User:Inthar/Generator variety: Difference between revisions
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== Relationship between step variety and generator variety == | == Relationship between step variety and generator variety == | ||
MOS scales have step variety 2 and generator variety 1 and 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: | MOS scales have step variety 2 and generator variety 1, and 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''', | # 2'''x''' + 2'''y''', | ||
# '''x''' + 3'''y''', | # '''x''' + 3'''y''', | ||