%% This file is part of the OpusTeX system.
%% You are not allowed to change this file.
%% For distribution see the copyright notice in 00readme.txt

% additional macros for OpusTeX 0.73 (February 21, 1997)
% written by Youping Huang (huang@cupat.ccc.columbia.edu)

\immediate\write16{OPUSTEX additional macros \oversion\space<\odate>}

\ifx\undefined\autospacing \else \endinput \fi

\chardef\atcode=\catcode`\@ \catcode`\@=11

\chardef\cccu@=34
\chardef\ccccu@=35

\newwrite\fout
\newread\fin
\newtoks\oldseq % store the original sequence of notes
\newtoks\newseq % store the reversed sequence of notes
\newtoks\temptoks % store accidental and octave symbols
\newcount\on@i  % save \n@i of the previous note
\newcount\nvoice

%%%%%%%%%%%%%%%%%%%% auto spacing

% \flagspacing = 0: auto spacing is not in use
%                1: output to \jobname.as1
%                2: input from \jobname.as2
\clr@\flagspacing

\def\autospacing{\openin\fin\jobname.as2
 \ifeof\fin \global\set@\flagio \immediate\openout\fout\jobname.as1
  \message{(output to \jobname.as1)}%
 \else \global\let\flagio\tw@ \message{(input from \jobname.as2)}\fi
 \global\@clr\autospacing}

% #1 = # of \elemskip after each note when \flagspacing = 1
\def\Anotes#1{\autospacing \let\flagspacing\flagio
 \@clr\firstinsert \@clr\lowvoice \set@\liftpoint
 \ifnum\flagspacing=\tw@
  \read\fin to\temp \ifcase\temp \or \let\firstinsert\Firstinsert \fi
  \read\fin to\temp \ifcase\temp \or \let\lowvoice\Lowvoice \fi\fi
 \vnotes#1\elemskip}

%% start autospace
\def\an{\Anotes{2}}

%% redefine
\def\en{\e@ff \set@\n@op
 \ifcase\flagspacing \or
  \edef\temp{0 \the\barno\space\the\nvoice}\immediate\write\fout{\temp}\fi
 \clr@\flagspacing \@clr\firstinsert}

% \firstinsert in action
\def\Firstinsert{\read\fin to\temp \insert{\temp}}

% \lowvoice in action
\def\Lowvoice{\read\fin to\temp
 \ifcase\temp \or \let\liftpoint\m@ne \else \set@\liftpoint \fi}

%% insert a space in all staffs
\def\ins#1{%
 \ifcase\flagspacing
  \message{Use \string\ins\space with \string\an..\string\en\space only.}%
 \or \edef\temp{\the\nvoice\space-2 #1}\immediate\write\fout{\temp}\fi}

% redefine
\def\vnotes#1\elemskip{\noteskip#1\@l@m \noteskip\sc@l\noteskip
  \nor@\transpose \check@no \clr@\n@op \kern\n@skip \advance\x@skip\n@skip
  \loc@skip\x@skip \n@skip\noteskip \no@ins\z@ \nvoice\z@ \b@in}

% redefine
\def\b@ff{\sel@clef \altst@ff\a@in \advance\altst@ff\nst@ff\@ist
 \advance\nst@ff\@ne \advance\nvoice\@ne \expandafter\get@refs\the\toks@
 \setbox\tw@\hbox\bgroup \loc@skip\x@skip
 \ifcase\flagspacing
  \or \edef\temp{\the\nvoice\space-4 \the\nst@ff}\immediate\write\fout{\temp}%
  \or \firstinsert \lowvoice \fi}

% input \c@fg
\def\spacing{%
 \ifcase\flagspacing \y@i\noteskip
 \or \edef\temp{\the\nvoice\space\the\c@fg\space\the\point}%
  \immediate\write\fout{\temp}\y@i\noteskip
 \or \read\fin to\temp \y@i\temp\noteskip \fi
 \off\y@i
 \global\st@bot\maxdimen \global\st@top-\st@bot}

% signal start/end of beam, used in \Beam
\def\outbeam#1{\ifcase\flagspacing \or
 \edef\temp{\the\nvoice\space-1 \the#1}\immediate\write\fout{\temp}\fi}

% input for beam calculation, used in \bHilo
\def\inbHilo{%
 \ifnum\flagspacing=\tw@ \read\fin to\temp \advance\y@iii\temp\y@ii
 \else \advance\y@iii\y@ii \fi}

%%%%%%%%%%%%%%%%%%%% rests

% #1: w12 h11 q14 e15 ee16 eee17 eeee18, lift 2*#2 \internote
\def\rest#1#2{\c@fg#1\relax
 \n@i#2\relax \multiply\n@i\tw@
 \ifnum\c@fg=\@l@v@n \advance\n@i\si@ \else \advance\n@i\f@ur \fi
 \raise\n@i\internote \hbox{\f@nt#1}% point??
 \spacing}

%% lifted rests
\def\Liftwr{\rest\tw@lv@}
\def\Lifthr{\rest\@l@v@n}
\def\Liftqr{\rest\fourt@@n}
\def\Lifter{\rest\fivet@@n}
\def\Lifteer{\rest\sixt@@n}
\def\Lifteeer{\rest\sevent@@n}
\def\Lifteeeer{\rest\eight@@n}

%% unlifted rests
\def\Wr{\Liftwr\z@}
\def\Hr{\Lifthr\z@}
\def\Qr{\Liftqr\z@}
\def\Er{\Lifter\z@}
\def\Eer{\Lifteer\z@}
\def\Eeer{\Lifteeer\z@}
\def\Eeeer{\Lifteeeer\z@}

