In the context of characterizing a completely arbitrary instrument or piece of world music, when trying to describe the number of notes or tones per octave we tend quickly to get grounded in notions such as temperament or intonation.
I need to find a universal term for the number of notes (or tones) per octave which is completely independent of the above: a term equally applicable to
- equal temperament as just, Pythagorean, well, meantone, syntonic or tempered (and any others you may care to name)
- any number of tones per octave.
Clearly, I can have (say) nn notes or tones in an octave more or less irrespective of which temperament or intonation is in use, making nnTET, nnEDO, nnJI subsets of this higher-level definition.
I've come across cobbled-together or not-quite fitting terms such as:
- xenharmonic index (--> 'other-than-12TET')
- n tone per octave index (no abbreviation)
- tones per temperament or intonation (too specific, no abbreviation)
There must be a term that is all-encompassing, widely accepted, and has an abbreviation, right?