lilypond-devel
[Top][All Lists]

## Re: Lilypond's internal pitch representation and microtonal notation

 From: Hans Aberg Subject: Re: Lilypond's internal pitch representation and microtonal notation Date: Tue, 21 Sep 2010 15:19:38 +0200

```On 21 Sep 2010, at 14:16, Carl Sorensen wrote:

```
```A sharp is M-m and a flat m-M.
```
```
```
If I understand right, this is a key "trick" of your system, since such representations allow you to raise or lower the pitch without affecting
```the degree.

```
So by extension, if we say that q is a quarter-tone, to raise or lower by a quarter-tone would be to add (m-q) or (q-m); and to raise or lower
```by 3/4-tone would be to add (M-q) or (q-M).

```
.... but where/how in that system do we distinguish between for example
```natural + 1/4 and sharp - 1/4 .... ?  Presumably the former is (m-q)
whereas the latter is (M-m)+(q-m) ... ?
```
```
```
It seems to me that the pitches natural+1/4 and sharp - 1/4 are the same
```pitch (i.e. enharmonic equivalents) and that it is appropriate to have
either one represent the same pitch.
```
```
```
They will be the same in a particular tuning, but they may transpose differently in the staff system. Change the amount so that one raises with 1/3, then that will be paired with one lowering 2/3, and similarly, one lowering with 1/3 will be paired with one raising 2/3. The sum of those distances is that of a sharp.
```
```
In algebraic terms, choose a neutral n between m and M. The total pitch system will be i m + j M + k n, where i, j, k are integers. But the staff system only has the pitches i' m + j' M. When taking the difference with the staff note, reducing the degree to 0, and taking away the sharps/flat (a multiple of M - m), there will result a multiple n - m or n - M.
```
```
Now choose n so that n - m is neutral plus 1/3. Then n - M lowers 2/3, and m - n with 1/3. In with an exact quartertone, both will work. A sharp is M - m, so there are two candidates for sharp - 1/4: (M-m) + (m-n) = M-n and (M-m)+(n-M) = n-m.
```
```
With one choice, they are actually equal in any tuning, but with the other choice, they will become separate.
```
```
The display of the accidentals leading to that pitch should likely be a property of a key-signature that shows how to display a given pitch. I'm not sure exactly how to accomplish this, but it seems the proper logical
```structure to me.
```
```
```
So one can do both. But the staff system will work on the algebraic level.
```

```