SN scale

A Step-nested scale, or SN scale, is a scale generated through iteratively placing an incidence of

a) A new small(est) step at the top or bottom of every existing step, or

b) The existing small(est) step at the top or bottom of every larger step

The diatonic scale, for example, can be generated by iterating a) twice, introducing first the octave, then the perfect fifth, and then iterating b) 3 times

MET-24 can be generated from the diatonic scale by iterating b) once more, and then applying a), introducing a quarter-tone type step.

The double harmonic scale can be generated by iterating a) three times, introducing first the octave, then the fifth, then the major third, leading to a major seven tetrad, and then applying b) once.

Each iteration of a) increasing the rank of the scale by 1.

An SN scale of rank 2, a 2-SN scale, is a MOS scale. Accordingly, SN scales are a generalization of MOS scales into arbitrary rank.