%%%%%%%%%%%%%%%%%%%% reverse a sequence of notes

\def\reverseseq#1{\temptoks={}\newseq={}\getreverseseq#1\end}

\def\getreverseseq#1{%
 \ifx\end#1\else
  \ifcat#1a\edef\next{\noexpand\newseq={\the\temptoks#1\the\newseq}}\next
   \temptoks={}%
  \else \edef\next{\noexpand\temptoks={\the\temptoks#1}}\next \fi
  \expandafter\getreverseseq \fi}

%%%%%%%%%%%%%%%%%%%% single chords

% \@nhw    notehead width
% \@qnw    1/4 notehead width
% \c@fg   note type: w28, h27, q26, c32/37, cc33/38, ccc34/39, cccc35/40,
%                     b101, bb102, bbb103, bbbb104
% \n@sy

% \point      point
% \stemdir    stem direction +/-: up/down
% \shiftnote  +/-: shift / 'do not shift' the current note
% \flagshift  +/-/*: flag
% \cbuffer    stores note-part of a chord for \bchord
% \fBuffer    stores feature-part of a sequence of chords for \Chord and \Beam

% search for comma, with \n@i as the flag
\def\findcomma#1{\findComma#1,\end\@end}
\def\findComma#1,#2\@end{\ifx\end#2\n@i\z@ \else \n@i\@ne \fi}

% chord = {[feature-part,][note-part]}
% order of notes is either ascending or decending
\def\chord#1#2#3{%
 \c@fg#1\relax \def\stemdir{#2}%
 \findcomma{#3}\ifcase\n@i \nchord{#3}\or \fchord#3\@end \fi}

% determine direction of stem by comparing 4 - #1 and #2 - 4
\def\pickstem#1#2{\n@i#1\advance\n@i#2%
 \ifnum\n@i>\s@v@n \def\stemdir{-}\else \def\stemdir{+}\fi}

\def\fchord#1,#2\@end{#1\nchord{#2}}

% scan - stem - reverse - accid/head - point - stem/flag - accent - space
\def\nchord#1{\def\temp{#1}%
 \ifx\temp\empty \else
% scan the chord and pick stem direction
  \def\flagshift{-}\@clr\noteorder \on@i\@c
  \let\writeorscan\scanshift
  \n@ix\transpose \nhilo{#1}\transpose\n@ix
  \if?\stemdir \pickstem\n@ii\n@iii \fi
% adjust \c@fg for down flag
  \if-\stemdir \ifnum\c@fg>\ccccu@ \else \ifnum\c@fg<\cu@@ \else
   \advance\c@fg\fiv@ \fi\fi\fi
  \oldseq={#1}\let\noteseq\oldseq \let\pointseq\oldseq
% reverse order if necessary
  \ifx\noteorder\empty \def\noteorder{-}\fi
  \if+\flagshift
   \n@i\stemdir\@ne \n@i\noteorder\n@i
   \ifcase\n@i \or \def\flagshift{*}\let\noteseq\newseq \fi
   \ifnum\point=\@ne \else
    \n@i\noteorder\liftpoint
    \ifnum\n@i=\m@ne \def\flagshift{*}\let\pointseq\newseq \fi\fi\fi
  \if*\flagshift \reverseseq{#1}\def\flagshift{+}\fi
% define note head type and width
  \y@iii\@nhw
  \ifnum\c@fg=\wh@@ \let\n@sy\wh@@ \advance\y@iii\@qnw \else
  \ifnum\c@fg=\hu@@ \let\n@sy\hu@@ \else \let\n@sy\qu@@ \fi\fi
% write accidentals and note heads
  \on@i\@c \@clr\accid \def\shiftnote{-}%
  \let\writeorscan\writena
  \edef\next{\noexpand\getsymbol\the\noteseq\end}\next
% write points (points are shifted with up stem and shifted note)
  \ifnum\point=\@ne \else
   \ifnum\n@sy=\wh@@ \dimen@ii.25\@nhw \else \dimen@ii\z@ \fi
   \if-\flagshift \else \if+\stemdir \advance\dimen@ii\y@iii \fi\fi
   \on@i\@c \let\writeorscan\writep
   \edef\next{\noexpand\getsymbol\the\pointseq\end}\offs@t\next \fi
  \@clr\r@sm \writestemflag
  \writeaccent \writeslur
  \let\r@sm\resetstem \resetstem \fi
 \spacing \set@\point}

\def\offs@t#1{\off\dimen@ii#1\dimen@ii-\dimen@ii\off\dimen@ii}

% recursively scan a symbol (octave, accidental or note) for \nchord and \nhilo
\def\getsymbol#1{%
 \ifx\end#1\else
  \if'#1\advance\transpose\s@v@n \else
  \if`#1\advance\transpose-\s@v@n \else \writeorscan#1\fi\fi
  \expandafter\getsymbol \fi}

% substitute \writeorscan in \nchord to write note head and accidental
\def\writena#1{%
 \ifcat#1a\notetonum#1%
  \advance\on@i-\n@i \if+\stemdir \on@i-\on@i \fi
  \ifnum\on@i=\@ne \flip\shiftnote \else \def\shiftnote{-}\fi
  \on@i\n@i
% accidental is shifted for if \stemdir = - and \flagshift = +
  \ifx\accid\empty \else
   \edef\next{\noexpand\accid{\the\n@i}}%
   \dimen@ii\z@
   \if+\flagshift \if-\stemdir \dimen@ii-\y@iii \fi\fi
   \offs@t\next \@clr\accid \fi
% note is shifted if \shiftnote = +
  \if+\shiftnote \dimen@ii\stemdir\y@iii \else \dimen@ii\z@ \fi
  \offs@t\writenote
 \else
  \if=#1\let\accid\na \else
  \if^#1\let\accid\sh \else
  \if_#1\let\accid\fl \else
  \if>#1\let\accid\dsh \else
  \if<#1\let\accid\dfl \else
   \errmessage{Unexpected symbol}\fi\fi\fi\fi\fi
 \fi}

