Re: Diatonic notation system

[Graham Breed]

2008/12/7 Hans Aberg <address@hidden>:
> On 7 Dec 2008, at 11:42, Graham Breed wrote:
>
>> The only 12-ness is in the tuning of MIDI files, which I think you can
>> change to get extended meantone.
>
> The implementations in Turkish music seemed to force a multiple of 12,
> whereas it should be E53.

Ah.  Well, that's one configuration file, which you can change.  The
tunings are expressed as a fraction of a whole tone but I don't think
there's a limit on the precision.

>> What do you mean by "a diatonic
>> notation system"?
>
> It is what yo get by adjoining to the notes A B C D E F G, octaves, sharps
> and flats. When reducing in octaves, this is a finite system exactly when it
> is an n-equal temperament. The underlying mathematical structure is simple:
>
> It is the set of pitches that is generated by p m + q M, where p and q are
> integers, and m (resp. M) is a minor (resp. major) (abstract) second. Sharps
> (resp. flats) raise (resp. lower) with the amount M - m.

I think you can do that in the configuration files.  I haven't tried
it yet, mind.  I think you have to specify every note you might use in
advance.  At least that's the way I've always seen it.  Check that
Turkish example file.  I don't think the nominals have to start in
equal temperament.

It's all Scheme code.

There would be a problem in using a notation system with more than 7
nominals to the octave.  That's hard-wired.

(I'm talking about the development branch here.  There's a different
system for accidentals in the stable release.  But you can't be
looking at that because it doesn't have the Turkish accidentals,
right?)

> When choosing values for m and M, and a tuning frequency, one gets a tuning
> of the notated music; one of them suffices if the octave is assumed. For
> example, one extended meantone tuning popular during the Renaissance uses M
> = sqrt(5/4).
>
> One can also describe intermediate pitches on top of this. It works with
> oriental music, I think this is what the Sagittal microtonal notation system
> notation does.

Sagittal is a big set of accidentals that can have different meanings
in different contexts.  I expect there'd need to be a different
configuration file for each of those contexts when it eventually
works.

As Sagittal isn't working we are a bit short of sharp symbols.  There
are some arrowed accidentals on the way, though.


                            Graham