Rank-3 scale: Difference between revisions
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== 3-SN scales == | == 3-SN scales == | ||
The scales a…ba…c and abacaba are [[step-nested scale|step-nested]] (SN) scales, which are mirror-symmetric, and can be uniquely defined by a signature. | The scales ''a…ba…c'' and ''abacaba'' are [[step-nested scale|step-nested]] (SN) scales, which are mirror-symmetric, and can be uniquely defined by a signature. | ||
SN scales are generated iteratively by placing an instance of a new or the existing smallest step at the top or bottom of every larger step. | SN scales are generated iteratively by placing an instance of a new or the existing smallest step at the top or bottom of every larger step. | ||
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3-SN scales are generated from MOS scales, and 4-SN scales are generated from 3-SN scales, etc. | 3-SN scales are generated from MOS scales, and 4-SN scales are generated from 3-SN scales, etc. | ||
'''Conjecture''': The only SN scale that is trivalent is abacaba. | '''Conjecture''': The only SN scale that is trivalent is ''abacaba''. | ||
'''Conjecture''': The only SN scales that are MV3 are abacaba, and scales of the form a…ba…c. | '''Conjecture''': The only SN scales that are MV3 are abacaba, and scales of the form ''a…ba…c''. | ||
'''Conjecture''': The only SN scales that are MV3, and have mean variety < 3 are those of the form a…ba…c. | '''Conjecture''': The only SN scales that are MV3, and have mean variety < 3 are those of the form ''a…ba…c''. | ||
See [[Gallery of 3-SN scales]] for examples of 3-SN scales. | See [[Gallery of 3-SN scales]] for examples of 3-SN scales. | ||