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Re: Lilypond's internal pitch representation and microtonal notation

From: Benkő Pál
Subject: Re: Lilypond's internal pitch representation and microtonal notation
Date: Tue, 21 Sep 2010 21:31:10 +0200

> 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.

a minor point: wouldn't it be clearer to use d (degree) and a (alteration)
instead of M and m?  d should be a second, i.e. M (or m), while a should
be the augmented prime, i.e. M - m.
then multiples of d gives the staff system (very roughly equivalent to
the diatonic scale), linear combinations of d and a would give the usual
chromatic system (all notes that can be notated with sharps and flats),
and for microtonal and exotic music one should use (one or several) n.

anyway, I'm a big fan of using such a system: I've tried Pythagorean
and meantone MIDI-output by defining alterations, and MIDI was all
right, but the score had all the naturals which weren't defined to
be exactly zero (i.e. all except a); your system distinguishes nicely
between pitch systems and tuning (thoretical pitch and its physical


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