% substitute \writeorscan in \nchord to write point
\def\writep#1{%
 \ifcat#1a\notetonum#1%
  \ifodd\n@i \else
   \advance\n@i\liftpoint
   \ifnum\n@i=\on@i \advance\n@i-\liftpoint \advance\n@i-\liftpoint \fi\fi
  \raise\n@i\internote \hbox{\f@nt\point}\on@i\n@i \fi}

% substitute \writeorscan in \bHIlo
\def\scan#1{%
 \ifcat#1a\notetonum#1%
  \ifnum\n@ii>\n@i  \n@ii\n@i  \fi
  \ifnum\n@iii<\n@i \n@iii\n@i \fi\fi}

% substitute \writeorscan in \nchord
\def\scanshift#1{%
 \ifcat#1a\notetonum#1%
  \ifnum\n@ii>\n@i  \n@ii\n@i  \fi
  \ifnum\n@iii<\n@i \n@iii\n@i \fi
  \ifnum\on@i=\@c \else % skip the first note
   \advance\on@i-\n@i
   \ifx\noteorder\empty % define \noteorder for first two notes
    \ifnum\on@i>\z@ \def\noteorder{+}\else      % decending
    \ifnum\on@i<\z@ \def\noteorder{-}\fi\fi\fi  % ascending
   \on@i\noteorder\on@i
   \ifnum\on@i>\z@ \ifcase\on@i \or \def\flagshift{+}\fi
   \else \message{(wrong order in \number\no@ins:\number\nvoice)}\fi
   \ifcase\on@i \or \def\flagshift{+}\fi \fi
  \on@i\n@i \fi}

% do not accumulate the effect of ` and '
\def\notetonum#1{%
 \n@i\expandafter`#1\relax \advance\n@i-\@lxxxiii
 \ifnum\n@i>\@ight \advance\n@i-\eight@@n \fi
 \advance\n@i\@ref \advance\n@i\transpose \transpose\nor@}

%%%%%%%%%%%%%%%%%%%% routine for writing notes and leger lines

% write leger lines and note, copied from \writ@not, input \n@i
\def\writenote{%
 \if+\flagxstaff
  \ifnum\lowstaff=\nst@ff \n@ii\i@ff \else \n@ii-\i@ff \fi
  \n@iii\n@ii \advance\n@iii\m@ne
 \else \n@iii\m@ne \fi
 \ifnum\n@i<\n@iii % leger lines below staff
  \if+\flagxstaff \n@v\n@ii \else \n@v\z@ \fi
  \loop \advance\n@v\m@ne \ifnum\n@v>\n@i \advance\n@v\m@ne \h@ln \repeat
 \else % leger lines above staff
  \if+\flagxstaff \n@v\n@ii \advance\n@v\@ight \n@iii\n@v \advance\n@iii\@ne
  \else \n@iii\nin@ \n@v\@ight \fi
  \ifnum\n@i>\n@iii
   \loop \advance\n@v\@ne \ifnum\n@v<\n@i \advance\n@v\@ne \h@ln \repeat \fi
 \fi
%
 \y@i\n@i\internote
 \advance\y@i\altst@ff
 \ifdim\st@bot>\y@i \global\st@bot\y@i \fi
 \ifdim\st@top<\y@i \global\st@top\y@i \fi
 \advance\y@i-\altst@ff
 \raise\y@i\hbox{\f@nt\n@sy}}

% adjust \st@bot and \st@top after \b@sm
\def\writestemflag{%
 \ifnum\c@fg=\wh@@ \else
 \ifnum\c@fg<\wh@@ \if+\stemdir \u@sm \else \d@sm \fi \else
 \ifnum\c@fg>\@c \b@sm
  \if+\stemdir \advance\st@top\b@amthik \else \advance\st@bot-\b@amthik \fi
 \else \if+\stemdir \upfl@g \advance\st@top\y@v \else \downfl@g \fi\fi\fi\fi}

%\def\rsetst@m{\showthe\st@bot\showthe\st@top}

\def\resetstem{\global\st@bot\maxdimen \global\st@top-\st@bot \clr@\st@s}

%%%%%%%%%%%%%%%%%%%% lowest and highest notes of one or many chords

% \n@i     temp
% \n@ii    min (last), initialized in \nhilo
% \n@iii   max (last), initialized in \nhilo
% \n@iv    min (first)
% \n@v     max (first)
% \n@vi    min (overall)
% \c@fg   max (overall)
% \n@ix    save \transpose
% \y@i     temp
% \y@ii    \noteskip or rise/fall of beam for each \noteskip
% \y@iii   length or total rise/fall of beam
% \y@iv    note head width or rise/fall of beam for each note head width
%          at first scan in \HILO, \y@iii = length
%          at second scan in \avpos / \xvpos, \y@iii = rise/fall

% find min/max of note-part of a chord, output \n@ii and \n@iii
% called by \bHilo and \fHilo
\def\nhilo#1{\n@ii\@c \n@iii-\@c \getsymbol#1\end}

% find min/max of first/last/overall and length of a sequence of chord
\def\HILO#1{%
 \n@ii\@c \n@iv\@c \n@vi\@c \c@fg-\@c \y@ii\noteskip \y@iii\z@ \y@iv\@nhw
 \n@ix\transpose \getHILO#1\end \transpose\n@ix \restorex}

\def\getHILO#1{%
 \ifx\end#1\else
  \bHilo{#1}%
  \ifnum\n@ii=\@c \else
   \ifnum\n@vi>\n@ii   \n@vi\n@ii \fi
   \ifnum\c@fg<\n@iii \c@fg\n@iii \fi\fi
  \expandafter\getHILO \fi}

