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Re: Diatonic notation system

From: Hans Aberg
Subject: Re: Diatonic notation system
Date: Sun, 7 Dec 2008 16:27:49 +0100

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
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.


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