On 7 Dec 2008, at 14:59, Graham Breed wrote:
As Sagittal isn't working we are a bit short of sharp symbols.
There
are some arrowed accidentals on the way, though.
This would be the long haul.
I made good progress during the summer. It'll hopefully work as soon
as someone looks at setting the relevant tables in the Sagittal font.
A python function in Font Forge is how I'm told it's done.
The paper
Sagittal A Microtonal Notation System
by George D. Secor and David C. Keenan
says:
The Sagittal notation uses a conventional staff on which the
natural notes are in a
single series of fifths, with sharps and flats (and doubles
thereof) indicating tones
that are members of that same series, regardless of the particular
tonal system being
notated2. Therefore, if the notation is used for just intonation,
these notes will
indicate a Pythagorean tuning. For an equal division of the
octave, they will indicate
the tones in a
series built on that division’s best approximation of a fifth.
Now, that leads to the model I indicated if one uses an abstract
perfect fifth, as the m and m can extracted from it by iteration and
octave transpositions.
It then says
To indicate alterations to tones in a chain of fifths, the
Sagittal notation makes use
of new symbols that combine three excellent features of prior
notations:
1) Arrows pointing up or down that have been used to indicate
alterations in pitch in
each direction, most often (but not always) for quartertones;
2) Multiple vertical strokes used by Tartini to indicate multiples
of a semi-sharp;
3) Sloping lines used by Bosanquet to indicate commatic
alterations in pitch.
Here I am not sure if the idea is to indicate specific pitch
alterations. The problem with that is the same as with fixing a
tuning system: it may differ with musical interpretational context,
even if one agrees on that there should be alteration.
So then using neutral seconds seems right.
There is also a paper
Tuning, Tonality, and Twenty-Two-Tone Temperament
Paul Erlich
which constructs generalized 10-tone diatonic scales in E22.
He then does not seem to realize that standard Western music notation
will work, if one only alters the number of notes per octave.
This is rather special, but the model I gave will work with that, too.
Hans
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