory anyway just to do some
look-ahead for normalization, but if <code>s</code> represents an hour-long
stereo recording,
or if there are many other sounds bound in local variables and captured
in closures, the memory overhead can be too great. The solution is to
override the default scopes and bindings to achieve the variable
lifetimes we want. At any time, we can set a variable to <code>nil</code>,
freeing the previous value to allow garbage collection. In LISP, we
can write <code>(prog1 s (setf s nil))</code> to evaluate <code>s</code>, then
free <code>s</code> by setting it to <code>nil</code>. The original value of <code>s</code>
is returned from the <code>prog1</code> expression.
In SAL, we can use the same trick, using
<code>setf</code> rather than the typical SAL assignment operator
(<code>=</code>).

To change the example to be memory efficient, we change the definition
of <code>rev-with-tail</code> to:
</p>
<pre>
function rev-with-tail(s, rt)
  return reverb(seq(prog1(s, setf(s, nil)), s-rest(rt * 2)), rt)
</pre>

<p>
Note in this example that the variable <code>s</code> loses its reference to the
<code>long-tone()</code> sound right after it is evaluated by <code>prog1</code>,
so now <code>reverb</code> has the only reference to this sound, and it can 
free samples from <code>long-tone()</code> as they are
consumed. (In case you are wondering, the actual mechanism is that when
<code>reverb</code> frees samples, their reference count goes to zero since no
other reference exists to the possibly shared list of samples. There is
no other reference because the reference previously bound to <code>s</code>
is released by the garbage collector.)

It should be noted that the variable <code>rt</code> is retained in the
closure and remains accessible there, so when <code>s</code> 
terminates, <code>s-rest(rt</code>)
will evaluate as expected, using the value that <code>rt</code> acquired way
back when <code>rev-with-tail</code> was called. This illustrates why
the local variables must be saved in closures at the time <code>seq</code> is called.
</p>
<dt><code>seqrep(<a name="index631"></a><i>var</i>, <i>limit</i>, <i>beh</i>)</code> [SAL]<br>

<code>(seqrep (<i>var</i> <i>limit</i>) <i>beh</i>)</code> [LISP]</dt>
<dd>Iteratively 
evaluates <i>beh</i> with the atom
<i>var</i> set with values from 0 to <i>limit</i>-1, inclusive.  These sounds
are placed sequentially in time as if by <code>seq</code>. The symbol <i>var</i> is
a <i>read-only</i> local variable to <i>beh</i>. Assignments are not restricted
or detected, but may cause a run-time error or crash. In LISP, the syntax is
<code>(seqrep (<i>var</i> <i>limit</i>) <i>beh</i>)</code>.<br><br>
<dt>

<code>sim(<a name="index632"></a>[<i>beh<sub>1</sub></i>, <i>beh<sub>2</sub></i>, <span style="font-style:normal">...</span>])</code> [SAL]<br>

<code>(sim [<i>beh<sub>1</sub></i> <i>beh<sub>2</sub></i> <span style="font-style:normal">...</span>])</code> [LISP]</dt>
<dd>Returns 
a sound which is the sum of the given behaviors evaluated with the current
value of <code>*warp*</code>.  If behaviors return multiple channel sounds,
the corresponding channels are added.  If the number of channels does
not match, the result has as many channels as the argument with the
most channels.  For example, if a two-channel
sound [L, R] is added to a four-channel sound [C1, C2, C3, C4], the
result is [L + C1, R + C2, C3, C4].  Arguments to <code>sim</code> may also
be numbers.  If all arguments are numbers, <code>sim</code> is equivalent
(although slower than) the LISP <code>+</code> function.  If a number is added to
a sound, <code>snd-offset</code> is used to add the number to each sample of
the sound.  The result of adding a number to two or more sounds with
different durations is not defined.  Use <code>const</code> to coerce a
number to a sound of a specified duration.  An important limitation of
<code>sim</code> is that it cannot handle hundreds of behaviors due to a
stack size limitation in XLISP.  To compute hundreds of sounds
(e.g. notes) at specified times, see <code>timed-seq</code>, below.  See
also <code>sum</code> below. Notce that <code>sim</code> is not transitive due to
coercion rules: Using SAL syntax, <code>sim(a, sim(b, c))</code> may not produce the
same result as <code>sim(sim(a, b), c)</code>.<br><br>
<dt><code>simrep(<a name="index633"></a><i>var</i>, <i>limit</i>, <i>beh</i>)</code> [SAL]<br>

<code>(simrep <i>var</i> <i>limit</i> <i>beh</i>)</code> [LISP]</dt>
<dd>Iteratively 
evaluates <i>beh</i> with the atom
<i>var</i> set with values from 0 to <i>limit</i>-1, inclusive.  These sounds
are then placed simultaneously in time as if by <code>sim</code>.
In LISP, the syntax is
<code>(seqrep (<i>var</i> <i>limit</i>) <i>beh</i>)</code>.<br><br>
<dt><code>set-logical-stop(<a name="index634"></a><i>beh</i>, <i>time</i>)</code> [SAL]<br>

<code>(set-logical-stop <i>beh</i> <i>time</i>)</code> [LISP]</dt>
<dd>Returns a sound with <i>time</i> as 
the logical stop time.<br><br>
<dt><code>sum(<a name="index635"></a><a name="index636"></a><i>a</i> [, <i>b</i>, <span style="font-style:normal">...</span>])</code>[SAL]<br>

<code>(sum <i>a</i> [<i>b</i> <span style="font-style:normal">...</span>])</code> [LISP]</dt>
<dd>Returns
the sum of <i>a</i>, <i>b</i>, ..., allowing mixed addition of sounds, 
multichannel sounds and numbers.  Identical to <i>sim</i>. In SAL, 
use the infix &ldquo;+&rdquo; operator. See <code>sim</code> just above for more
detail.<br><br>
<dt><code>mult(<a name="index637"></a><a name="index638"></a><a name="index639"></a><i>a</i> [, <i>b</i>, <span style="font-style:normal">...</span>])</code> [SAL]<br>

<code>(mult <i>a</i> [<i>b</i> <span style="font-style:normal">...</span>])</code> [LISP]</dt>
<dd>Returns the product of <i>a</i>, <i>b</i>, ..., allowing mixed multiplication of sounds, multichannel sounds and numbers.<br><br>
<dt><code>diff(<a name="index640"></a><a name="index641"></a><i>a</i>, <i>b</i>)</code> [SAL]<br>

<code>(diff <i>a</i> <i>b</i>)</code> [LISP]</dt>
<dd>Returns the difference between <i>a</i> and <i>b</i>. This function is defined as <code>(sum a (prod -1 b))</code>.<br><br>
<dt>
<code>timed-seq(<a name="index642"></a><a name="index643"></a><a name="index644"></a><i>score</i>)</code> [SAL]<br>

<code>(timed-seq <i>score</i>)</code> [LISP]</dt>
<dd>Computes sounds from a note list or &ldquo;score.&rdquo; The <i>score</i> 
is of the form: <code>`((<i>time1</i> <i>stretch1</i> <i>beh1</i>) (<i>time2</i> 
<i>stretch2</i> <i>beh2</i>) <span style="font-style:normal">...</span>)</code>, where <i>timeN</i> is the starting time, 
<i>stretchN</i> is the stretch factor, and <i>behN</i> is the behavior. Note 
that <i>score</i> is normally a <i>quoted list</i>! The times must be in 
increasing order, and each <i>behN</i> is evaluated using lisp's <code>eval</code>, 
so the <i>behN</i> behaviors cannot refer to local parameters or local 
variables. The advantage of this form over <code>seq</code> is that the 
behaviors are evaluated one-at-a-time which can take much less stack 
space and overall memory. One special &ldquo;behavior&rdquo; expression is
interpreted directly by <code>timed-seq</code>: <code>(SCORE-BEGIN-END)</code> 
is ignored, not evaluated as a function. Normally, this special
behavior is placed at time 0 and has two parameters: the score
start time and the score end time. These are used in Xmusic
functions. If the behavior has a <code>:pitch</code> keyword parameter
which is a list, the list represents a chord, and the expression is 
replaced by a set of behaviors, one for each note in the chord. 
It follows that if <code>:pitch</code> is <code>nil</code>, the behavior 
represents a rest and is ignored.
</dd></dl><a name = "100"><h3>Sound File Input and Output</h3></a><a name="index645"></a><dl>
<dt>

<code>play <a name="index646"></a><i>sound</i></code> [SAL]<br>

<code>(play <i>sound</i>)</code> [LISP]</dt>
<dd>Play the sound 
through the DAC.  
In XLISP, it is a function.  In SAL, you can invoke <code>play</code>
as either a command or a function:

<p></p>
<pre>
play pluck(c4)
;; or call the function #play like this:
exec #play(pluck(c4))
</pre>

<p>
The <code>play</code> command or function writes a file and plays it.  The
<i>sound</i> is any expression that evaluates to a SOUND. Typically, this
should be function call, in which case the samples are computed
incrementally and not retained in main memory (an advantage for large
sounds). If the expression is a variable containing a SOUND (which may
or may not be fully evaluated yet), the SOUND is fully evaluated and
all samples are retained in the variable. The <code>play</code> function is
defined in the file <code>system.lsp</code>.  The variable
<code>*default-sf-dir*</code><a name="index647"></a><a name="index648"></a><a name="index649"></a><a name="index650"></a><a name="index651"></a> names a directory into which to save a sound
file, and <code>*default-sound-file*</code><a name="index652"></a><a name="index653"></a> names the file. If <code>*default-sound-file*</code> contains a slash (<code>/</code>), it is treated as an absolute path or path relative to the current directory, ignoring <code>*default-sf-dir*</code>. Be careful not to call <code>play</code> or <code>sound-play</code> within a
function and then invoke that function from another <code>play</code>
command. By default, Nyquist will try to
normalize sounds using the method named by <code>*autonorm-type*</code>,
which is <code>'lookahead</code> by default.  The <i>lookahead</i> method
precomputes and buffers <code>*autonorm-max-samples*</code> samples, finds
the peak value, and normalizes accordingly. The <code>'previous</code>
method bases the normalization of the current sound on the peak value
of the (entire) previous sound. This might be good if you are working
with long sounds that start rather softly. See Section
<a href = "part6.html#46">Memory Space and Normalization</a> for more details.

If you want precise control over output levels, you should turn this feature off by typing (using SAL syntax):
</p>
<pre>
autonorm-off()<a name="index654"></a>
</pre>

<p>
Reenable the automatic normalization feature by typing:
</p>
<pre>
autonorm-on()<a name="index655"></a>
</pre>

<p>
Play normally produces real-time output.  The default is to send audio data to the DAC as it is computed in addition to saving samples in a file.  If computation is slower than real-time, output will be choppy, but since the samples end up in a file, you can type <code>(r)</code> to replay the stored sound. Real-time playback can be disabled by (using SAL syntax):
</p>
<pre>
sound-off()<a name="index656"></a>
</pre>

<p>
and reenabled by:
</p>
<pre>
sound-on()<a name="index657"></a>
</pre>

<p>
Disabling real-time playback has no effect on <code>(play-file)</code> or <code>(r)</code>.
While sounds are playing, typing control-A<a name="index658"></a> to Nyquist (or clicking the Mark button in the NyquistIDE) will push the estimated
elapsed<a name="index659"></a> audio time onto the head of the list 
stored in <code>*audio-markers*</code>.
<a name="index660"></a><a name="index661"></a><a name="index662"></a>
Because samples are computed in blocks and because there is latency 
between sample computation and sample playback, the elapsed time may not
be too accurate, and the computed elapsed time may not advance after all
samples have been computed but the sound is still playing.</p>
<dt><code>play-file(<a name="index663"></a><i>filename</i>)</code> [SAL]<br>

<code>(play-file <i>filename</i>)</code> [LISP]</dt>
<dd>Play the contents of a sound file named by <i>filename</i>. The <code>s-read</code> function is used to read the file, and unless 
<i>filename</i> specifies an absolute path or starts with &ldquo;.&rdquo;, it will be read from 
<code>*default-sf-dir*</code>.<br><br>
<dt><code>autonorm-on(<a name="index664"></a>)</code> [SAL]<br>

<code>(autonorm-on)</code> [LISP]</dt>
<dd>Enable automatic adjustment of a scale factor applied to sounds computed using the <code>play</code> command.<br><br>
<dt><code>autonorm-off(<a name="index665"></a>)</code> [SAL]<br>

<code>(autonorm-off)</code> [LISP]</dt>
<dd>Disable automatic adjustment of a scale factor applied to sounds computed using the <code>play</code> command.<br><br>
<dt><code>sound-on(<a name="index666"></a>)</code> [SAL]<br>

<code>(sound-on)</code> [LISP]</dt>
<dd>Enable real-time audio output when sound is computed by the the <code>play</code> command.<br><br>
<dt><code>sound-off(<a name="index667"></a>)</code> [SAL]<br>

