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..."
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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 '''x''' have step variety '''x''' + 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'''.
* 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'''.