User:CompactStar/Nonoctave extension of ups and downs notation

There seems to be somewhat less standardization of notation for nonoctave scales compared to octave-equivalent scales. So, here I will outline some notations for nonoctave scales, largely based on ups and downs notation and TAMNAMS, with the most common periods (e.g. 3/2, 3/1, 4/1) being prioritized.

3/1-equivalent notation

For no-twos scales we can apply the Pythagorean principle of using the next highest prime number as the generator, and use ~5/3 (rather than ~3/2) as a generator for the equivalent of the diatonic scale.