<code>(sound-off)</code> [LISP]</dt>
<dd>Disable real-time audio output when sound is computed by the the <code>play</code> command.<br><br>
<dt>
<code>s-save(<a name="index668"></a><a name="index669"></a><a name="index670"></a><a name="index671"></a><i>expression</i>, [<i>maxlen</i>, <i>filename</i>, <i>progress</i>], format: <i>format</i>, mode: <i>mode</i>, bits: <i>bits</i>, swap: <i>flag</i>, play: <i>play</i>)</code> [SAL]<br>

<code>(s-save <i>expression</i> [<i>maxlen</i> <i>filename</i> <i>progress</i>] :format <i>format</i> :mode <i>mode</i> :bits <i>bits</i> :swap <i>flag</i> :play <i>play</i>)</code> [LISP]</dt>
<dd>Evaluates the <i>expression</i>, which should result in a sound
or an array of sounds, and writes the result to the given <i>filename</i>. (If
omitted, <code>*default-sound-file*</code> is used instead.) A
<code>FLONUM</code> is returned giving the maximum absolute value of all samples
written. (This is useful for normalizing sounds and detecting sample
overflow.) If <i>play</i> is not <code>NIL</code>, the sound will be output
through the computer's audio output system. (<i>play:</i> [SAL]
or <i>:play</i> [LISP] is not implemented on all systems; if it is implemented, and <i>filename</i> is <code>NIL</code>, then this will play the file without also writing a file.)
The latency (length of audio buffering) used to play the sound is 0.3s by default, but see <code>snd-set-latency</code>.
If
a multichannel sound (array) is written, the channels are up-sampled to the
highest rate in any channel so that all channels have the same sample rate.
The maximum number of samples written per channel is optionally given by <i>maxlen</i>,
which allows writing the initial part of a very long or infinite sound.
Progress is indicated by printing the sample count after
writing each 10 seconds of frames.  If <i>progress</i> is specified and greater
than 10,000, progress is printed at this specified frame count increment.
A header is written according to <i>format</i>, samples are encoded according to
<i>mode</i>, using <i>bits</i> bits/sample, and bytes are swapped if <i>flag</i> is not NIL.  Defaults for these are
<code>*default-sf-format*</code>, <code>*default-sf-mode*</code>, and
<code>*default-sf-bits*</code>. The default for <i>flag</i> is NIL.
The <i>bits</i> parameter may be 8, 16, or 32.  The values for the <i>format</i> and <i>mode</i> options are described below:
</dd></dl>

<b>Format</b>
<dl>
<dt>
<code>snd-head-none</code></dt>
<dd>The format is unknown and should be determined
by reading the file.<br><br>
<dt><code>snd-head-raw</code></dt>
<dd>A raw format file has no header. <br><br>
<dt><code>snd-head-AIFF</code></dt>
<dd>AIFF format header.<br><br>
<dt><code>snd-head-IRCAM</code></dt>
<dd>IRCAM format header.<br><br>
<dt><code>snd-head-NeXT</code></dt>
<dd>1024-byte NeXT/SUN format header followed by IRCAM
header ala CMIX.  Note that the NeXT/SUN format has a header-length field,
so it really is legal to have a large header, even though the normal minimal
header is only 24 bytes.  The additional space leaves room for maximum
amplitudes, which can be used for normalizing floating-point soundfiles, and
for other data.  Nyquist follows the CMIX convention of placing an IRCAM
format header immediately after the NeXT-style header.<br><br>
<dt><code>snd-head-Wave</code></dt>
<dd>Microsoft Wave format header.<br><br>
<dt><code>snd-head-WaveX</code></dt>
<dd>Microsoft Wave with WAVEFORMATEX format header.<br><br>
<dt><code>snd-head-flac</code></dt>
<dd>FLAC lossless compressed audio.<br><br>
<dt><code>snd-head-ogg</code></dt>
<dd>OGG-VORBIS compressed audio.<br><br>
<dt><code>snd-head-*</code></dt>
<dd>See sndfnint.lsp in the <code>nyquist/runtime</code> directory
 for more formats. The current list includes
<code>paf</code>, <code>svx</code>, <code>nist</code>, <code>voc</code>, <code>w64</code>, <code>mat4</code>, <code>mat5</code>,
<code>pvf</code>, <code>xi</code>, <code>htk</code>, <code>sds</code>, <code>avr</code>, <code>sd2</code>, and <code>caf</code>.
</dd></dl><b>Mode</b>
<dl>
<dt>
<code>snd-mode-adpcm</code></dt>
<dd>ADPCM mode (not supported).<br><br>
<dt><code>snd-mode-pcm</code></dt>
<dd>signed binary PCM mode.<br><br>
<dt><code>snd-mode-ulaw</code></dt>
<dd>8-bit U-Law mode.<br><br>
<dt><code>snd-mode-alaw</code></dt>
<dd>8-bit A-Law mode (not supported).<br><br>
<dt><code>snd-mode-float</code></dt>
<dd>32-bit floating point mode.<br><br>
<dt><code>snd-mode-upcm</code></dt>
<dd>unsigned binary PCM mode.<br><br>
<dt><code>snd-mode-*</code></dt>
<dd>See sndfnint.lsp in the <code>nyquist/runtime</code> for more modes. The current list includes 
<code>double</code>, <code>gsm610</code>, <code>dwvw</code>, <code>dpcm</code>, and <code>msadpcm</code>.
</dd></dl>
<p>The defaults for format, mode, and bits are as follows:
<dl>
<dt>
NeXT and Sun machines:</dt>
<dd><code>snd-head-NeXT</code>, <code>snd-mode-pcm</code>,
<code>16</code></p>
<dt>SGI and Macintosh machines:</dt>
<dd><code>snd-head-AIFF</code>, <code>snd-mode-pcm</code>, <code>16</code>
</dd></dl><dl>
<dt>

<code>s-read(<a name="index672"></a><a name="index673"></a><i>filename</i>, time-offset: <i>offset</i>, srate: <i>sr</i>, dur: <i>dur</i>, nchans: <i>chans</i>, format: <i>format</i>, mode: <i>mode</i>, bits: <i>n</i>, swap: <i>flag</i>)</code> [SAL]<br>

<code>(s-read <i>filename</i> :time-offset <i>offset</i> :srate <i>sr</i>
 :dur <i>dur</i> :nchans <i>chans</i> :format <i>format</i> :mode <i>mode</i> :bits <i>n</i>
 :swap <i>flag</i>)</code> [LISP]</dt>
<dd>Reads a sound from
<i>filename</i>. The global <code>*default-sf-dir*</code> applies. If a header is
detected, the header is used to determine the format
of the file, and header information overrides format information provided by
keywords (except for <code>time-offset:</code> and <code>dur:</code>). 

<p></p>
<pre>
s-read("mysound.snd", srate: 44100)
</pre>

<p>
specifies a sample rate of 44100 hz, but if the file has a header specifying 22050 hz, the resulting sample rate will be 22050.  The parameters are:
<ul>
<li>
<i>offset</i> &ndash; the amount of time (in seconds) to skip from
the beginning of the file.  The default is 0.0.</li>
<li><i>sr</i> &ndash; the sample rate of the samples in the file.  Default is
<code>*default-sf-srate*</code> <a name="index674"></a>, which is normally 44100.</li>
<li><i>dur</i> &ndash; the maximum duration in seconds to read.  Default is
10000.</li>
<li><i>chans</i> &ndash; the number of channels to read.  It is assumed that
samples from each channel are interleaved.  Default is 1.</li>
<li><i>format</i> &ndash; the header format.  See <code>s-save</code> for details.
Default is <code>*default-sf-format*</code>, although this parameter is currently
ignored.</li>
<li><i>mode</i> &ndash; the sample representation, e.g. PCM or float.  See
<code>s-save</code> for details.  Default is <code>*default-sf-format*</code>.</li>
<li><i>n</i> &ndash; the number of bits per sample.  See <code>s-save</code> for
details.  Default is <code>*default-sf-bits*</code>.</li>
<li><i>flag</i> &ndash; (T or NIL) swap byte order of each sample. Default is NIL.
</li></ul>
If there is an error, for example if <i>offset</i> is greater than the length
of the file, then <code>NIL</code> is returned rather than a sound. Information
about the sound is also returned by <code>s-read</code>
through <code>*rslt*</code> <a href = "foot.html#foot4">(Footnote 4)</a> . The list assigned
to <code>*rslt*</code> is of the form: (<i>format</i> <i>channels</i> <i>mode</i> <i>bits</i> <i>swap</i> <i>samplerate</i> <i>duration</i> <i>flags</i>), which are defined as follows:
<ul>
<li>
<i>format</i> &ndash; the header format. See <code>s-save</code> for details. Access
this element of <code>*rslt*</code> by calling <code>snd-read-format(*rslt*)</code>.</li>
<li><i>channels</i> &ndash; the number of channels. Access
this element of <code>*rslt*</code> by calling <code>snd-read-channels(*rslt*)</code>.</li>
<li><i>mode</i> &ndash; the sample representation, e.g. PCM or float. Access
this element of <code>*rslt*</code> by calling <code>snd-read-mode(*rslt*)</code>.
See <code>s-save</code> for details.</li>
<li><i>bits</i> &ndash; the number of bits per sample.  Access
this element of <code>*rslt*</code> by calling <code>snd-read-bits(*rslt*)</code>.</li>
<li><i>swap</i> &ndash; 1 if byte-swapping is needed, 0 otherwise. Access
this element of <code>*rslt*</code> by calling <code>snd-read-swap(*rslt*)</code>.</li>
<li><i>samplerate</i> &ndash; the sample rate, expressed as a <code>FLONUM</code>. Access
this element of <code>*rslt*</code> by calling <code>snd-read-srate(*rslt*)</code>.</li>
<li><i>duration</i> &ndash; the duration of the sound, in seconds. Access
this element of <code>*rslt*</code> by calling <code>snd-read-dur(*rslt*)</code>.</li>
<li><i>flags</i> &ndash; The values
for <i>format</i>, <i>channels</i>, <i>mode</i>, <i>bits</i>, <i>samplerate</i>,
and <i>duration</i> are initially just the values passed in as
parameters or default values to <code>s-read</code>.  If a value is actually
read from the sound file header, a flag is set.  The flags
are: <code>snd-head-type</code> (format), <code>snd-head-channels</code>, <code>snd-head-mode</code>, <code>snd-head-bits</code>, <code>snd-head-srate</code>, and <code>snd-head-dur</code>.  For example,
</p>
<pre>
(let ((flags (s-read-flags *rslt*)))
  (not (zerop (logand flags snd-head-srate))))
</pre>

<p>
tells whether the sample rate was specified in the file. See also <code>sf-info</code> below.
Access this element of <code>*rslt*</code> by calling <code>snd-read-flags(*rslt*)</code>.
</li></ul></p>
<dt><code>s-add-to(<a name="index675"></a><a name="index676"></a><a name="index677"></a><i>expression</i>, <i>maxlen</i>, <i>filename</i> [, <i>offset</i>, <i>progress</i>])</code> [SAL]<br>

<code>(s-add-to <i>expression</i> <i>maxlen</i> <i>filename</i> [<i>offset</i> <i>progress</i>])</code> [LISP]</dt>
<dd>Evaluates the <i>expression</i>, which should result in a sound
or an array of sounds, and adds the result to the given <i>filename</i>.  
The global <code>*default-sf-dir*</code> applies. A <code>FLONUM</code> is returned, 
giving the maximum absolute value of all samples written. The
sample rate(s) of <i>expression</i> must match those of the file.
The maximum number of samples written per channel is given by <i>maxlen</i>,
which allows writing the initial part of a very long or infinite sound. 
If <i>offset</i> is specified, the new sound is added to the file beginning at
an <i>offset</i> from the beginning (in seconds).
Progress is indicated by printing the sample count after
writing each 10 seconds of frames.  If <i>progress</i> is specified and greater
than 10,000, progress is printed at this specified frame count increment.
The file is extended if
necessary to accommodate the new addition, but if <i>offset</i>
falls outside of the original file, the file is not modified. (If necessary,
use <code>s-add-to</code> to extend the file with zeros.) 
The file must be a recognized
sound file with a header (not a raw sound file).<br><br>
<dt><code>s-overwrite(<a name="index678"></a><a name="index679"></a><a name="index680"></a><i>expression</i>, <i>maxlen</i>, <i>filename</i> [, <i>offset</i>, <i>progress</i>])</code> [SAL]<br>

