Re: Diatonic notation system

[Hans Aberg]

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.

> 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.

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.

  Hans