% scan one beam chord for \getHILO, \getavpos and \getxvpos
% update \n@iv and \n@v at the second call
% update \y@iii starting at the second chord, including null chord
\def\bHilo#1{%
 \ifnum\n@ii=\@c \else \ifnum\n@iv=\@c \n@iv\n@ii \n@v\n@iii \fi\fi
 \let\writeorscan\scan
 \findcomma{#1}\ifcase\n@i \nhilo{#1}\or \fHilo#1\@end \fi
 \ifnum\n@iv=\@c \else \inbHilo \fi}

\def\fHilo#1,#2\@end{\n@i\z@ \getfHilo#1\end \nhilo{#2}}

% \n@i = 1: flag for \ins
% recursively scan feature-part of one chord for \fHilo
\def\getfHilo#1{%
 \ifx\end#1\else
  \ifcase\n@i
   \ifx#1\Sk     \n@i\@ne \else
   \ifx#1\xstaff \xstaff \else
   \ifx#1\xstem  \xstem \else
   \ifx#1\xover  \xover \fi\fi\fi\fi
  \or \advance\y@iii#1\y@ii \n@i\z@ \fi
  \expandafter\getfHilo \fi}

%%%%%%%%%%%%%%%%%%%% single chord

%% single chord with specified stem
\def\Wu{\chord\wh@@+}
\def\Wd{\chord\wh@@-}
\def\Hu{\chord\hu@@+}
\def\Hd{\chord\hu@@-}
\def\Qu{\chord\qu@@+}
\def\Qd{\chord\qu@@-}
\def\Cu{\chord\cu@@+}
\def\Cd{\chord\cu@@-}
\def\Ccu{\chord\ccu@+}
\def\Ccd{\chord\ccu@-}
\def\Cccu{\chord\cccu@+}
\def\Cccd{\chord\cccu@-}
\def\Ccccu{\chord\ccccu@+}
\def\Ccccd{\chord\ccccu@-}

%% single chord with automatic stem
\def\Wh{\chord\wh@@?}
\def\Ha{\chord\hu@@?}
\def\Qa{\chord\qu@@?}
\def\Ca{\chord\cu@@?}
\def\Cca{\chord\ccu@?}
\def\Ccca{\chord\cccu@?}
\def\Cccca{\chord\ccccu@?}

%%%%%%%%%%%%%%%%%%%% sequence of chords

% a sequence of chords may have a common feature-part, which saved in \fBuffer

\def\Chord#1#2#3{\let\numvii#1\def\Stemdir{#2}%
 \findcomma{#3}%
 \ifcase\n@i \@clr\fBuffer \getChord#3\end \or \fChord#3\@end \fi}

\def\fChord#1,#2\@end{\def\fBuffer{#1}\getChord#2\end}

\def\getChord#1{%
 \ifx\end#1\else \fBuffer \chord\numvii\Stemdir{#1}\expandafter\getChord \fi}

%% sequence of chords with fixed stem
\def\WU{\Chord\wh@@+}
\def\WD{\Chord\wh@@-}
\def\HU{\Chord\hu@@+}
\def\HD{\Chord\hu@@-}
\def\QU{\Chord\qu@@+}
\def\QD{\Chord\qu@@-}
\def\CU{\Chord\cu@@+}
\def\CD{\Chord\cu@@-}
\def\CCu{\Chord\ccu@+}
\def\CCd{\Chord\ccu@-}
\def\CCcu{\Chord\cccu@+}
\def\CCcd{\Chord\cccu@-}
\def\CCccu{\Chord\ccccu@+}
\def\CCccd{\Chord\ccccu@-}

%% sequence of chords with automatic stem
\def\WH{\Chord\wh@@?}
\def\HA{\Chord\hu@@?}
\def\QA{\Chord\qu@@?}
\def\CA{\Chord\cu@@?}
\def\CCa{\Chord\ccu@?}
\def\CCca{\Chord\cccu@?}
\def\CCcca{\Chord\ccccu@?}

%%%%%%%%%%%%%%%%%%%% routines for beams

% automatic beams use beam number 0
% \b@ni  \@N    number of pending beams
% \D@i   \b@sl  slope number
% \U@i   \b@z   v-pos
% \V@i   \b@x   h-pos of 1st beam
% \W@i   \c@x   h-pos of 2nd beam
% \X@i   \d@x   h-pos of 3rd beam
% \Y@i   \e@x   h-pos of 4th beam

% \endb holds #beams, \startb = 0
% in \tbba (\trbba), \startb holds #beams of the following chords, while
% \endb holds #beams of current chord
% \clr@\startb in \initb and \bchord

% initialize beam number 0, #1 = \endb (# of pending beams)
\def\initb#1{%
 \clr@\startb
 \b@ni-\stemdir#1%
 \g@tpos \if+\stemdir\advance\y@v\@nhw \fi
 \V@i\y@v
 \ifcase#1\or
  \or \W@i\y@v
  \or \W@i\y@v \X@i\y@v
  \or \W@i\y@v \X@i\y@v \Y@i\y@v \fi}

% read a sequence of beam chords, \cbuffer stores note-part of a chord
\def\bchord#1{\@clr\cbuffer
 \sel@beam0\@end
 \getbchord#1\end \restorex
 \ifx\startb\z@ \else \let\endb\startb \clr@\startb \fi}

% recursively read a sequence of beam chords for \bchord
% insert \tha before the last chord
\def\getbchord#1{%
 \ifx\end#1%
  \c@fg\endb \advance\c@fg\@c
  \tba \edef\next{\noexpand\nchord{\cbuffer}}\next \@clr\cbuffer
 \else
  \ifx\empty\cbuffer \else
   \c@fg\endb \advance\c@fg\@c
   \edef\next{\noexpand\nchord{\cbuffer}}\next \fi
  \fBuffer
  \findcomma{#1}\ifcase\n@i \def\cbuffer{#1}\or \fbchord#1\@end \fi
  \expandafter\getbchord
 \fi}