<code>(s-overwrite <i>expression</i> <i>maxlen</i> <i>filename</i> [<i>offset</i> <i>progress</i>])</code> [LISP]</dt>
<dd>Evaluates 
the <i>expression</i>, which should result in a sound
or an array of sounds, and replaces samples in the given <i>filename</i>.  
The global <code>*default-sf-dir*</code> applies.
A <code>FLONUM</code> is returned, giving the maximum absolute value of all 
samples written. The
sample rate(s) of <i>expression</i> must match those of the file.
The maximum number of samples written per channel is given by <i>maxlen</i>,
which allows writing the initial part of a very long or infinite sound. 
If <i>offset</i> is specified, the new sound is written to the file beginning at
an <i>offset</i> from the beginning (in seconds). The file is extended if
necessary to accommodate the new insert, but if <i>offset</i> falls outside of
the original file, the file is not modified. (If necessary, use
<code>s-add-to</code> to extend the file with zeros.)
Progress is indicated by printing the sample count after
writing each 10 seconds of frames.  If <i>progress</i> is specified and greater
than 10,000, progress is printed at this specified frame count increment.
The file must be a recognized
sound file with a header (not a raw sound file).<br><br>
<dt><code>sf-info(<a name="index681"></a><a name="index682"></a><i>filename</i>)</code> [SAL]<br>

<code>(sf-info <i>filename</i>)</code> [LISP]</dt>
<dd>Prints information about a sound file. The parameter <i>filename</i> is a string.  The file is assumed to be in *default-sf-dir* (see <code>soundfilename</code> below) unless the filename begins with &ldquo;.&rdquo; or &ldquo;/&rdquo;. The source for this function is in the <code>runtime</code> and provides an example of how to determine sound file parameters. <br><br>
<dt><code>soundfilename(<a name="index683"></a><i>name</i>)</code> [SAL]<br>

<code>(soundfilename <i>name</i>)</code> [LISP]</dt>
<dd>Converts a string <i>name</i> to a soundfile name.  If <i>name</i> begins with &ldquo;.&rdquo; or &ldquo;/&rdquo;, the name is returned without alteration.  Otherwise,  a path taken from <code>*default-sf-dir*</code> is prepended to <i>name</i>.  The <code>s-plot</code>, <code>s-read</code>, and <code>s-save</code> functions all use <code>soundfilename</code> to translate filenames.<br><br>
<dt>
<code>s-plot(<a name="index684"></a><a name="index685"></a><i>sound</i> 
 [, <i>dur</i>, <i>n</i>])</code> [SAL]<br>

<code>(s-plot <i>sound</i> 
 [<i>dur</i> <i>n</i>])</code> [LISP]</dt>
<dd>Plots sound in a window.  This function was designed to run a <code>plot</code> program on a Unix workstation, but now is
primarily used with <code>NyquistIDE</code>, which has self-contained plotting. Normally,
time/value pairs in ascii are written to <code>points.dat</code> and system-dependent code
(or the <code>NyquistIDE</code> program) takes it from there. If the <i>sound</i> is 
longer than the optional <i>dur</i> (default is 2 seconds), only the 
first <i>dur</i> seconds are plotted. 
If there are more than <i>n</i> samples to be plotted, the signal is interpolated
to have <i>n</i> samples before plotting.
The data file used is <code>*default-plot-file*</code>:<br><br>
<dt><code>*default-plot-file*</code><a name="index686"></a></dt>
<dd>The file containing the data points, defaults to "points.dat".<br><br>
<dt><code>spec-plot(<a name="index687"></a><a name="index688"></a><a name="index689"></a><a name="index690"></a><i>sound</i> [, offset: <i>offset</i>, dur: <i>dur</i>, res: <i>res</i>, bw: <i>bw</i>, db: <i>db</i>])</code> [SAL]<br>

<code>(spec-plot <i>sound</i> [:offset <i>offset</i> :dur <i>dur</i> :res <i>res</i> :bw <i>bw</i> :db <i>db</i>])</code> [LISP]</dt>
<dd>Computes
and plots the short-time magnitude spectrum of sound (a SOUND or STRING).
If sound is a filename (a STRING), a sound is read from the file.
The bandwidth of each bin
is given by the <i>res</i>
(resolution) keyword parameter, which defaults to <code>*spec-plot-res*. Since one
is often interested in lower frequencies, the <i>bw</i> (bandwidth</code> keyword parameter
limits the range of bins which are plotted, and defaults to <code>*spec-plot-bw*</code>.
The output can be presented on a dB scale by setting the <i>db</i> keyword parameter to
<code>t</code> (true). The default is to use a linear scale.
The <i>offset</i> (in seconds) skips initial samples before taking a frame of
samples from <i>sound</i>. The <i>dur</i> keyword parameter (in seconds) limits the number of samples
taken from sound. If <i>dur</i> is shorter than the FFT window size, the sound is zero-padded.
If <i>dur</i> is longer than the FFT window size, the extra samples are ignored.
The magnitude spectrum is sent to <code>s-plot</code> as a signal.
The sample rate of the signal is set so that the plot labels on the horizontal axis
represent Hz (not bin numbers.) To align bins with grid lines, one normally specifies
<i>res</i> values in round numbers, e.g. 10 or 20. To achieve an arbitrary bin size,
<code>spec-plot</code> resamples <i>sound</i> to a carefully computed sample rate that, after
a power-of-2-sized FFT, yields the desired bin size.<br><br>
<dt><code>spec-print(<a name="index691"></a><a name="index692"></a><a name="index693"></a><a name="index694"></a><i>file</i> <i>sound</i> [, offset: <i>offset</i>, dur: <i>dur</i>, res: <i>res</i>, bw: <i>bw</i>, threshold: <i>threshold</i>])</code> [SAL]<br>

<code>(spec-print <i>file</i> <i>sound</i> [:offset <i>offset</i> :dur <i>dur</i> :res <i>res</i> :bw <i>bw</i> :threshold <i>threshold</i>])</code> [LISP]</dt>
<dd>Computes
and prints an ASCII plot of the short-time magnitude spectrum of sound using <code>sa-print</code>
(see <a href = "part11.html#122">Spectral Processing</a>).
The <i>file</i> can be <code>T</code> to print to the console or a file open for writing. Other parameters
are as in <code>spec-plot</code> (see above) except for <i>threshold</i>, which is passed to <code>sa-print</code>.
Note that <i>bw</i> is passed to <code>sa-print</code> as <i>cutoff</i>. The global
variables <code>*spec-plot-res*</code> and <code>*spec-plot-bw*</code> apply to <code>spec-print</code> as well
as <code>spec-plot</code>. Important: The printed and plotted magnitudes are <i>normalized</i> to a peak
value of 1 (see <code>sa-normalize</code>).<br><br>
<dt><code>*spec-plot-res*</code><a name="index695"></a></dt>
<dd>The default bin resolution
(separation in Hz between adjacent bins) for <code>spec-plot</code>. Defaults to 20 Hz. You
can override this by using a keyword parameter when you call <code>spec-plot</code> or <code>spec-print</code>,
or for
convenience, you can change this variable which will affect all future calls to
<code>spec-plot</code> where the keyword parameter is omitted.<br><br>
<dt><code>*spec-plot-bw*</code><a name="index696"></a></dt>
<dd>The default highest frequency to
include in <code>spec-plot</code>. Defaults to 8000 Hz. You
can override this by using a keyword parameter when you call <code>spec-plot</code> or <code>spec-print</code>, or for
convenience, you can change this variable which will affect all future calls to
<code>spec-plot</code> where the keyword parameter is omitted.<br><br>
<dt><code>*spec-plot-db*</code><a name="index697"></a></dt>
<dd>The default output from
<code>spec-plot</code> displays magnitude on a linear scale, but there is an option to
display on a dB scale. You can change the default behavior by setting this variable to
<code>t</code> (true), or you can override the default in any call to 
<code>spec-plot</code> using a keyword parameter.<br><br>
<dt><code>s-print-tree(<a name="index698"></a><a name="index699"></a><i>sound</i>)</code> [SAL]<br>

<code>(s-print-tree <i>sound</i>)</code> [LISP]</dt>
<dd>Prints an ascii
representation of the internal data structures representing a sound.  This
is useful for debugging<a name="index700"></a> Nyquist.  Identical 
to <code>snd-print-tree</code>.
</dd></dl><a name = "101"><h3>Low-level Functions</h3></a>
<p>Nyquist includes many low-level functions that are used to implement the functions and behaviors described in previous sections. For completeness, these functions are described here.  Remember that
these are low-level functions that are not intended for normal use.  Unless
you are trying to understand the inner workings of Nyquist, you can skip this section.</p>
<a name = "102"><h4>Creating Sounds</h4></a>
<p>The basic operations that create sounds are described here.  
<dl>
<dt>
<code>snd-const(<a name="index701"></a><i>value</i>, <i>t0</i>, <i>srate</i>,
<i>duration</i>)</code> [SAL]<br>

<code>(snd-const <i>value</i> <i>t0</i> <i>srate</i> <i>duration</i>)</code> [LISP]</dt>
<dd>Returns a sound with constant <i>value</i>, starting at <i>t0</i>
with the given <i>duration</i>, at the sample rate <i>srate</i>.  You might want
to use <code>pwl</code> (see Section <a href = "#92">Piece-wise Approximations</a>) instead.</p>
<dt><code>snd-read(<a name="index702"></a><i>filename</i>, <i>offset</i>, <i>t0</i>, <i>format</i>,
<i>channels</i>, <i>mode</i>, <i>bits</i>, <i>swap</i>, <i>sr</i>,
<i>dur</i>)</code> [SAL]<br>

<code>(snd-read <i>filename</i> <i>offset</i> <i>t0</i> <i>format</i> <i>channels</i> <i>mode</i> <i>bits</i> <i>swap</i> <i>sr</i> <i>dur</i>)</code> [LISP]</dt>
<dd>Loads a sound from a file with name <i>filename</i>.  Files are
assumed to consist of a header followed by frames consisting of one sample
from each channel.  The <i>format</i> specifies the type of header, but this
information is currently ignored.  Nyquist looks for a number of header
formats and automatically figures out which format to read.  If a header can
be identified, the header is first read from the file.  Then, the file
pointer is advanced by the indicated
<i>offset</i> (in seconds).  If there is an unrecognized header, Nyquist will
assume the file has no header.  If the header size is a multiple of the
frame size (bytes/sample * number-of-channels), you can use <i>offset</i> to
skip over the header.  To skip N bytes, use an <i>offset</i> of:

<p></p>
<pre>
(/ (float N) <i>sr</i> (/ <i>bits</i> 8) <i>channels</i>)
</pre>

<p>
If the header is not a multiple of the frame size, either write a header or
contact the author (dannenberg@cs.cmu.edu) for assistance.  Nyquist will
round <i>offset</i> to the nearest sample.  The resulting sound will start at
time <i>t0</i>.  If a header is found, the file will be interpreted according
to the header information.  If no header was found, <i>channels</i> tells how
many channels there are, the samples are encoded according to <i>mode</i>, the
sample length is <i>bits</i>, and <i>sr</i> is the sample rate.  The <i>swap</i> flag is 0 or 1, where 1 means to swap sample bytes. The duration to
be read (in seconds) is given by <i>dur</i>.  If <i>dur</i> is longer than the
data in the file, then a shorter duration will be returned.  If the file
contains one channel, a sound is returned.  If the file contains 2 or more
channels, an array of sounds is returned.  <b><i>Note:</i></b> you probably want to
call <code>s-read</code> (see Section <a href = "#100">Sound File Input and Output</a>) instead of
<code>snd-read</code>.  Also, see Section <a href = "#100">Sound File Input and Output</a> for information on the
<i>mode</i> and <i>format</i> parameters.</p>
<dt><code>snd-save(<a name="index703"></a><i>expression</i>, <i>maxlen</i>,
<i>filename</i>, <i>format</i>, <i>mode</i>, <i>bits</i>, <i>swap</i>, <i>play</i>, <i>progress</i>)</code> [SAL]<br>

<code>(snd-save <i>expression</i> <i>maxlen</i> <i>filename</i> <i>format</i> <i>mode</i> <i>bits</i> <i>swap</i> <i>play</i> <i>progress</i>)</code> [LISP]</dt>
<dd>Evaluates 
the <i>expression</i>, which should result in a sound
or an array of sounds, and writes the result to the given <i>filename</i>.  If
a multichannel sound (array) is written, the channels are up-sampled to the
highest rate in any channel so that all channels have the same sample rate.
The maximum number of samples written per channel is given by <i>maxlen</i>,
which allows writing the initial part of a very long or infinite sound. A
header is written according to <i>format</i>, samples are encoded according to
<i>mode</i>, using <i>bits</i> bits/sample, and swapping bytes if <i>swap</i> is 1 (otherwise it should be 0).  
If <i>play</i> is not null, the audio is played in real time (to the extent possible) as it is computed.
Progress is indicated by printing the sample count after
writing each 10 seconds of frames.  If <i>progress</i> is specified and greater
than 10,000, progress is printed at this specified frame count increment.
The peak value of the sound is returned. In addition,
the symbol <code>*RSLT*</code> is bound to a list containing the sample rate, 
number of channels, and duration (in that order) of the saved sound.
<b><i>Note:</i></b> you probably want to call
<code>s-save</code> (see Section <a href = "#100">Sound File Input and Output</a>) instead.  The <i>format</i> and
<i>mode</i> parameters are described in Section <a href = "#100">Sound File Input and Output</a>.<br><br>
<dt><code>snd-overwrite(<a name="index704"></a><i>expression</i>, <i>maxlen</i>, <i>filename</i>, <i>offset</i>, <i>progress</i>)</code> [SAL]<br>

