User:Inthar/Generator variety: Difference between revisions
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Created page with "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 b..." Tags: Mobile edit Mobile web edit |
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* MOS scales have step variety 2 and generator variety 1 | * MOS scales have step variety 2 and generator variety 1 | ||
* MOS substitution scales have step variety 3 and generator variety 2 | * MOS substitution scales have step variety 3 and generator variety 2 | ||
* However, not all scales with generator variety '' | * 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: 2'''x''' + 2'''y''', '''x''' + 3'''y''', 2'''x''' + '''y'' + '''z''', and '''x''' + 2'''y'' + '''z'''. | ||
Revision as of 22:27, 22 May 2024
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.