\def\fbchord#1,#2\@end{\n@ix\transpose #1\transpose\n@ix \def\cbuffer{#2}}

%% add beam
\def\nbba{\nbb0\let\endb\tw@}
\def\nbbba{\nbbb0\let\endb\thr@@}
\def\nbbbbba{\nbbbb0\let\endb\f@ur}

\def\tba{\tb0}

%% terminate beam
\def\tbba{\tbb0\let\startb\endb \let\endb\tw@}
\def\tbbba{\tbbb0\let\startb\endb \let\endb\thr@@}
\def\tbbbba{\tbbbb0\let\startb\endb \let\enbb\f@ur}

%% terminate beam from right
\def\trbba{\trbb0\let\endb\tw@}
\def\trbbba{\trbbb0\let\endb\thr@@}
\def\trbbbba{\trbbbb0\let\endb\f@ur}

%%%%%%%%%%%%%%%%%%%% stuffs for staff change and stem change

% keep track of stam and staff change
\@clr\stemchanged  % flag of stem change for a beam, not a toggle
                   % send signal for different slope calculation
\def\flagxstem{-}  % keep track of stem change, a toggle
\def\flagxstaff{-} % keep track of staff change, a toggle

% restore stem and staff status to the start of beam
\def\restorex{%
 \if+\flagxstem  \xstem \fi
 \if+\flagxstaff \xstaff \fi}

% compute \@ref for \xstaff, #1 = +/-: going up/down a staff
\def\xref#1{%
 \advance\nst@ff#1\@ne \expandafter\get@refs\the\toks@ \advance\nst@ff#1\m@ne
 \n@i#1\i@ff \advance\n@i\@ref \@ref\n@i}

%% define \lowstaff, to be compared with \nst@ff
\def\twostaffs{\set@\lowstaff} % for piano
\def\threestaffs{\let\lowstaff\tw@} % for organ
\twostaffs

%% change the stem of a beam, a toggle
% update \y@iii to adjust beam length in \HILO, to adjust rise/fall of beam
% in \xvpos, and have no effect in writing note
\def\xstem{%
 \if?\stemdir \errmessage{Pick a stem direction before using \string\xstem}\fi
 \def\stemchanged{+}\flipflagxstem \flip\stemdir \advance\y@iii\stemdir\y@iv}

\def\flipflagxstem{\flip\flagxstem
 \if+\flagxstem \clr@\inv@ \else \set@\inv@ \fi}

%% change the staff of a beam, a toggle
\def\xstaff{%
% \if?\stemdir \errmessage{Pick a stem direction before using \string\xstaff}\fi
 \flip\flagxstaff
 \if+\flagxstaff \ifnum\nst@ff=\lowstaff \xref+\else \xref-\fi
 \else \expandafter\get@refs\the\toks@ \fi}

%% change both the stem and the staff of a beam, a toggle
\def\xover{\xstem \xstaff}

%%%%%%%%%%%%%%%%%%%% stuffs for beam

%% specify a beam slope, compare with 9 not \m@bs, reset when exit \beam
\def\slope#1{\D@i#1\relax \checkslope\nin@}
\D@i\@c

% input: \n@i = rise/fall, \y@iii = length; output: \D@i
\def\calcslope{%
 \y@i\n@i\internote
 \multiply\y@i\tw@nty
 \Divide\y@i\y@iii \D@i\y@i
 \checkslope\m@bs}

\def\checkslope#1{%
 \ifnum\D@i>#1\D@i#1\fi
 \ifnum\D@i<-#1\D@i-#1\fi}

% adjust length of stem, \interb@m=3.75pt \internote=2.5pt
\def\adjuststem{\y@i\cutBeamstem\interb@m
 \ifcase\y@i \else
  \multiply\y@i\tw@ \divide\y@i\thr@@ \advance\U@i-\stemdir\y@i \fi}

%% in unit of \internote
\def\cutbeamstem#1{\def\cutBeamstem{#1}}
\cutbeamstem{0}

%%%%%%%%%%%%%%%%%%%% beams without stem change

% determine slope from max(last)-max(first) if \stemdir = +
%                      min(last)-min(first) if \stemdir = -
\def\abeam#1{%
 \if?\stemdir \pickstem\n@vi\c@fg \fi
 \ifnum\D@i=\@c
  \if+\stemdir \n@i\n@iii \advance\n@i-\n@v
  \else        \n@i\n@ii  \advance\n@i-\n@iv \fi
  \calcslope \fi
 \avpos{#1}% to move 1 \interb@m (1.5 \internote) outward per beam
 \advance\U@i\stemdir\startb\interb@m
 \initb\endb
 \bchord{#1}}

% compute vertical position of \abeam
% \U@i    v-pos of beam
% \y@ii   rise/fall of beam for each \noteskip
% \y@iii  rise/fall of beam
\def\avpos#1{%
 \n@ii\@c \n@iv\@c \y@iii\z@ \U@i\z@
 \y@ii\D@i\noteskip \divide\y@ii\tw@nty
 \n@ix\transpose \getavpos#1\end \transpose\n@ix
 \if+\stemdir \advance\U@i\n@v\internote
 \else        \advance\U@i\n@iv\internote \fi % \U@i is at first chord
 \advance\U@i\altst@ff
 \y@i\stemdir\t@n\interb@m \divide\y@i\thr@@
 \advance\U@i\y@i % move 10/3 \interb@m (5 \internote) outward
 \adjuststem \restorex}

\def\getavpos#1{%
 \ifx\end#1\else
  \bHilo{#1}% \y@iii = v vector from first chord to current beam
  \ifnum\n@ii=\@c \else \ifnum\n@iv=\@c \else % skip first and null chord
   \if+\stemdir \n@i\n@iii \advance\n@i-\n@v
   \else        \n@i\n@ii  \advance\n@i-\n@iv \fi % \n@i = vec (first, current)
   \y@i\n@i\internote % \y@i = v vector from first chord to current chord
   \advance\y@i-\y@iii % \y@i = adjustment needed for current chord
   \if+\stemdir \ifnum\y@i>\U@i \U@i\y@i \fi
   \else        \ifnum\y@i<\U@i \U@i\y@i \fi\fi
  \fi\fi
  \expandafter\getavpos \fi}