<code>(snd-overwrite <i>expression</i> <i>maxlen</i> <i>filename</i> <i>offset</i> <i>progress</i>)</code> [LISP]</dt>
<dd>Evaluates 
the <i>expression</i>, which should result in a sound
or an array of sounds, and replaces samples in the given <i>filename</i>, 
writing the first frame at a time of <i>offset</i> seconds. The <i>offset</i> must 
be less than or equal to the duration of the existing file.
Progress is indicated by printing the sample count after
writing each 10 seconds of frames.  If <i>progress</i> is specified and greater
than 10,000, progress is printed at this specified frame count increment.
The duration of the written samples may be greater than that of the file,
in which case the file is extended as necessary. The
sample rate(s) of <i>expression</i> and the number of channels 
must match those of the file. 
Up to a maximum of <i>maxlen</i>
samples will be written per channel. The peak value of the sound is returned.
In addition, the symbol <code>*RSLT*</code> is bound to a list containing the
duration of the written sound (which may not be the duration of the sound
file).
Use <code>s-add-to</code> (in Section <a href = "#100">Sound File Input and Output</a> or
<code>s-overwrite</code> (in Section <a href = "#100">Sound File Input and Output</a> instead of this function.<br><br>
<dt><code>snd-coterm(<a name="index705"></a><a name="index706"></a><a name="index707"></a><i>s1</i>, <i>s2</i>)</code> [SAL]<br>

<code>(snd-coterm <i>s1</i> <i>s2</i>)</code> [LISP]</dt>
<dd>Returns a copy of <i>s1</i>, except the start
time is the maximum of the start times of <i>s1</i> and <i>s2</i>, and the
termination time is the minimum of <i>s1</i> and <i>s2</i>. (After the termination
time, the sound is zero as if <i>s1</i> is gated by <i>s2</i>.)  Some rationale
follows: In order to implement <code>s-add-to</code>, we need to read from the
target sound file, add the sounds to a new sound, and overwrite the result
back into the file.  We only want to write as many samples into the file as
there are samples in the new sound. However, if we are adding
in samples read from
the file, the result of a <code>snd-add</code> in Nyquist will have the maximum
duration of either sound.  Therefore, we may read to the end of the file.
What we need is a way to truncate the read, but we cannot easily do that,
because we do not know in advance how long the new sound will be. The
solution is to use <code>snd-coterm</code>, which will allow us to truncate the
sound that is read from the file (<i>s1</i>) according to the duration of the
new sound (<i>s2</i>).  When this truncated sound is added to the new sound,
the result will have only the duration of the new sound, and this can be
used to overwrite the file. This function is used in the implementation of
<code>s-add-to</code>, which is defined in <code>runtime/fileio.lsp</code>.<br><br>
<dt><code>(snd-from-array <span style="font-style:normal">...</span>)</code> [SAL]<br>

<code>(snd-from-array <span style="font-style:normal">...</span>)</code> [LISP]</dt>
<dd>See <a href = "#86">Accessing and Creating Sound</a>.<br><br>
<dt><code>snd-white(<a name="index708"></a><i>t0</i>, <i>sr</i>, <i>d</i>)</code> [SAL]<br>

<code>(snd-white <i>t0</i> <i>sr</i> <i>d</i>)</code> [LISP]</dt>
<dd>Generate white noise, starting at
<i>t0</i>, with sample rate <i>sr</i>, and duration <i>d</i>.  You probably want to
use <code>noise</code> (see Section <a href = "#97">More Behaviors</a>).<br><br>
<dt><code>snd-zero(<a name="index709"></a><i>t0</i>, <i>srate</i>)</code> [SAL]<br>

<code>(snd-zero <i>t0</i> <i>srate</i>)</code> [LISP]</dt>
<dd>Creates a sound that is
zero everywhere, starts at <i>t0</i>, and has sample rate <i>srate</i>.  The
logical stop time is immediate, i.e. also at <i>t0</i>.  You probably want
to use <code>pwl</code> (see Section <a href = "#92">Piece-wise Approximations</a>) instead.
</dd></dl><a name = "103"><h4>Signal Operations</h4></a>
<p>This next set of functions take sounds as arguments, operate on them, and
return a sound.</p>
<dl>
<dt>
<code>snd-abs(<a name="index710"></a><a name="index711"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-abs <i>sound</i>)</code> [LISP]</dt>
<dd>Computes a new 
sound where each sample is the absolute value of the corresponding sample in
<i>sound</i>. You should probably use <code>s-abs</code> instead. (See Section <a href = "#97">More Behaviors</a>.)<br><br>
<dt><code>snd-sqrt(<a name="index712"></a><a name="index713"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-sqrt <i>sound</i>)</code> [LISP]</dt>
<dd>Computes a new 
sound where each sample is the square root of the corresponding sample in
<i>sound</i>. If a sample is negative, it is taken to be zero to avoid raising a floating point error. You should probably use <code>s-sqrt</code> instead. (See Section <a href = "#97">More Behaviors</a>.)<br><br>
<dt><code>snd-add(<a name="index714"></a><i>sound1</i>, <i>sound</i>)</code> [SAL]<br>

<code>(snd-add <i>sound1</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Adds two sounds.  The
resulting start time is the minimum of the two parameter start times, the
logical stop time is the maximum of the two parameter stop times, and the
sample rate is the maximum of the two parameter sample rates.  Use
<code>sim</code> or <code>sum</code> instead of <code>snd-add</code> (see Section <a href = "#99">Combination and Time Structure</a>).<br><br>
<dt><code>snd-offset(<a name="index715"></a><a name="index716"></a><a name="index717"></a><i>sound</i>, <i>offset</i>)</code> [SAL]<br>

<code>(snd-offset <i>sound</i> <i>offset</i>)</code> [LISP]</dt>
<dd>Add an offset to a sound. The 
resulting start time, logical stop time, stop time, and sample rate are 
those of <i>sound</i>. Use <code>sum</code> instead (see Section <a href = "#99">Combination and Time Structure</a>).<br><br>
<dt><code>snd-avg(<a name="index718"></a><a name="index719"></a><a name="index720"></a><a name="index721"></a><i>sound</i>, <i>blocksize</i>, <i>stepsize</i>, <i>operation</i>)</code> [SAL]<br>

<code>(snd-avg <i>sound</i> <i>blocksize</i> <i>stepsize</i> <i>operation</i>)</code> [LISP]</dt>
<dd>Use <code>s-avg</code> instead (see Section <a href = "#97">More Behaviors</a>). The <code>s-avg</code> function extends <code>snd-avg</code> to multichannel input sounds.<br><br>
<dt><code>snd-clip(<a name="index722"></a><a name="index723"></a><i>sound</i>, <i>peak</i>)</code> [SAL]<br>

<code>(snd-clip <i>sound</i> <i>peak</i>)</code> [LISP]</dt>
<dd>Hard limit <i>sound</i> 
to the given <i>peak</i>, a positive number. The samples of <i>sound</i> are constrained between an upper value
of <i>peak</i> and a lower value of -<i>peak</i>. Use <code>clip</code> instead (see Section <a href = "#97">More Behaviors</a>).<br><br>
<dt><code>snd-compose(<a name="index724"></a><a name="index725"></a><a name="index726"></a><i>f</i>, <i>g</i>)</code> [SAL]<br>

<code>(snd-compose <i>f</i> <i>g</i>)</code> [LISP]</dt>
<dd>Compose two signals, i.e.
compute <i>f</i>(<i>g</i>(<i>t</i>)), where <i>f</i> and <i>g</i> are sounds. This function
is used primarily to implement time warping, but it can be used in other
applications such as frequency modulation.  For each sample <i>x</i> in <i>g</i>,
<i>snd-compose</i> looks up the value of <i>f</i>(<i>x</i>) using linear
interpolation.  The resulting sample rate, start time, etc. are taken from
<i>g</i>.  The sound <i>f</i> is used in effect as a lookup table, but it is
assumed that <i>g</i> is non-decreasing, so that <i>f</i> is accessed in time
order.  This allows samples of <i>f</i> to be computed and discarded
incrementally.  If in fact <i>g</i> decreases, the current sample of <i>g</i>  is
replaced by the previous one, forcing <i>g</i> into compliance with the
non-decreasing restriction.  See also <code>sref</code>, <code>shape</code>, and
<code>snd-resample</code>.  

For an extended example that uses <code>snd-compose</code> for variable pitch shifting,
see <code>nyquist/demos/pitch_change.htm</code>.<a name="index727"></a><a name="index728"></a>
<a name="index729"></a><a name="index730"></a><br><br>
<dt>
<code>snd-tapv(<a name="index731"></a><a name="index732"></a><a name="index733"></a><a name="index734"></a><a name="index735"></a><i>sound</i>, <i>offset</i>, <i>vardelay</i>, <i>maxdelay</i>)</code> [SAL]<br>

<code>(snd-tapv <i>sound</i> <i>offset</i> <i>vardelay</i> <i>maxdelay</i>)</code> [LISP]</dt>
<dd>A 
variable delay: <i>sound</i> is delayed by the sum of <i>offset</i> (a <code>FIXNUM</code> or <code>FLONUM</code>) 
and <i>vardelay</i> (a <code>SOUND</code>).  The specified delay is adjusted to lie in the range 
of zero to <i>maxdelay</i> seconds to yield the actual delay, and the delay is 
implemented using linear interpolation. This function was designed specifically 
for use in a chorus effect: the <i>offset</i> is set to half of <i>maxdelay</i>, and 
the <i>vardelay</i> input is a slow sinusoid. The maximum delay is limited to 
<i>maxdelay</i>, which determines the length of a fixed-sized buffer. The function
<code>tapv</code> is equivalent and preferred (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-tapf(<a name="index736"></a><a name="index737"></a><a name="index738"></a><i>sound</i>, <i>offset</i>, <i>vardelay</i>, <i>maxdelay</i>)</code> [SAL]<br>

<code>(snd-tapf <i>sound</i> <i>offset</i> <i>vardelay</i> <i>maxdelay</i>)</code> [LISP]</dt>
<dd>A
variable delay like <code>snd-tapv</code> except there is no linear interpolation. By 
eliminating interpolation, the output is an exact copy of the input with no filtering
or distortion. On the other hand, delays jump by samples causing samples to double or
skip even when the delay is changed smoothly.<br><br>
<dt><code>snd-copy(<a name="index739"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-copy <i>sound</i>)</code> [LISP]</dt>
<dd>Makes a copy of <i>sound</i>.
Since operators always make (logical) copies of their sound parameters, this
function should never be needed.  This function is here for debugging<a name="index740"></a>.<br><br>
<dt><code>snd-down(<a name="index741"></a><i>srate</i>, <i>sound</i>)</code> [SAL]<br>

<code>(snd-down <i>srate</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Linear interpolation
of samples down to the given sample rate <i>srate</i>, which must be lower than
the sample rate of <i>sound</i>.  Do not call this function.  Nyquist performs
sample-rate conversion automatically as needed.  If you want to force a
conversion, call <code>force-srate</code> (see Section <a href = "#90">Sound Synthesis</a>).<br><br>
<dt><code>snd-exp(<a name="index742"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-exp <i>sound</i>)</code> [LISP]</dt>
<dd>Compute the exponential of each sample of <i>sound</i>. Use <code>s-exp</code> instead (see Section <a href = "#97">More Behaviors</a>).<br><br>
<dt>
<code>snd-follow(<a name="index743"></a><a name="index744"></a><a name="index745"></a><i>sound</i>, <i>floor</i>, <i>risetime</i>, <i>falltime</i>, <i>lookahead</i>)</code> [SAL]<br>

