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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: |
Tue, 21 Sep 2010 18:28:28 +0200 |
On 21 Sep 2010, at 16:52, Carl Sorensen wrote:
Here are scans from the relevant section of Stone's book. It
explicitly
*says* that natural+1/4 and sharp-1/4 are enharmonic equivalents,
and that
the notation for those pitches must be chosen with care.
Another interpretation might be slightly sharp/flat, that is, not
exact E24. Exact quarter-tones look like these, or some variation:
http://en.wikipedia.org/wiki/Modern_musical_symbols#Quarter-tone_accidentals
Assume it is a small amount, denote the interval of the up (resp.
down) arrow by n-m (resp. m-n), where n is a neutral second. Then
sharp + down = (M-m)+(m-n) = M-n, which is an accidental that would be
needed. And also flat + up = (m-M) + (n-m) = n-M. Call these large up
and large down.
My algorithm produces the accidental as a combination of these four:
up, down, large up and large down. But the accidentals can be
rewritten. Here, I reasoned that it would be simplest first finding
the smallest amount of accidentals and then rewrite them.
So if one gets a M-n, rewrite it to (M-m)+(m-n), add 1 to the number
of sharps to typeset, and then select the symbol with the down arrow.
Similarly, rewrite n-M to (m-M) + (n-m), add 1 to the number flats,
and then select the symbol with the up arrow.
The implementation would need to just do the rewriting, because the
selection is done by a map from positive coefficient linear
combinations of pairs of seconds (which is the internal representation
of accidentals). In other words, the rewriting is done as to make sure
one is choosing from the set of existing symbols.
Re: Lilypond's internal pitch representation and microtonal notation, Han-Wen Nienhuys, 2010/09/21
Re: Lilypond's internal pitch representation and microtonal notation, Joseph Wakeling, 2010/09/21
Re: Lilypond's internal pitch representation and microtonal notation,
Hans Aberg <=