[ajuc]

C is 0. Each half-tone up is +1.

If you really want to keep it concise you can write it as base-12 numbers.

    C1 C1# D1 D1# E1 F1 F1# G1 G1# A1 A1# B1 C2 C2# D2 D2# E2 F2 F2# G2 G2# A2 A2# B2 ...
    00 01  02 03  04 05 06  07 08  09 0a  0b 10 11  12 13  14 15 16  17 18  19 1a  1b ...

First number is octave. Second number is half-tone in that octave. Translating is just mechanical addition.

EDIT: on second thought making it base-12 just to save some space makes no sense, people are good with base-10, just keep the numbers.

[pkolaczk]

It looks better on paper for an engineer, but not for someone who actually plays an instrument and reads the notation. With most western music, not all 12 pitches in an octave are used most of the time, but only a subset determined by the key and scale. Although the currently used notation may look weird for a newbie, it takes just a quick look at the key signature and you know which pitches will be used in a piece of music. When you know the scale (and practicing scales is just a standard part of learning), then "decoding" a note by counting tones is much easier than counting individual semitones (12 seems just too many). After a little practice you get it intuitively and you really don't count; you just know where each tone (or chord) is in a given scale and what function it has. And then when you suddenly see an additional flat or sharp symbol before a note, you know that this is an out-of-scale note, so it is also easier to play it. Disclaimer: I'm an engineer.

[andrepd]

That completely misses the point. Without wanting to sound brash, you know jack about music and you should act accordingly, that is, don't spout ill informed suggestions when you clearly don't play an instrument or studied this mater well enough to give an informed opinion.

Scales have 7 notes, not 12. A musician plays music in a scale, they aren't a computer outputting pitches, they are a person playing notes. Music notation has a reason to be this way: notes in the scale don't have flats or sharps next to them, accidentals do. Reducing everything to a number describing absolute pitches is the right thing to do for a computer to play (see midi). It's not the way to go for a person that actually has to understand the logic and patterns in the music.

[meggar]

What would D Flat be, 0.5? what about D Double flat?

[hiddenkrypt]

Db would be 01. Dbb would be 00. (or 11 and 10 for the octave)

The point ajuc is making is that the flat-sharp accidentals aren't used or needed at all if you just assign numbers to each tone. There's no concept of flat or sharp, unless you want to deal with microtones.

[meggar]

The letters and flats/sharps give you key/value over frequencies, which is better than just a numeric index over a chromatic scale. Working with the keys allows for the same abstractions to be used with all 12 keys at the same time, on the same staff.

[hiddenkrypt]

I'm not really arguing one way or the other, just pointing out that they're functionally equivalent. It's two different maps keying to the same set of frequencies. The BASE12 system described above would allow for keys as well, just with a different notation. Instead of flats/sharps marked next to the clef in traditional sheet music, the BASE12 system could start each line with a list of 'prohibited' notes. For example, when indicating that a piece is in the key of Gm, the staff in BASE12 could start with : [01,04,06,08,0b]. This indicates that the majority of the song will be made of the notes 7,9,b,0,2,3, and 5, and serves the same purpose as having two flats next to the treble clef, one on the middle line and one in the top space. Which of these systems would be easier for humans to grok is up for debate. I personally don't think either one is better.

Thinking about it, the traditional notation is just mapping to an octal system, with the key accidentals acting as modifiers to the map and the base-8 values being displayed graphically as vertical position on the staff.

[andrepd]

You need to stop thinking about things in engineer terms. The scale going 7,9,b,0,2,3 instead of G,A,B,C,D,E,F with B and E flat may be functionally identical, but one is sure a better representation of the actual patterns in the music than simply referring to a number proportional to the log(frequency).