<code>(snd-follow <i>sound</i> <i>floor</i> <i>risetime</i> <i>falltime</i> <i>lookahead</i>)</code> [LISP]</dt>
<dd>An envelope 
follower. The basic goal of this function is to generate a smooth signal 
that rides on the peaks of the input signal. The usual objective is to 
produce an amplitude envelope given a low-sample rate (control rate) 
signal representing local RMS measurements. The first argument is the 
input signal. The <i>floor</i> is the minimum output value. The <i>risetime</i> is the time (in seconds) it takes for the output to rise (exponentially) from <i>floor</i> to unity (1.0) and the <i>falltime</i> is the time it takes for the output to fall (exponentially) from unity to <i>floor</i>. The algorithm looks ahead for peaks and will begin to increase the output signal according to <i>risetime</i> in anticipation of a peak. The amount of anticipation (in samples) is given by <i>lookahead</i>.  The algorithm is as follows: the output value is allowed to increase according to <i>risetime</i> or decrease according to <i>falltime</i>. If the next input sample is in this range, that sample is simply output as the next output sample.  If the next input sample is too large, the algorithm goes back in time as far as necessary to compute an envelope that rises according to <i>risetime</i> to meet the new value. The algorithm will only work backward as far as <i>lookahead</i>.  If that is not far enough, then there is a final forward pass computing a rising signal from the earliest output sample. In this case, the output signal will be at least momentarily less than the input signal and will continue to rise exponentially until it intersects the input signal. If the input signal falls faster than indicated by <i>falltime</i>, the output fall rate will be limited by <i>falltime</i>, and the fall in output will stop when the output reaches <i>floor</i>. This algorithm can make two passes througth the buffer on sharply rising inputs, so it is not particularly fast. With short buffers and low sample rates this should not matter. See <code>snd-avg</code> above for a function that can help to generate a low-sample-rate input for <code>snd-follow</code>. See <code>snd-chase</code> in Section <a href = "#104">Filters</a> for a related filter.<br><br>
<dt><code>snd-gate(<a name="index746"></a><a name="index747"></a><a name="index748"></a><i>sound</i>, <i>lookahead</i>, <i>risetime</i>, <i>falltime</i>, <i>floor</i>, <i>threshold</i>)</code> [SAL]<br>

<code>(snd-gate <i>sound</i> <i>lookahead</i> <i>risetime</i> <i>falltime</i> <i>floor</i> <i>threshold</i>)</code> [LISP]</dt>
<dd>This function generates an exponential
rise and decay intended for noise gate implementation. The decay
starts when the signal drops below threshold and stays there for
longer than lookahead. Decay continues until the value reaches floor,
at which point the decay stops and the output value is held
constant. Either during the decay or after the floor is reached, if
the signal goes above threshold, then the output value will rise to
unity (1.0) at the point the signal crosses the threshold. Again,
look-ahead is used, so the rise actually starts before the signal
crosses the threshold. The rise is a constant-rate exponential and set
so that a rise from <i>floor</i> to unity occurs in <i>risetime</i>.
Similarly, the fall is a constant-rate exponential such that a fall
from unity to <i>floor</i> takes <i>falltime</i>. The result is delayed by
<i>lookahead</i>, so the output is not actually synchronized with the
input. To compensate, you should drop the initial <i>lookahead</i> of
samples. Thus, <code>snd-gate</code> is not recommended for direct use. Use
<code>gate</code> instead (see Section <a href = "#87">Miscellaneous Functions</a>).<br><br>
<dt><code>snd-inverse(<a name="index749"></a><a name="index750"></a><i>signal</i>, <i>start</i>, <i>srate</i>)</code> [SAL]<br>

<code>(snd-inverse <i>signal</i> <i>start</i> <i>srate</i>)</code> [LISP]</dt>
<dd>Compute the function inverse of <i>signal</i>, that is, compute <i>g</i>(<i>t</i>) such that <i>signal</i>(<i>g</i>(<i>t</i>)) = <i>t</i>.  This function assumes that <i>signal</i> is non-decreasing, it uses linear interpolation, the resulting sample rate is <i>srate</i>, and the result is shifted to have a starting time of <i>start</i>.  If <i>signal</i> decreases, the true inverse may be undefined, so we define <code>snd-inverse</code> operationally as follows: for each output time point <i>t</i>, scan ahead in <i>signal</i> until the value of signal exceeds <i>t</i>.  Interpolate to find an exact time point <i>x</i> from <i>signal</i> and output <i>x</i> at time <i>t</i>.  This function is intended for internal system use in implementing time warps.<br><br>
<dt><code>snd-log(<a name="index751"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-log <i>sound</i>)</code> [LISP]</dt>
<dd>Compute the natural logorithm of each sample of <i>sound</i>. Use <code>s-log</code> instead (see Section <a href = "#97">More Behaviors</a>).<br><br>
<dt>
<code>peak(<a name="index752"></a><a name="index753"></a><i>expression</i>, <i>maxlen</i>)</code> [SAL]<br>

<code>(peak <i>expression</i> <i>maxlen</i>)</code> [LISP]</dt>
<dd>Compute 
the maximum absolute value of the amplitude of a sound.  The sound is
created by evaluating <i>expression</i> (as in <code>s-save</code>).  Only the
first <i>maxlen</i> samples are evaluated. The <i>expression</i> is
automatically quoted (<code>peak</code> is a macro), so do not quote this
parameter.  If <i>expression</i> is a variable, then the <i>global
binding</i> of that variable will be used.  Also, since the variable
retains a reference to the sound, the sound will be evaluated and left
in memory.  See Section <a href = "part6.html#46">Memory Space and Normalization</a> on <a href = "part6.html#46">Memory Space and Normalization</a> for examples.<br><br>
<dt>
<code>snd-max(<a name="index754"></a><a name="index755"></a><i>expression</i>, <i>maxlen</i>)</code> [SAL]<br>

<code>(snd-max <i>expression</i> <i>maxlen</i>)</code> [LISP]</dt>
<dd>Compute the maximum absolute value of the amplitude of a sound.  The sound is created by evaluating <i>expression</i> (as in <code>snd-save</code>), which is therefore normally quoted by the caller.  At most <i>maxlen</i> samples are computed.  The result is the maximum of the absolute values of the samples.  <b><i>Notes:</i></b> It is recommended to use <code>peak</code> (see above) instead.  If you want to find the maximum of a sound bound to a local variable and it is acceptable to save the samples in memory, then this is probably the function to call.  Otherwise, use <code>peak</code>.<br><br>
<dt><code>snd-maxv(<a name="index756"></a><a name="index757"></a><i>sound1</i>, <i>sound2</i>)</code> [SAL]<br>

<code>(snd-maxv <i>sound1</i> <i>sound2</i>)</code> [LISP]</dt>
<dd>Compute
the maximum of <i>sound1</i> and <i>sound2</i> on a sample-by-sample
basis. The resulting sound has its start time at the maximum of the
input start times and a logical stop at the minimum logical stop of
the inputs. The physical stop time is the minimum of the physical stop
times of the two sounds. <i>Note that this violates the &ldquo;normal&rdquo;
interpretation that sounds are zero outside their start and stop
times. For example, even if</i> sound1 <i>extends beyond</i> sound2 <i>and
is greater than zero, the result value in this extension will be zero
because it will be after the physical stop time, whereas if we simply
treated</i> sound2 <i>as zero in this region and took the maximum, we
would get a non-zero result.</i> Use <code>s-max</code> instead (see Section
<a href = "#97">More Behaviors</a>).<br><br>
<dt><code>snd-normalize(<a name="index758"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-normalize <i>sound</i>)</code> [LISP]</dt>
<dd>Internally, sounds
are stored with a scale factor that applies to all samples of the sound.
All operators that take sound arguments take this scale factor into account
(although it is not always necessary to perform an actual multiply per
sample), so you should never need to call this function.  This function
multiplies each sample of a sound by its scale factor, returning a sound
that represents the same signal, but whose scale factor is 1.0.  <br><br>
<dt><code>snd-oneshot(<a name="index759"></a><a name="index760"></a><a name="index761"></a><i>sound</i>, <i>threshold</i>, <i>ontime</i>)</code> [SAL]<br>

<code>(snd-oneshot <i>sound</i> <i>threshold</i> <i>ontime</i>)</code> [LISP]</dt>
<dd>Computes a new sound that is zero
except where <i>sound</i> exceeds threshold. From these points, the result is 
1.0 until <i>sound</i> remains below <i>threshold</i> for <i>ontime</i> (in seconds).
The result has the same sample rate, start time, logical stop time, and 
duration as <i>sound</i>.<br><br>
<dt><code>snd-prod(<a name="index762"></a><a name="index763"></a><a name="index764"></a><i>sound1</i>, <i>sound2</i>)</code> [SAL]<br>

<code>(snd-prod <i>sound1</i> <i>sound2</i>)</code> [LISP]</dt>
<dd>Computes the
product of <i>sound1</i> and <i>sound2</i>.  The resulting sound has its start
time at the maximum of the input start times and a logical stop at the minimum
logical stop of the inputs.  Do not use this function.  Use <code>mult</code> or
<code>prod</code> instead (see Section <a href = "#90">Sound Synthesis</a>).  Sample rate, start time, etc. are taken from <i>sound</i>.<br><br>
<dt><code>snd-pwl(<a name="index765"></a><a name="index766"></a><i>t0</i>, <i>sr</i>,
<i>lis</i>)</code> [SAL]<br>

<code>(snd-pwl <i>t0</i> <i>sr</i> <i>lis</i>)</code> [LISP]</dt>
<dd>Computes a piece-wise linear function according to the breakpoints
in <i>lis</i>.  The starting time is <i>t0</i>, and the sample rate is <i>sr</i>.
The breakpoints are passed in an XLISP list (of type <code>LVAL</code>) where the
list alternates sample numbers (<code>FIXNUM</code>s, computed in samples 
from the beginning of the pwl function) and values (the value of the pwl
function, given as a <code>FLONUM</code>).  There is an implicit starting
point of (0, 0).  The list must contain an odd number of points, the omitted 
last
value being implicitly zero (0).  The list is assumed to be well-formed.  Do
not call this function.  Use <code>pwl</code> instead (see Section <a href = "#92">Piece-wise Approximations</a>).<br><br>
<dt><code>snd-quantize(<a name="index767"></a><i>sound</i>, <i>steps</i>)</code> [SAL]<br>

<code>(snd-quantize <i>sound</i> <i>steps</i>)</code> [LISP]</dt>
<dd>Quantizes a sound. See Section
<a href = "#97">More Behaviors</a> for details.<br><br>
<dt><code>snd-recip(<a name="index768"></a><i>sound</i>)</code> [SAL]<br>

<code>(snd-recip <i>sound</i>)</code> [LISP]</dt>
<dd>Compute the reciprocal of each sample of <i>sound</i>. Use <code>recip</code> instead (see Section <a href = "#97">More Behaviors</a>).<br><br>
<dt><code>snd-resample(<a name="index769"></a><a name="index770"></a><i>f</i>,
<i>rate</i>)</code> [SAL]<br>

<code>(snd-resample <i>f</i> <i>rate</i>)</code> [LISP]</dt>
<dd>Resample sound <i>f</i> using high-quality interpolation, yielding
a new sound with the specified <i>rate</i>. The result is scaled by 0.95 because often,
in resampling, interpolated values exceed the original sample values, and this 
could lead to clipping.
The resulting start time, etc. are taken from
<i>f</i>. Use <code>resample</code> instead.<br><br>
<dt><code>snd-resamplev(<a name="index771"></a><a name="index772"></a><a name="index773"></a><i>f</i>, <i>rate</i>, <i>g</i>)</code> [SAL]<br>

<code>(snd-resamplev <i>f</i> <i>rate</i> <i>g</i>)</code> [LISP]</dt>
<dd>Compose two
signals, i.e.  compute <i>f</i>(<i>g</i>(<i>t</i>)), where <i>f</i> and <i>g</i> are
sounds. The result has sample rate given by <i>rate</i>.  At each time <i>t</i>
(according to the <i>rate</i>), <i>g</i> is linearly interpolated to yield an
increasing sequence of high-precision score-time values. <i>f</i> is then
interpolated at each value to yield a result sample. If in fact <i>g</i>
decreases, the current sample of <i>g</i>  is replaced by the previous one,
forcing <i>g</i> into compliance with the non-decreasing restriction. 
The result is scaled by 0.95 because often,
in resampling, interpolated values exceed the original sample values, and this 
could lead to clipping. Note that
if <i>g</i> has a high sample rate, this may introduce unwanted jitter into
sample times. See <code>sound-warp</code> for a detailed discussion. See
<code>snd-compose</code> for a fast, low-quality alternative to this function.
Normally, you should use <code>sound-warp</code> instead of this function.<br><br>
<dt><code>snd-scale(<a name="index774"></a><i>scale</i>, <i>sound</i>)</code> [SAL]<br>

<code>(snd-scale <i>scale</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Scales the amplitude of <i>sound</i> by the factor <i>scale</i>.  Use <code>scale</code> instead (see Section
<a href = "#90">Sound Synthesis</a>).<br><br>
<dt><code>snd-shape(<a name="index775"></a><i>signal</i>, <i>table</i>, <i>origin</i>)</code> [SAL]<br>

<code>(snd-shape <i>signal</i> <i>table</i> <i>origin</i>)</code> [LISP]</dt>
<dd>A waveshaping function.  This is the primitive upon which <code>shape</code> is based. The <code>snd-shape</code> function is like <code>shape</code> except that <i>signal</i> and <i>table</i> must be (single-channel) sounds.  Use <code>shape</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-up(<a name="index776"></a><i>srate</i>, <i>sound</i>)</code> [SAL]<br>

