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Re: Lilypond's internal pitch representation and microtonal notation

From: Hans Aberg
Subject: Re: Lilypond's internal pitch representation and microtonal notation
Date: Wed, 22 Sep 2010 13:18:15 +0200

On 22 Sep 2010, at 08:18, Benkő Pál wrote:

I didn't mean to replace the whole of your system
by d and a, only M and m.  similarly to your P5-P8 example,
(1  0)(d) = (M)
(1 -1)(a)   (m)

But it becomes complicated when adding pitches. If one has seconds s_1, ..., s_k, then there is an accidental for each difference s_j - s_i and each s_i - s_j. With just m, M and n, one gets besides sharp M-m, flat m-M, also n-m, n-M, m-n, M-n. All four are used in Turkish music, but this system can
handle it algebraically by adding just one second n.

well, the two systems are equivalent, as M and m can be expressed by d and a: M = d, m = d-a (and n is common to both). I just think that d and a suits
better to classical music than M and n.

Your system uses M and the sharp instead of m. Then the octave will be represented by 7Mbb, a double-flat of seven M, instead of 2m+5M. Perhaps you are used thinking in terms of E12 equivalence? Because there are no values assigned to these intervals, such simplifications are not done in the first stage finding the accidentals. One will have to apply enharmonic equivalences after by adding/subtracting M - 2m. But this also gives more control over it.

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