%%%%%%%%%%%%%%%%%%%% beams with stem change

% determine slope from min(last)-max(first) if \stemdir = +
%                      max(last)-min(first) if \stemdir = -
\def\xbeam#1{%
 \ifnum\D@i=\@c
  \if+\stemdir \n@i\n@ii  \advance\n@i-\n@v
  \else        \n@i\n@iii \advance\n@i-\n@iv \fi
  \calcslope \fi
 \xvpos{#1}% to move \U@i from vertical center of beams to outer beam
 \n@i\endb \advance\n@i\m@ne
 \y@i\n@i\interb@m \divide\y@i\tw@ \advance\U@i\stemdir\y@i
 \initb\endb \bchord{#1}}

% compute vertical position of \xbeam
% use a test beam starting from the reference note of the first chord
% \U@i (or \V@i)       vertical adjustment of beam for stems having the
%                      same (or opposite) direction as \stemdir
% \stemdir = + (or -)  \U@i (or V@i) from beam to current reference note
%                      \V@i (or U@i) from current reference note to beam
% \y@iii               rise/fall of beam
\def\xvpos#1{%
 \n@ii\@c \n@iv\@c \y@ii\D@i\noteskip \divide\y@ii\tw@nty \y@iii\z@
 \y@iv\D@i\@nhw \divide\y@iv\tw@nty
 \U@i\z@ \V@i-\maxdimen
 \n@ix\transpose \getxvpos#1\end \transpose\n@ix \restorex
 \if+\stemdir \V@i-\V@i \else \U@i-\U@i \fi
 \advance\V@i+\U@i \divide\V@i\tw@
 \U@i\n@iv\internote
 \advance\U@i\V@i
 \advance\U@i\altst@ff
 \adjuststem}

\def\getxvpos#1{%
 \ifx\end#1\else
  \ifnum\n@ii=\@c \else \ifnum\n@iv=\@c % save first chord at second call
   \if+\stemdir \n@iv\n@iii \else \n@iv\n@ii \fi\fi\fi
  \bHilo{#1}%
  \ifnum\n@ii=\@c \else \ifnum\n@iv=\@c \else % skip first and null chord
   \if+\stemdir \n@i\n@iii \else \n@i\n@ii \fi % \n@i = v-pos of current chord
   \advance\n@i-\n@iv % \n@i = vector (first chord, current chord)
   \y@i\n@i\internote \advance\y@i-\y@iii % \y@i = vector(beam,note)
   \y@i\stemdir\y@i
   \if+\flagxstem \ifdim\V@i<\y@i \V@i\y@i \fi
   \else          \ifdim\U@i<\y@i \U@i\y@i \fi\fi
  \fi\fi
  \expandafter\getxvpos \fi}

%%%%%%%%%%%%%%%%%%%% automatic beams

% first scan to determine stem direction, slope of beam, and the existence
% of \stemchanged
% second scan to compute vertical position of beam
% third scan to write notes

\def\Beam#1#2#3#4{\def\stemdir{#1}\let\endb#2\let\startb#3%
 \outbeam\@ne
 \findcomma{#4}\ifcase\n@i \@clr\fBuffer \beam{#4}\or \fBeam#4\@end \fi
 \outbeam\tw@}

\def\fBeam#1,#2\@end{\def\fBuffer{#1}\beam{#2}}

\def\beam#1{%
 \@clr\stemchanged \HILO{#1}%
 \ifx\stemchanged\empty \abeam{#1}\else \xbeam{#1}\fi
 \global\D@i\@c}

%% beam notes with automatic stem
\def\Ba{\Beam?\@ne\@ne}
\def\bBa{\Beam?\@ne\tw@}
\def\bbBa{\Beam?\@ne\thr@@}
\def\bbbBa{\Beam?\@ne\f@ur}
\def\Bba{\Beam?\tw@\@ne}
\def\BBa{\Beam?\tw@\tw@}
\def\bBBa{\Beam?\tw@\thr@@}
\def\bbBBa{\Beam?\tw@\f@ur}
\def\Bbba{\Beam?\thr@@\@ne}
\def\BBba{\Beam?\thr@@\tw@}
\def\BBBa{\Beam?\thr@@\thr@@}
\def\bBBBa{\Beam?\thr@@\f@ur}
\def\Bbbba{\Beam?\f@ur\@ne}
\def\BBbba{\Beam?\f@ur\tw@}
\def\BBBba{\Beam?\f@ur\thr@@}
\def\BBBBa{\Beam?\f@ur\f@ur}

%% beam notes with up stem
\def\Bu{\Beam+\@ne\@ne}
\def\bBu{\Beam+\@ne\tw@}
\def\bbBu{\Beam+\@ne\thr@@}
\def\bbbBu{\Beam+\@ne\f@ur}
\def\Bbu{\Beam+\tw@\@ne}
\def\BBu{\Beam+\tw@\tw@}
\def\bBBu{\Beam+\tw@\thr@@}
\def\bbBBu{\Beam+\tw@\f@ur}
\def\Bbbu{\Beam+\thr@@\@ne}
\def\BBbu{\Beam+\thr@@\tw@}
\def\BBBu{\Beam+\thr@@\thr@@}
\def\bBBBu{\Beam+\thr@@\f@ur}
\def\Bbbbu{\Beam+\f@ur\@ne}
\def\BBbbu{\Beam+\f@ur\tw@}
\def\BBBbu{\Beam+\f@ur\thr@@}
\def\BBBBu{\Beam+\f@ur\f@ur}