<code>(snd-up <i>srate</i> <i>sound</i>)</code> [LISP]</dt>
<dd>Increases sample rate by linear
interpolation.  The <i>sound</i> is the signal to be up-sampled, and <i>srate</i>
is the output sample rate.  Do not call this function.  Nyquist performs
sample-rate conversion automatically as needed.  If you want to force a
conversion, call <code>force-srate</code> (see Section <a href = "#90">Sound Synthesis</a>).<br><br>
<dt>
<code>snd-xform(<a name="index777"></a><i>sound</i>, <i>sr</i>, <i>time</i>, <i>start</i>,
<i>stop</i>, <i>scale</i>)</code> [SAL]<br>

<code>(snd-xform <i>sound</i> <i>sr</i> <i>time</i> <i>start</i> <i>stop</i> <i>scale</i>)</code> [LISP]</dt>
<dd>Makes a copy of <i>sound</i> and then alters it in
the following order:  (1) the start time (<code>snd-t0</code>) of the sound is shifted to 
<i>time</i>, (2) the sound is stretched as a result of setting the sample rate
to <i>sr</i> (the start time is unchanged by this), (3) the sound is clipped
 from <i>start</i> to <i>stop</i>, (4) if <i>start</i> is greater than <i>time</i>, the sound is shifted
shifted by <i>time</i> - <i>start</i>, so that the start time is <i>time</i>, (5) the
sound is scaled by <i>scale</i>.  An empty (zero) sound at <i>time</i> will be
returned if all samples are clipped.  Normally, you should accomplish all
this using transformations.  A transformation applied to a sound has no
effect, so use <code>cue</code> or <code>sound</code> to create a transformable sound (see Section
<a href = "#89">Using Previously Created Sounds</a>).<br><br>
<dt>
<code>snd-yin(<a name="index778"></a><i>sound</i>, <i>minstep</i>, <i>maxstep</i>, <i>rate</i>)</code> [SAL]<br>

<code>(snd-yin <i>sound</i> <i>minstep</i> <i>maxstep</i> <i>rate</i>)</code> [LISP]</dt>
<dd>Identical to
<code>yin</code>. See Section <a href = "#97">More Behaviors</a>.
</dd></dl><a name = "104"><h4>Filters</h4></a>
<p>These are also &ldquo;Signal Operators,&rdquo; the subject of the previous section, 
but there are so many filter functions, they are
documented in this special section.</p>

<p>Some filters allow time-varying filter parameters.  In these functions,
filter coefficients are calculated at the sample rate of the filter
parameter, and coefficients are not interpolated.</p>
<dl>
<dt>
<code>snd-alpass(<a name="index779"></a><i>sound</i>, <i>delay</i>, <i>feedback</i>)</code> [SAL]<br>

<code>(snd-alpass <i>sound</i> <i>delay</i> <i>feedback</i>)</code> [LISP]</dt>
<dd>An all-pass filter.  This produces a repeating echo effect without the resonances of <code>snd-delay</code>.  The <i>feedback</i> should be less than one to avoid exponential amplitude blowup.  Delay is rounded to the nearest sample.  You should use <code>alpass</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-alpasscv(<a name="index780"></a><i>sound</i>, <i>delay</i>,
<i>feedback</i>)</code> [SAL]<br>

<code>(snd-alpasscv <i>sound</i> <i>delay</i> <i>feedback</i>)</code> [LISP]</dt>
<dd>An all-pass filter with variable <i>feedback</i>.  
This is just like <i>snd-alpass</i> except <i>feedback</i> is a sound.
You should use <code>alpass</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-alpassvv(<a name="index781"></a><i>sound</i>, <i>delay</i>, <i>feedback</i>, <i>maxdelay</i>)</code> [SAL]<br>

<code>(snd-alpassvv <i>sound</i> <i>delay</i> <i>feedback</i> <i>maxdelay</i>)</code> [LISP]</dt>
<dd>An all-pass filter with variable <i>feedback</i> and <i>delay</i>. This is just like <i>snd-alpass</i> except <i>feedback</i> and <i>delay</i> are sounds, and there is an additional <code>FLONUM</code> parameter, <i>maxdelay</i>, that gives an upper bound on the value of <i>delay</i>. <b><i>Note:</i></b> <i>delay</i> must remain between zero and <i>maxdelay</i>. If not, results are undefined, and Nyquist may crash. You should use <code>alpass</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-areson(<a name="index782"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-areson <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>A notch filter modeled after the <code>areson</code>
unit generator in Csound.  The <code>snd-areson</code> filter is an exact
complement of <code>snd-reson</code> such that if both are applied to the
same signal with the same parameters, the sum of the results yeilds
the original signal.  Note that because of this complementary design,
the power is not normalized as in <code>snd-reson</code>.  See <code>snd-reson</code>
for details on <i>normalization</i>.  You should use <code>areson</code> instead (see
Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-aresoncv(<a name="index783"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-aresoncv <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-areson</code> except
the <i>bw</i> (bandwidth) parameter is a sound.  Filter coefficients are
updated at the sample rate of <i>bw</i>.  The &ldquo;<code>cv</code>&rdquo; suffix stands for Constant,
Variable, indicating that <i>hz</i> and <i>bw</i> are constant (a number) and
variable (a sound), respectively.  This naming convention is used throughout.
You should use <code>areson</code> instead (see
Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-aresonvc(<a name="index784"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-aresonvc <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-areson</code> except
the <i>hz</i> (center frequency) parameter is a sound.  Filter coefficients are
updated at the sample rate of <i>hz</i>.  
You should use <code>areson</code> instead (see
Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-aresonvv(<a name="index785"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-aresonvv <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-areson</code> except
both <i>hz</i> (center frequency) and <i>bw</i> (bandwidth) are sounds.  Filter
coefficients are updated at the next sample of either <i>hz</i> or <i>bw</i>.
You should use <code>areson</code> instead (see
Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-atone(<a name="index786"></a><i>sound</i>, <i>hz</i>)</code> [SAL]<br>

<code>(snd-atone <i>sound</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A high-pass filter 
modeled after the <code>atone</code> unit generator in Csound.  The <code>snd-atone</code> filter is an exact
complement of <code>snd-tone</code> such that if both are applied to the
same signal with the same parameters, the sum of the results yeilds
the original signal.  You should use <code>hp</code> instead (see
Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-atonev(<a name="index787"></a><i>sound</i>, <i>hz</i>)</code> [SAL]<br>

<code>(snd-atonev <i>sound</i> <i>hz</i>)</code> [LISP]</dt>
<dd>This is just like
<code>snd-atone</code> except that the <i>hz</i> cutoff frequency is a sound.  Filter
coefficients are updated at the sample rate of <i>hz</i>.  You should use
<code>hp</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-biquad(<a name="index788"></a><i>sound</i>, <i>b0</i>, <i>b1</i>, <i>b2</i>, <i>a1</i>, <i>a2</i>, <i>z1init</i>, <i>z2init</i>)</code> [SAL]<br>

<code>(snd-biquad <i>sound</i> <i>b0</i> <i>b1</i> <i>b2</i> <i>a1</i> <i>a2</i> <i>z1init</i> <i>z2init</i>)</code> [LISP]</dt>
<dd>A general second order IIR filter, where <i>a0</i> is assumed to be unity. For <i>a1</i> and <i>a2</i>, the sign convention is opposite to that of Matlab. All parameters except the input <i>sound</i> are of type <code>FLONUM</code>. You should probably use one of <code>lowpass2</code>, <code>highpass2</code>, <code>bandpass2</code>, <code>notch2</code>, <code>allpass2</code>, <code>eq-lowshelf</code>, <code>eq-highshelf</code>, <code>eq-band</code>, <code>lowpass4</code>, <code>lowpass6</code>, <code>lowpass8</code>, <code>highpass4</code>, <code>highpass6</code>, or <code>highpass8</code>, which are all based on <code>snd-biquad</code> and described in Section <a href = "#93">Filter Behaviors</a>. For completeness, you will also find <code>biquad</code> and <code>biquad-m</code> described in that section.<br><br>
<dt>
<code>snd-chase(<a name="index789"></a><i>sound</i>, <i>risetime</i>, <i>falltime</i>)</code> [SAL]<br>

<code>(snd-chase <i>sound</i> <i>risetime</i> <i>falltime</i>)</code> [LISP]</dt>
<dd>A slew rate limiter. The output &ldquo;chases&rdquo; the input at rates determined by <i>risetime</i> and <i>falltime</i>.  If the input changes too fast, the output will lag behind the input. This is a form of lowpass filter, but it was created to turn hard-switching square waves into smoother control signals that could be used for linear crossfades. If the input switches from 0 to 1, the output will linearly rise to 1 in <i>risetime</i> seconds. If the input switches from 1 to 0, the output will linearly fall to 0 in <i>falltime</i> seconds.  The generated slope is constant; the transition is linear; this is not an exponential rise or fall.  The <i>risetime</i> and <i>falltime</i> must be scalar constants; complain to the author if this is not adequate. The <code>snd-chase</code> function is safe for ordinary use. See <code>snd-follow</code> in Section <a href = "#103">Signal Operations</a> for a related function. <br><br>
<dt><code>snd-congen(<a name="index790"></a><i>gate</i>, <i>risetime</i>, <i>falltime</i>)</code> [SAL]<br>

<code>(snd-congen <i>gate</i> <i>risetime</i> <i>falltime</i>)</code> [LISP]</dt>
<dd>A simple &ldquo;contour generator&rdquo; based 
on analog synthesizers.  The <i>gate</i> is a sound that normally steps from 0.0 to 1.0 at the start of an envelop and goes from
1.0 back to 0.0 at the beginning of the release. At each sample, the output converges to the input exponentially.  If <i>gate</i> is greater than the output, e.g. the attack, then the output converges half-way to the output in <i>risetime</i>.  If the <i>gate</i> is less than the output, the half-time is <i>falltime</i>.  The sample rate, starting time, logical-stop-time, and terminate time are taken from  <i>gate</i>. You should use <code>congen</code> instead (see Section <a href = "#93">Filter Behaviors</a>.<br><br>
<dt><code>snd-convolve(<a name="index791"></a><i>sound</i>, <i>response</i>)</code> [SAL]<br>

<code>(snd-convolve <i>sound</i> <i>response</i>)</code> [LISP]</dt>
<dd>Convolves
<i>sound</i> by <i>response</i> using a fast convolution algorithm. The <i>sound</i>
can be any length, but the <i>response</i> is computed and stored in in memory. 
The required compuation time per sample and total space are proportional to
the length of <i>response</i>. Use <code>convolve</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-delay(<a name="index792"></a><i>sound</i>, <i>delay</i>, <i>feedback</i>)</code> [SAL]<br>

<code>(snd-delay <i>sound</i> <i>delay</i> <i>feedback</i>)</code> [LISP]</dt>
<dd>Feedback
delay.  The output, initially <i>sound</i>, is recursively delayed by <i>delay</i>, scaled by <i>feedback</i>, and added to itself, producing an repeating echo effect.  The <i>feedback</i> should be less than one to avoid exponential amplitude blowup.  Delay is rounded to the nearest sample.  You should use <code>feedback-delay</code> instead (see Section <a href = "#93">Filter Behaviors</a>)<br><br>
<dt><code>snd-delaycv(<a name="index793"></a><i>sound</i>, <i>delay</i>,
<i>feedback</i>)</code> [SAL]<br>

<code>(snd-delaycv <i>sound</i> <i>delay</i> <i>feedback</i>)</code> [LISP]</dt>
<dd>Feedback delay with variable <i>feedback</i>.  This is just like
<i>snd-delay</i> except <i>feedback</i> is a sound.  You should use
<code>feedback-delay</code> instead (see Section <a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-reson(<a name="index794"></a><i>sound</i>, <i>hz</i>, <i>bw</i>, <i>normalization</i>)</code> [SAL]<br>

<code>(snd-reson <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>A
second-order resonating (bandpass) filter with center frequency <i>hz</i> and
bandwidth <i>bw</i>, modeled after the <code>reson</code> unit generator in Csound.  
The <i>normalization</i> parameter must be an integer and (like in Csound)
specifies a scaling factor.  A value of 1 specifies a peak amplitude
response of 1.0; all frequencies other than <i>hz</i> are attenuated.  A
value of 2 specifies the overall RMS value of the amplitude response
is 1.0; thus filtered white noise would retain the same power.  A value of
zero specifies no scaling.  The result sample rate, start time, etc. are takend from <i>sound</i>.
You should use <code>reson</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-resoncv(<a name="index795"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-resoncv <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-reson</code> except
<i>bw</i> (bandwidth) is a sound.  Filter coefficients are updated at the
sample rate of <i>bw</i>.  You should use <code>reson</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-resonvc(<a name="index796"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-resonvc <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-reson</code> except
<i>hz</i> (center frequency) is a sound.  Filter coefficients are updated at the
sample rate of <i>hz</i>.  You should use <code>reson</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-resonvv(<a name="index797"></a><i>sound</i>, <i>hz</i>, <i>bw</i>,
<i>normalization</i>)</code> [SAL]<br>

