User:Inthar/Generator variety: Difference between revisions
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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 ''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'''. | * 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'''. 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. | ||