User:Inthar/Generator variety

If a scale has a generator sequence, then the generator variety is the number of generators in that sequence, not including the closing generator.

Relationship between step variety and generator variety

• MOS scales have step variety 2 and generator variety 1
• MOS substitution scales have step variety 3 and generator variety 2
• However, not all scales with generator variety n have step variety at most n + 1: Consider a 13-note scale with a well-formed generator sequence GS(x, y, y, x, y) and suppose one scale step is reached via 4 generators: xyyxyxyyxyxyz. Then there are 4 step sizes: 2x + 2y, x + 3y, 2x + y + z, and x + 2y + z. More trivially, a MOS generator when not stacked so that the resulting scale is a MOS size (denominator of semiconvergent to the generator) will not have variety 2.