<code>(snd-resonvv <i>sound</i> <i>hz</i> <i>bw</i> <i>normalization</i>)</code> [LISP]</dt>
<dd>This function is identical to <code>snd-reson</code> except
botth <i>hz</i> (center frequency) and <i>bw</i> (bandwidth) are sounds.  Filter
coefficients are updated at the next sample from either <i>hz</i> or <i>bw</i>.  You should use <code>reson</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-stkchorus(<a name="index798"></a><a name="index799"></a><a name="index800"></a><a name="index801"></a><i>sound</i>, <i>delay</i>, <i>depth</i>, <i>freq</i>, <i>mix</i>)</code> [SAL]<br>

<code>(snd-stkchorus <i>sound</i> <i>delay</i> <i>depth</i> <i>freq</i> <i>mix</i>)</code> [LISP]</dt>
<dd>A chorus implemented in STK. The parameter <i>delay</i> is a <code>FIXNUM</code> 
representing the median desired delay length in samples. A typical
value is 6000. The <code>FLONUM</code> parameters <i>depth</i> and <i>freq</i> set the modulation
depth (from 0 to 1) and modulation frequency (in Hz), <i>mix</i> sets the mixture
of input sound and chorused sound, where a value of 0.0 means input sound 
only (dry) and a value of 1.0 means chorused sound only (wet). 
You should use <code>stkchorus</code> instead
(see Section <a href = "#94">Effects</a>).<br><br>
<dt><code>snd-stkpitshift(<a name="index802"></a><a name="index803"></a><a name="index804"></a><a name="index805"></a><i>sound</i>, <i>shift</i>, <i>mix</i>)</code> [SAL]<br>

<code>(snd-stkpitshift <i>sound</i> <i>shift</i> <i>mix</i>)</code> [LISP]</dt>
<dd>A 
pitch shifter implemented in STK. The <i>sound</i> is shifted in pitch by
<i>shift</i>, a <code>FLONUM</code> representing the shift factor. A value of 1.0 means
 no shift.  The parameter <i>mix</i> sets the mixture of input and shifted sounds.
A value of 0.0 means input only (dry) and a value of 1.0 means shifted 
sound only (wet). You should use <code>pitshift</code> instead
(see Section <a href = "#94">Effects</a>).<br><br>
<dt><code>snd-stkrev(<a name="index806"></a><a name="index807"></a><a name="index808"></a><a name="index809"></a><i>rev-type</i>, <i>sound</i>, <i>decay</i>, <i>mix</i>)</code> [SAL]<br>

<code>(snd-stkrev <i>rev-type</i> <i>sound</i> <i>decay</i> <i>mix</i>)</code> [LISP]</dt>
<dd>A reverb implemented in STK. The parameter rev-type is a 
<code>FIXNUM</code> ranging from zero to 
two and selects the type of reverb. Zero selects NRev type, one selects JCRev, 
and two selects PRCRev. The input <i>sound</i> is processed by the reverb with
a <i>decay</i> time in seconds (a <code>FLONUM</code>). The <i>mix</i>, a <code>FLONUM</code>, 
sets the 
mixture of dry input and reverb output. A value of 0.0 means input only (dry)
and a value of 1.0 means reverb only (wet). The sample rate 
is that of <i>sound</i>. You
should use <code>nrev</code>, <code>jcrev</code> or <code>prcrev</code> instead (see 
Section <a href = "#94">Effects</a>).<br><br>
<dt><code>snd-tone(<a name="index810"></a><a name="index811"></a><i>sound</i>, <i>hz</i>)</code> [SAL]<br>

<code>(snd-tone <i>sound</i> <i>hz</i>)</code> [LISP]</dt>
<dd>A
first-order recursive low-pass filter, based on the <i>tone</i> unit generator
of Csound.  The <i>hz</i> parameter is the cutoff frequency, the response
curve's half-power point.  The result sample rate, start time, etc. are takend from <i>sound</i>.
You should use <code>lp</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).<br><br>
<dt><code>snd-tonev(<a name="index812"></a><i>sound</i>, <i>hz</i>)</code> [SAL]<br>

<code>(snd-tonev <i>sound</i> <i>hz</i>)</code> [LISP]</dt>
<dd>This function is
identical to <code>snd-tone</code> except <i>hz</i> (cutoff frequency) is a sound.
The filter coefficients are updated at the sample rate of <i>hz</i>.  You
should use <code>lp</code> instead (see Section
<a href = "#93">Filter Behaviors</a>).
</dd></dl><a name = "105"><h4>Table-Lookup Oscillator Functions</h4></a>
<p>These functions all use a sound to describe one period of a periodic
waveform.  In the current implementation, the sound samples are copied to an
array (the waveform table) when the function is called.  To make a
table-lookup oscillator generate a specific pitch, we need to have several
pieces  of information:
<ul>
<li>
A waveform to put into the table.  This comes from the <i>sound</i> parameter.</li>
<li>The length (in samples) of the waveform.  This is obtained by reading
samples (starting at the sound's start time, not necessarily at time zero)
until the physical stop time of the sound.  (If you read the waveform from a
file or generate it with functions like <code>sim</code> and <code>sine</code>, then the
physical and logical stop times will be the same and will correspond to the
duration you specified, rounded to the nearest sample.)  </li>
<li>The intrinsic sample rate of the waveform.  This sample rate is simply the
sample rate property of <i>sound</i>.</li>
<li>The pitch of the waveform.  This is supplied by the <i>step</i> parameter and
indicates the pitch (in steps) of <i>sound</i>.  You might expect that the
pitch would be related to the period (length) of <i>sound</i>, but there is the
interesting case that synthesis based on sampling often loops over multiple
periods.  This means that the fundamental frequency of a generated tone may
be some multiple of the looping rate.  In Nyquist, you always specify the
perceived pitch of the looped <i>sound</i> if the sound is played at the
<i>sound</i>'s own sample rate.</li>
<li>The desired pitch.  This is specified by the <i>hz</i> parameter
in Hertz (cycles per second) in these low-level functions.  Note that this
is not necessarily the &ldquo;loop&rdquo; rate at which the table is scanned.
Instead, Nyquist figures what sample rate conversion would be necessary to
&ldquo;transpose&rdquo; from the <i>step</i> which specifies the original pitch of
<i>sound</i> to <i>hz</i>, which gives the desired pitch.  The mixed use of steps
and Hertz came about because it seemed that sample tables would be tagged
with steps (&ldquo;I sampled a middle-C&rdquo;), whereas frequency deviation in the
<code>fmosc</code> function is linear, thus calling for a specification in Hertz.</li>
<li>The desired sample rate.  This is given by the <i>sr</i> parameter in Hertz.
</li></ul></p>

<p>Other parameters common to all of these oscillator functions are:
<ul>
<li>
<i>t0</i>, the starting time, and</li>
<li><i>phase</i>, the starting phase in degrees.  Note that if the <i>step</i>
parameter indicates that the table holds more than one fundamental period, then a starting phase of 360 will be different than a starting phase of 0.
</li></ul></p>
<dl>
<dt>
<code>snd-amosc(<a name="index813"></a><i>sound</i>, <i>step</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>,
<i>am</i>, <i>phase</i>)</code> [SAL]<br>

<code>(snd-amosc <i>sound</i> <i>step</i> <i>sr</i> <i>hz</i> <i>t0</i> <i>am</i> <i>phase</i>)</code> [LISP]</dt>
<dd>An oscillator with amplitude modulation.  The sound
<i>am</i> specifies the amplitude and the logical stop time.  The physical stop
time is also that of <i>am</i>.  You should use <code>amosc</code> instead (see
Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-fmosc(<a name="index814"></a><i>s</i>, <i>step</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>, <i>fm</i>,
<i>phase</i>)</code> [SAL]<br>

<code>(snd-fmosc <i>s</i> <i>step</i> <i>sr</i> <i>hz</i> <i>t0</i> <i>fm</i> <i>phase</i>)</code> [LISP]</dt>
<dd>A Frequency Modulation oscillator.  The sound <i>fm</i> specifies
frequency deviation (in Hertz) from <i>hz</i>.  You should use <code>fmosc</code>
instead (see Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-fmfb(<a name="index815"></a><i>t0</i>, <i>hz</i>, <i>sr</i>, <i>index</i>, <i>dur</i>)</code> [SAL]<br>

<code>(snd-fmfb <i>t0</i> <i>hz</i> <i>sr</i> <i>index</i> <i>dur</i>)</code> [LISP]</dt>
<dd>A Feedback FM oscillator. The resulting sound starts
at <i>t0</i>, has a fundamental frequency of <i>hz</i>, a sample rate of <i>sr</i>,
and a duration of <i>dur</i> seconds. The <i>index</i> is a <code>FLONUM</code> that
specifies the amount of feedback. You should use <code>fmfb</code> instead (see
Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-fmfbv(<a name="index816"></a><i>t0</i>, <i>hz</i>, <i>sr</i>, <i>index</i>)</code><br>

<code>(snd-fmfv <i>t0</i> <i>hz</i> <i>sr</i> <i>index</i>)</code> [LISP]</dt>
<dd>A
 Feedback FM oscillator. The resulting sound starts
at <i>t0</i>, has a fundamental frequency of <i>hz</i>, and
a sample rate of <i>sr</i>. The <i>index</i> is a <code>SOUND</code> that
specifies the amount of feedback and determines the duration. 
You should use <code>fmfb</code> instead (see Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-buzz(<a name="index817"></a><i>n</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>, <i>fm</i>)</code> [SAL]<br>

<code>(snd-buzz <i>n</i> <i>sr</i> <i>hz</i> <i>t0</i> <i>fm</i>)</code> [LISP]</dt>
<dd>A
buzz oscillator, which generates <i>n</i> harmonics of equal amplitude.
The <i>fm</i> specifies
frequency deviation (in Hertz) from <i>hz</i>.  You should use <code>buzz</code>
instead (see Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-pluck(<a name="index818"></a><i>sr</i>, <i>hz</i>, <i>t0</i>, <i>d</i>,
<i>final-amp</i>)</code> [SAL]<br>

<code>(snd-pluck <i>sr</i> <i>hz</i> <i>t0</i> <i>d</i> <i>final-amp</i>)</code> [LISP]</dt>
<dd>A Karplus-Strong plucked string oscillator with sample rate
<i>sr</i>, fundamental frequency <i>hz</i>, starting time <i>t0</i>, duration <i>d</i>,
initial amplitude approximately 1.0 (not exact because the string is
initialized with random values) and final amplitude approximately 
<i>final-amp</i>. You should use <code>pluck</code> instead (see Section
<a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-osc(<a name="index819"></a><i>s</i>, <i>step</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>, <i>d</i>, <i>phase</i>)</code> [SAL]<br>

<code>(snd-osc <i>s</i> <i>step</i> <i>sr</i> <i>hz</i> <i>t0</i> <i>d</i> <i>phase</i>)</code> [LISP]</dt>
<dd>A simple table lookup oscillator with fixed frequency.  The duration
is <i>d</i> seconds.  You should use <code>osc</code> instead (see Section
<a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-partial(<a name="index820"></a><i>sr</i>, <i>hz</i>, <i>t0</i>, <i>env</i>)</code> [SAL]<br>

<code>(snd-partial <i>sr</i> <i>hz</i> <i>t0</i> <i>env</i>)</code> [LISP]</dt>
<dd>This is a
special case of <code>snd-amosc</code> that generates a sinusoid starting at phase
0 degrees.  The <i>env</i> parameter gives the envelope or any other amplitude
modulation.  You should use <code>partial</code> instead (see Section
<a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-sine(<a name="index821"></a><i>t0</i>, <i>hz</i>, <i>sr</i>, <i>d</i>)</code> [SAL]<br>

<code>(snd-sine <i>t0</i> <i>hz</i> <i>sr</i> <i>d</i>)</code> [LISP]</dt>
<dd>This is a
special case of <code>snd-osc</code> that always generates a sinusoid with initial
phase of 0 degrees.  You should use <code>sine</code> instead (see Section
<a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-sampler(<a name="index822"></a><i>s</i>, <i>step</i>,
<i>start</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>, <i>fm</i>, <i>npoints</i>)</code> [SAL]<br>