%% beam notes with down stem
\def\Bd{\Beam-\@ne\@ne}
\def\bBd{\Beam-\@ne\tw@}
\def\bbBd{\Beam-\@ne\thr@@}
\def\bbbBd{\Beam-\@ne\f@ur}
\def\Bbd{\Beam-\tw@\@ne}
\def\BBd{\Beam-\tw@\tw@}
\def\bBBd{\Beam-\tw@\thr@@}
\def\bbBBd{\Beam-\tw@\f@ur}
\def\Bbbd{\Beam-\thr@@\@ne}
\def\BBbd{\Beam-\thr@@\tw@}
\def\BBBd{\Beam-\thr@@\thr@@}
\def\bBBBd{\Beam-\thr@@\f@ur}
\def\Bbbbd{\Beam-\f@ur\@ne}
\def\BBbbd{\Beam-\f@ur\tw@}
\def\BBBbd{\Beam-\f@ur\thr@@}
\def\BBBBd{\Beam-\f@ur\f@ur}

%%%%%%%%%%%%%%%%%%%% multivoice

%%
\def\multivoice{\catcode`\/=\active}
\def\nomultivoice{\catcode`\/=\tw@lv@}

\multivoice

%% start a new voice
\def/{\egroup \ifdim\n@skip<\wd\tw@ \n@skip\wd\tw@ \fi
 \wd\tw@\z@ \raise\altst@ff\box\tw@ \advance\nvoice\@ne
 \setbox\tw@\hbox\bgroup \loc@skip\x@skip
 \ifcase\flagspacing
  \or \edef\temp{\the\nvoice\space-4 \the\nst@ff}\immediate\write\fout{\temp}%
  \or \firstinsert \lowvoice \fi}

\nomultivoice

%%%%%%%%%%%%%%%%%%%% points

\set@\point % \z@ gives 0.0pt

\def\Pt{\let\point\f@ur   \ifcase\flagspacing \set@\liftpoint \fi}
\def\Ppt{\let\point\fiv@  \ifcase\flagspacing \set@\liftpoint \fi}
\def\Dpt{\let\point\f@ur  \ifcase\flagspacing \let\liftpoint\m@ne \fi}
\def\Dppt{\let\point\fiv@ \ifcase\flagspacing \let\liftpoint\m@ne \fi}

%%%%%%%%%%%%%%%%%%%% accents

%% cancel accent
\def\noaccent{\clr@\flagaccent}
\noaccent

% #1     \flagaccent = 0: none, 1: small, 2: big
% #2     \accdir: +/-/?
% #3/#4  char for up/down accent
\def\Accent#1#2#3#4{\let\flagaccent#1\def\accdir{#2}%
 \def\uaccent{#3}\def\daccent{#4}}

% input \st@bot and \st@top, reset \flagaccent at exit
\def\writeaccent{%
 \ifcase\flagaccent \else
  \if?\accdir \if+\stemdir \def\accdir{-}\else \def\accdir{+}\fi\fi
  \if+\accdir \let\maccent\uaccent \else \let\maccent\daccent \fi
  \if+\flagxstaff
   \ifnum\lowstaff=\nst@ff \n@ii\i@ff \else \n@ii-\i@ff \fi
  \else \n@ii\z@ \fi
  \n@iii\n@ii \advance\n@iii\s@v@n \advance\n@ii\@ne
%
  \if+\accdir \y@i\st@top \else \y@i\st@bot \fi
  \if\stemdir\accdir
   \y@ii-\internote
   \ifnum\c@fg=\wh@@ \else \advance\y@i\accdir\y@ii \fi
   \advance\y@i\accdir.4\internote % to be adjusted
   \y@ii\y@i
   \Divide\y@ii\internote \n@i\y@ii
   \if+\accdir
    \ifnum\n@i<\n@iii \ifnum\flagaccent=\tw@ \n@i\n@iii \fi
    \else \n@i\@c \fi
   \else
    \ifnum\n@i>\n@ii \ifnum\flagaccent=\tw@ \n@i\n@ii \fi
    \else \n@i\@c \fi\fi
  \else \divide\y@i\internote \n@i\y@i \fi
%
  \ifnum\n@i=\@c \else
   \ifnum\flagaccent=\@ne
    \if+\accdir \ifnum\n@i<\n@iii \ifodd\n@i \else \advance\n@i\@ne  \fi\fi
    \else       \ifnum\n@i>\n@ii  \ifodd\n@i \else \advance\n@i\m@ne \fi\fi\fi
   \else
    \if+\accdir \ifnum\n@i<\n@iii \n@i\n@iii \fi
    \else       \ifnum\n@i>\n@ii  \n@i\n@ii  \fi\fi\fi
   \y@i\n@i\internote \fi
  \raise\y@i \hbox{\f@nt\maccent}%
  \clr@\flagaccent \fi}

%% accents at the opposite side of the stem
\def\Fz{\Accent\tw@?ab}    % ^ sforzato
\def\St{\Accent\@ne?cd}    % . staccato
\def\Stpo{\Accent\tw@?ef}  %   tenuto / staccato
\def\Po{\Accent\@ne?gh}    % - tenuto
\def\Ppz{\Accent\@ne?ij}   % ' pizzicato
\def\Sf{\Accent\tw@?kl}    % > sforzando

%% up accents
\def\Ufz{\Accent\tw@+ab}
\def\Ust{\Accent\@ne+cd}
\def\Ustpo{\Accent\tw@+ef}
\def\Upo{\Accent\@ne+gh}
\def\Uppz{\Accent\@ne+ij}
\def\Usf{\Accent\tw@+kl}

%% down accents
\def\Dfz{\Accent\tw@-ab}
\def\Dst{\Accent\@ne-cd}
\def\Dstpo{\Accent\tw@-ef}
\def\Dpo{\Accent\@ne-gh}
\def\Dppz{\Accent\@ne-ij}
\def\Dsf{\Accent\tw@-kl}

