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<HTML>
<TITLE>GEN09</TITLE>
<CENTER><P><A NAME="GEN09"></A>
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<H2>GEN09, GEN10, GEN19</H2>
<PRE><TT> <B>f</B> # time size 9 pna stra phsa pnb strb phsb . . .
<B>f</B> # time size 10 str1 str2 str3 str4 . . . .
<B>f</B> # time size 19 pna stra phsa dcoa pnb strb phsb dcob . . . </TT>
</PRE>
<P>
<HR></P>
<H4><U>DESCRIPTION</U></H4>
<P>These subroutines generate composite waveforms made up of weighted sums
of simple sinusoids. The specification of each contributing partial requires
3 pfields using <B>GEN09</B>, 1 using <B>GEN10</B>, and 4 using <B>GEN19</B>.
</P>
<H4><U>INITIALIZATION</U></H4>
<P><I>size </I>- number of points in the table. Must be a power of 2 or
power-of-2 plus 1 ( <A HREF="./../NumScore/f-stat.html">see f statement</A>).
</P>
<P><I>pna, pnb</I>, etc. - partial no. (relative to a fundamental that
would occupy <I>size</I> locations per cycle) of sinusoid a, sinusoid b,
etc. Must be positive, but need not be a whole number, i.e., non-harmonic
partials are permitted. Partials may be in any order. </P>
<P><I>stra, strb</I>, etc. - strength of partials <I>pna, pnb</I>, etc.
These are relative strengths, since the composite waveform may be rescaled
later. Negative values are permitted and imply a 180 degree phase shift.
</P>
<P><I>phsa, phsb</I>, etc. - initial phase of partials <I>pna, pnb,</I>
etc., expressed in degrees. </P>
<P><I>dcoa, dcob</I>, etc. - DC offset of partials <I>pna, pnb</I>, etc.
This is applied <I>after</I> strength scaling, i.e. a value of 2 will lift
a 2-strength sinusoid from range [-2,2] to range [0,4] (before later rescaling).
</P>
<P><I>str1, str2, str3,</I> etc. - relative strengths of the fixed harmonic
partial numbers 1,2,3, etc., beginning in p5. Partials not required should
be given a strength of zero. </P>
<P><B>Note:</B> </P>
<P>These subroutines generate stored functions as sums of sinusoids of
different frequencies. The two major restrictions on <B>GEN10</B>Ñthat
the partials be harmonic and in phaseÑdo not apply to <B>GEN09</B>
or <B>GEN19</B>. </P>
<P>In each case the composite wave, once drawn, is then rescaled to unity
if p4 was positive. A negative p4 will cause rescaling to be skipped. </P>
<H4><U>EXAMPLES:</U></H4>
<PRE><TT> f 1 0 1024 9 1 3 0 3 1 0 9 .3333 180
f 2 0 1024 19 .5 1 270 1 </TT>
</PRE>
<P>f 1 combines partials l, 3 and 9 in the relative strengths in which
they are found in a square wave, except that partial 9 is upside down.
f 2 creates a rising sigmoid [0 - 2]. Both will be rescaled.</P>
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