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.
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