Re: Diatonic notation system

[Hans Aberg]

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