%%%%%%%%%%%%%%%%%%%% slurs

\let\flagislur\m@ne
\let\flagtslur\m@ne

\def\Isluru#1{\def\flagislur{#1}\def\slurdir{+}}
\def\Islurd#1{\def\flagislur{#1}\def\slurdir{-}}
\def\Tsluru#1{\def\flagtslur{#1}\def\slurdir{+}}
\def\Tslurd#1{\def\flagtslur{#1}\def\slurdir{-}}

% input \st@bot and \st@top, reset \flagislur/\flagtslur at exit
\def\writeslur{%
 \on@i\c@fg
 \ifnum\flagislur>\m@ne \initslur \let\flagislur\m@ne \fi
 \ifnum\flagtslur>\m@ne \termslur \let\flagtslur\m@ne \fi
 \c@fg\on@i}

\def\initslur{%
 \global\advance\N@sl\@ne % update slurcounter
  \ifnum\flagislur>\fiv@ \ac@s\flagislur\@end \fi \n@i\flagislur\sel@slur
  \global\csname A@\ro@n@i\altst@ff % store altitude of current slur
  \if x\@sense \else \errmessage{no \string\tslur\flagislur}\fi
  \if+\slurdir \global\@S{u}\else \global\@S{d}\fi % store sense (u,d)
  \if+\slurdir \y@i\st@top \advance\y@i\h@lf\internote
  \else        \y@i\st@bot \advance\y@i-\h@lf\internote \fi
  \y@ii\y@i
  \divide\y@ii\internote \n@ii\y@ii
  \y@ii\n@ii\internote
  \advance\y@i-\y@ii
  \global\sl@y\y@i % store voffset (abs. dim. to rel. height)
  \global\csname H@\ro@n@i\n@ii % start vpos (steps of internote)
  \global\csname J@\ro@n@i\n@ii %
  \g@tpos \if+\slurdir \advance\y@v\@nhw \fi
  \global\sl@x\y@v} % start hpos (current pos including hoffset)

\def\termslur{%
 \n@i\flagtslur\sel@slur
 \if+\slurdir \y@iv\@nhw \else \y@iv\z@ \fi
 \if x\@sense \errmessage{no \@mis\string\islur\flagtslur}\fi
 \if D\@sense \@S{u}\clr@\@inv \fi
 \if U\@sense \@S{d}\clr@\@inv \fi
 \g@tpos
 \if+\slurdir \y@ii\st@top \else \y@ii\st@bot \fi
 \Divide\y@ii\internote \n@vi\y@ii
 \n@iv\csname H@\ro@n@i
 \ifcase\h@sl
   \ifdim\y@v=\afterruleskip
     \y@i\n@i\internote \advance\y@i\sl@y
     \raise\y@i\hbox{\f@nt\if u\@sense X\else Y\fi}%
   \else \C@hs \fi
 \or \C@hs \fi
 \global\@S{x}\set@\@tmp
 \global\advance\N@sl\m@ne}% update slur counter

%%%%%%%%%%%%%%%%%%%% transposition

% set choice of transpose, effective on +/- only
\def\setchoice#1#2{\if+#1\def#2{+}\else \if-#1\def#2{-}\fi\fi}

%% #1 = +/-: +5/-7, #2 = +/-: +6/-6, #3 = +/-: +7/-5
\def\transposechoice#1#2#3{%
 \setchoice#1\flaga \setchoice#2\flagb \setchoice#3\flagc}

\transposechoice++-

%% replace \transpose, #1 = number of half-steps to be transposed
\def\Transpose#1{\def\halfsteps{#1}}

\clr@\halfsteps

% compute \transpose
\def\signature#1{%
 \n@i#1\relax \transpose\halfsteps\relax
 \ifnum\transpose=\z@ \else
  \multiply\transpose\s@v@n
  \advance\n@i\transpose
  \transpose\n@i
  \divide\transpose\tw@lv@
  \multiply\transpose\tw@lv@
  \advance\n@i-\transpose
  \divide\transpose\tw@lv@
  \ifnum\n@i>\si@  \advance\n@i-\tw@lv@ \advance\transpose\@ne  \fi
  \ifnum\n@i<-\si@ \advance\n@i\tw@lv@  \advance\transpose-\@ne \fi
  \ifnum\n@i=\fiv@  \if-\flaga \n@i-\s@v@n \advance\transpose\@ne  \fi\fi
  \ifnum\n@i=\si@   \if-\flagb \n@i-\si@   \advance\transpose\@ne  \fi\fi
  \ifnum\n@i=-\si@  \if+\flagb \n@i\si@    \advance\transpose-\@ne \fi\fi
  \ifnum\n@i=-\fiv@ \if+\flagc \n@i\s@v@n  \advance\transpose-\@ne \fi\fi\fi}

%% replace \generalsignature
\def\Generalsignature#1{\signature{#1}\generalsignature{\number\n@i}}

%% replace \setsign
\def\Setsign#1#2{\signature{#2}\setsign#1{\number\n@i}}

%%%%%%%%%%%%%%%%%%%% others

%% similar to \sk
\def\Sk#1{\ifcase\flagspacing \off{#1\noteskip}\else
 \message{Do not use \string\Sk\space with \string\an..\string\en\space.}\fi}

% for debug
\def\tracing{\tracingcommands2\tracingmacros2}

\def\defend{\end}

% effective on +/- only
\def\flip#1{\if+#1\def#1{-}\else \if-#1\def#1{+}\fi\fi}

% round (#1 / #2), where #2 > 0
\def\Divide#1#2{%
 \ifnum#1>\z@ \advance#1\h@lf#2\else \advance#1-\h@lf#2\fi
 \divide#1#2}

\nostemcut
\relativeaccid

\catcode`\@=\atcode \endinput