Contents of Music typesetting is two-dimensional

Music typesetting is two-dimensional

Most of the people who just learnt a bit of music at college probably think that music is a linear sequence of symbols, just as literary texts to be TEX-ed. In fact, with the exception of strictly monodic instruments like most orchestral wind instruments and solo voices, one should be aware that reading music actually is a matricial operation : the non-soloist musician successively reads columns of simultaneous notes which he actually plays if he is a pianist, clavichordist or organist, which he actually reads and watches if he conducts an orchertra, and which he is supposed to check and partially play when he is a soloist who wants to play in time with the accompanying instrument or choir.

In fact, our personal experience of playing piano and organ as well as sometimes helping as an alternate Kapellmeister leads us to think that actual music reading and composing is a slightly more complicated intellectual process : music reading, music composing and music thinking seems to be a three layer process. The musician usually reads or thinks several consecutive notes (typically a long beat or a group of logically connected notes), then he goes down to the next instrument or voice and finally assembles the whole to build a part of music lasting roughly a few seconds. Then he handles the next beat or bar of his score.

Thus, it appears that the humanly logical way of coding music consists in horizontaly accumulating a set of vertical combs with horizontal teeth as described in Table $[*]$ .

Table: The order in which a musician reads music

note sequence one	note seq. four	note seq. seven	note seq. ten
note sequence two	note seq. five	note seq. eight	note seq. eleven
note seqence three	note seq. six	note seq. nine	note seq. twelve

This is the reason why, in MusicTEX the fundamental macro is of the form

\notes ... & ... & ... \enotes

where the character & is used to separate the notes to be typeset on respective staffs of the various instruments, starting from the bottom.

In the case of an instrument whose score has to be written with several staffs, these staffs are separated by the character || . Thus, a score written for a keyboard instrument and a monodic instrument (for example piano and violin) will be coded as follows :

\notes ... || ... & ... \enotes

for each column of simultaneous groups of notes. It is worth emphasizing that we actually said ``groups of notes'': this means that in each section of the previous macro, the music typesetter is welcome to insert, not only chord notes to be played at once, but small sequences of consecutive notes which build something he understands as a musical phrase. This is why note typing macros are of two kinds in MusicTEX, namely the note macros which are not followed by spacing afterwards, and those which induce horizontal spacing afterwards.