Re: Diatonic notation system

[Graham Breed]

2008/12/7 Hans Aberg <address@hidden>:

> 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.

Right.  But the actual fifth has to be specified so you need an init
file to do that.  The exact meaning of the alterations also have to be
specified in an init file.  So there has to be a different init file
for each Sagittal context if you want any reasonable MIDI output.

> 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.

They can be as fixed as the composer chooses.  But you can't expect a
computer to understand that interpretational context.  Specifying
fixed alterations is enough.

> So then using neutral seconds seems right.

For what?

> 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.

He does so!  There are examples on the last page.

> This is rather special, but the model I gave will work with that, too.

I am looking at other cases like this.  There's a list to discuss
microtonal tools, which started out very optimistically.  What you're
talking about are, indeed, "diatonic notations":

http://groups.google.com/group/microtools/web/diatonic-notations

I think they can be made to work in Lilypond.  The problems are:

- You have to override the standard octave numbers

- You need a different init file for MIDI and printing

I think that's about as much as we can expect given how obscure they
are.  Here's the shortlist of notation types we're trying to support:

http://groups.google.com/group/microtools/web/types-of-notation

MicroABC can do some of them.  I think Lilypond should be able to do
most of them with a bit of work.


                            Graham