<code>(snd-sampler <i>s</i> <i>step</i> <i>start</i> <i>sr</i> <i>hz</i>
<i>t0</i> <i>fm</i> <i>npoints</i>)</code> [LISP]</dt>
<dd>Returns a sound constructed
by reading a sample from beginning to end and then splicing on copies
of the same sound from a loop point to the end.  
The sound <i>s</i> is the source sound to be looped, and <i>step</i> (a
FLONUM) is the nominal fundamental frequency (in steps, not Hz) of
<i>s</i>. The <i>start</i> (a FLONUM) is the time in seconds at which to
start the loop, <i>sr</i> (a FLONUM) is the desired sample rate of the
output, <i>hz</i> is the nominal fundamental frequency of the output,
<i>t0</i> (a FLONUM) is the starting time of the output, and <i>fm</i> (a
SOUND) is frequency modulation that is added to <i>hz</i> to determine
the output fundamental frequency. The parameter <i>npoints</i> (a FIXNUM)
specifies how many points should be used for sample
interpolation.  Currently this parameter defaults to 2 and only 2-point
(linear) interpolation is implemented.  It is an error to modulate
such that the frequency is negative. Note also that the loop point may
be fractional. This function implements a typical sampling synthesis
algorithm, looping and resampling the input according to the ratio
between the desired fundamental frequency (which is the sum of <i>hz</i>
and <i>fm</i>) and the nominal fundamental of the looped sound (which is
assumed to be given by <i>step</i>). You should use <code>sampler</code>
instead (see Section <a href = "#91">Oscillators</a>).<br><br>
<dt><code>snd-siosc(<a name="index823"></a><i>tables</i>, <i>sr</i>, <i>hz</i>, <i>t0</i>,
<i>fm</i>)</code> [SAL]<br>

<code>(snd-siosc <i>tables</i> <i>sr</i> <i>hz</i> <i>t0</i> <i>fm</i>)</code> [LISP]</dt>
<dd>A Spectral Interpolation Oscillator with frequency modulation. The
<i>tables</i> is a list of sounds and sample counts as follows: (<i>table0</i>
<i>count1</i> <i>table1</i> ... <i>countN</i> <i>tableN</i>). The initial waveform is given by <i>table0</i>, which is interpolated linearly to <i>table1</i> over the first
<i>count1</i> samples. From <i>count1</i> to <i>count2</i> samples, the waveform is
interpolated from <i>table1</i> to <i>table2</i>, and so on.  If more than
<i>countN</i> samples are generated, <i>tableN</i> is used for the remainder of
the sound. The duration and logical stop time  of the sound is taken from
<i>fm</i>, which specified frequency modulation (deviation) in Hertz. You
should use <code>siosc</code> instead (see Section <a href = "#91">Oscillators</a>).
</dd></dl><a name = "106"><h4>Phase Vocoder Functions</h4></a><dl>
<dt>
<code>snd-phasevocoder(<a name="index824"></a><a name="index825"></a><i>s</i>, 
<i>map</i>, <i>fftsize</i>, <i>hopsize</i> <i>mode</i>)</code> [SAL]<br>

code{(snd-phasevocoder <i>s</i> <i>map</i> <i>fftsize</i>
<i>hopsize</i> <i>mode</i>) [LISP]}</dt>
<dd>Phase vocoder: Identical
to <code>phasevocoder</code> 
except that <i>fftsize</i>, <i>hopsize</i> and <i>mode</i> are not optional.
Specify -1 to get
the default values for <i>fftsize</i> and <i>hopsize</i>. Specify 0 for the
default value of <i>mode</i>. You should use <code>phasevocoder</code> instead 
(see Section <a href = "#96">Phase Vocoder</a>).
</dd></dl><a name = "107"><h4>Physical Model Functions</h4></a>
<p>These functions perform some sort of physically-based modeling synthesis.
<dl>
<dt>
<code>snd-bandedwg(<a name="index826"></a><a name="index827"></a><i>freq</i>, <i>bowpress-env</i>, <i>preset</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-bandedwg <i>freq</i> <i>bowpress-env</i> <i>preset</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A Banded Wave Guide 
Percussion instrument implemented in STK. The parameter <i>freq</i> is a 
<code>FLONUM</code> in Hz, <i>bowpress-env</i> is 
a <code>SOUND</code> that ranges from zero to one, <i>preset</i> is a <code>FIXNUM</code>, 
and <i>sr</i> is the desired sample rate in Hz. Currently, there are four 
presets: uniform-bar (0), tuned-bar (1), glass-harmonica (2), and 
tibetan-bowl (3). You should use <code>wg-uniform-bar</code>, <code>wg-tuned-bar</code>,
<code>wg-glass-harm</code>, or <code>wg-tibetan-bowl</code> instead (see Section 
<a href = "#95">Physical Models</a>).</p>
<dt><code>snd-bowed(<a name="index828"></a><a name="index829"></a><i>freq</i>,
<i>bowpress-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-bowed <i>freq</i> <i>bowpress-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A bowed string instrument implemented in
STK. The freq is a <code>FLONUM</code> in Hertz, bowpress-env is a
<code>SOUND</code> that ranges from z
ero to one, and sr is the desired sample rate (a <code>FLONUM</code>). 
You should use bowed instead  (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-bowed-freq(<a name="index830"></a><a name="index831"></a><i>freq</i>, <i>bowpress-env</i>, <i>freq-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-bowed-freq <i>freq</i> <i>bowpress-env</i> <i>freq-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A bowed model just like <code>snd-bowed</code> but with 
an additional parameter for continuous frequency control. You should use 
<code>bowed-freq</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-clarinet(<a name="index832"></a><a name="index833"></a><i>freq</i>, <i>breath-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-clarinet <i>freq</i> <i>breath-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A clarinet
model implemented in STK. The <i>freq</i> is a <code>FLONUM</code> in Hertz,
<i>breath-env</i> is
a <code>SOUND</code> that ranges from zero to one, and <i>sr</i> is the
 desired sample
rate (a <code>FLONUM</code>). You should use <code>clarinet</code> instead
 (see Section 
<a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-clarinet-freq(<a name="index834"></a><a name="index835"></a><i>freq</i>, <i>breath-env</i>, <i>freq-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-clarinet-freq <i>freq</i> <i>breath-env</i> <i>freq-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A clarinet model just like <code>snd-clarinet</code> but with 
an additional parameter for continuous frequency control. You should use 
<code>clarinet-freq</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-clarinet-all(<a name="index836"></a><i>freq</i>, <i>vibrato-freq</i>,
<i>vibrato-gain</i>, <i>freq-env</i>, <i>breath-env</i>, <i>reed-stiffness</i>, <i>noise</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-clarinet-all <i>freq</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>freq-env</i> <i>breath-env</i> <i>reed-stiffness</i> <i>noise</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A clarinet model just like 
<code>snd-clarinet-freq</code> but with 
additional parameters for vibrato generation and continuous control of
reed stiffness and breath noise. You should use 
<code>clarinet-all</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-flute(<a name="index837"></a><a name="index838"></a><i>freq</i>,
<i>breath-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-flute <i>freq</i> <i>breath-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A flute implemented in STK. The <i>freq</i> is a 
<code>FLONUM</code> in Hertz, <i>breath-env</i> is a <code>SOUND</code>
 that ranges from zero to one, and <i>sr</i> is
 the desired sample rate (a <code>FLONUM</code>). You should use <code>flute</code>
 instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-flute-freq(<a name="index839"></a><a name="index840"></a><i>freq</i>, <i>breath-env</i>,
<i>freq-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-flute-freq <i>freq</i> <i>breath-env</i> <i>freq-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A flute model just like <code>snd-flute</code> but with 
an additional parameter for continuous frequency control. You should use 
<code>flute-freq</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-flute-all(<a name="index841"></a><a name="index842"></a><i>freq</i>, <i>vibrato-freq</i>, <i>vibrato-gain</i>, <i>freq-env</i>, <i>breath-env</i>, <i>jet-delay</i>, <i>noise</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-flute-all <i>freq</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>freq-env</i> <i>breath-env</i> <i>jet-delay</i> <i>noise</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A flute model just like 
<code>snd-flute-freq</code> but with 
additional parameters for vibrato generation and continuous control of
breath noise. You should use 
<code>flute-all</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-mandolin(<a name="index843"></a><a name="index844"></a><i>t0</i>, <i>freq</i>, <i>dur</i>, <i>body-size</i>, <i>detune</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-mandolin <i>t0</i> <i>freq</i> <i>dur</i> <i>body-size</i> <i>detune</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A plucked
 double-string instrument model implemented in STK. The <i>t0</i> parameter
 is the starting time (in seconds), <i>freq</i> is a <code>FLONUM</code> in
 Hz, <i>body-size</i> and <i>detune</i> are <code>FLONUM</code>s, and <code>sr</code>
 is the desired sample
 rate. You should use <code>mandolin</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-modalbar(<a name="index845"></a><a name="index846"></a><i>t0</i>, <i>freq</i>, <i>preset</i>, <i>dur</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-modalbar <i>t0</i> <i>freq</i> <i>preset</i> <i>dur</i> <i>sr</i>)</code> [LISP]</dt>
<dd>Struck bar instrument
 model implemented in STK. The parameter <i>t0</i> is the starting 
time (in seconds), <i>freq</i> is a <code>FLONUM</code> in Hz,
<code>preset</code> is a <code>FIXNUM</code> ranging from 0 to 8, <i>dur</i> is a 
<code>FLONUM</code> that
 sets the duration (in seconds) and <i>sr</i> is the desired sample rate. You 
should use <code>modalbar</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-sax(<a name="index847"></a><a name="index848"></a><i>freq</i>, <i>breath-env</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-sax <i>freq</i> <i>breath-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A sax
model implemented in STK. The <i>freq</i> is a <code>FLONUM</code> in Hertz, <i>breath-env</i> is
a <code>SOUND</code> that ranges from zero to one, and <i>sr</i> is the desired sample
rate (a <code>FLONUM</code>). You should use <code>sax</code> instead (see Section 
<a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-sax-freq(<a name="index849"></a><i>freq</i>, <i>freq-env</i>, <i>breath-env</i>,
<i>sr</i>)</code> [SAL]<br>

<code>(snd-sax-freq <i>freq</i> <i>freq-env</i> <i>breath-env</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A sax model just like <code>snd-sax</code> but with 
an additional parameter for continuous frequency control. You should use 
<code>sax-freq</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-sax-all(<a name="index850"></a><i>freq</i>, <i>vibrato-freq</i>,
<i>vibrato-gain</i>, <i>freq-env</i>, <i>breath-env</i>, <i>reed-stiffness</i>, <i>noise</i>, <i>blow-pos</i>, <i>reed-table-offset</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-sax-all <i>freq</i> <i>vibrato-freq</i> <i>vibrato-gain</i> <i>freq-env</i> <i>breath-env</i> <i>reed-stiffness</i> <i>noise</i> <i>blow-pos</i> <i>reed-table-offset</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A 
sax model just like 
<code>snd-sax-freq</code> but with 
additional parameters for vibrato generation and continuous control of
reed stiffness, breath noise, excitation position, and reed table offset.
 You should use 
<code>sax-all</code> instead (see Section <a href = "#95">Physical Models</a>).<br><br>
<dt><code>snd-sitar(<a name="index851"></a><a name="index852"></a><i>t0</i>,
<i>freq</i>, <i>dur</i>, <i>sr</i>)</code> [SAL]<br>

<code>(snd-sitar <i>t0</i> <i>freq</i> <i>dur</i> <i>sr</i>)</code> [LISP]</dt>
<dd>A sitar model implemented in STK. The parameter 
<i>t0</i> is the starting time, <i>freq</i> is a <code>FLONUM</code> (in Hz), E
<i>dur</i> sets the duration and <i>sr</i> is the sample rate (in Hz) 
of the resulting sound. You should use <code>sitar</code> instead (see Section
<a href = "#95">Physical Models</a>).
</dd></dl><a name = "108"><h4>Sequence Support Functions</h4></a>
<p>The next two functions are used to implement Nyquist's <code>seq</code> construct.</p>
<dl>
<dt>
<code>snd-seq(<a name="index853"></a><i>sound</i>, <i>closure</i>)</code> [SAL]<br>

<code>(snd-seq <i>sound</i> <i>closure</i>)</code> [LISP]</dt>
<dd>This
function returns <i>sound</i> until the logical stop time of <i>sound</i>.
Then, the XLISP <i>closure</i> is evaluated, passing it the logical stop
time of <i>sound</i> as a parameter.  The closure must return a sound,
which is then added to <i>sound</i>.  (An add is used so that <i>sound</i>
can continue past its logical stop if desired.) 
Do not call this function directly.  
<br><br>
<dt><code>snd-multiseq(<a name="index854"></a><i>array</i>, <i>closure</i>)</code> [SAL]<br>

<code>(snd-multiseq <i>array</i> <i>closure</i>)</code> [LISP]</dt>
<dd>This
function is similar to <code>snd-seq</code> except the first parameter is a
multichannel sound rather than a single sound.  A multichannel sound is
simply an XLISP array of sounds.  An array of sounds is returned which is
the sum of <i>array</i> and another array of sounds returned by <i>closure</i>.
The <i>closure</i> is passed the logical stop time of the multichannel sound,
which is the maximum logical stop time of any element of <i>array</i>.
The sample rates and number of channels returned from the closure must
match the first multi-channel sound in the sequence.
Do not call this function directly.

</dd></dl><hr>
<a href = "part7.html">Previous Section</a> | <a href = "part9.html">Next Section</a> | <a href = "title.html#toc">Table of Contents</a> | <a href = "indx.html">Index</a> | <a href = "title.html">Title Page</a>
</body></html>