Language for describing music compositions in exact frequencies.

• Python (developed and tested with python 3.4.0)
• Music21
• Pyparsing
• Lilypond (for exporting to pdf)

This is an example of music arithmetic code. As you see you can just write notes from the equally tempered scale by the usual names.

(
    c (e, g) (f, a) (e, g) (d, f) (c, e) (g/2, (d d) | .5) c
)

The same piece but in pure notation is like this.

261.6 * (
    1 (5/4, 3/2) (4/3, 5/3) (5/4, 3/2) (9/8, 4/3) (1, 5/4) (3/4, (9/8 9/8) | .5) 1
)

One can store this into a file, like example.ma and export it to midi it using the command python3 export_midi.py example.ma example.mid.

• Convert music21 format to out own format
• Convert frequencies to vectors

Numbers can be constructed by the usual expressions. Numbers are frequencies by default. A duration parameter can be specified after a | symbol, which has a low precedence. Parenthesis are not needed for tuples anymore, so they can replace curly brackets.

So we have the rational numbers with the usual operators extended with frequency constants and the operators:

• * and / (precedence 4)
• | (duration operator, precedence 3)
• (serial operator, precedence 2)
• , (parallel operator, precedence 1)

The advantage of choosing this precedence order is that we can write multiple voices easily.

(
    c g a g f e d   c,
    c e f e d c g/2 c
)

An equivalent way of writing this piece in a chord-by-chord fashion could be as follows.

(
    c (e, g) (f, a) (e, g) (d, f) (c, e) (g/2, (d d) | .5) c
)

Here is a brief motivation why this syntax was chosen. If we swap the precedence order of , and , the parts would look like this.

(
   (c g a g f e (d d) | 1/2 c),
   (c e f e d c g           c) / 2
)
(
    c e, g f, a e, g f, a e, g g/2, (d d) | 1/2 c
)

Although it requires less parenthesis, it is also less readable, because intuitively commas are seperators, more than spaces.

In practice you would place parenthesis around chords and melodies anyway, to specify duration. So in the end it doesn't matter too much.