Mavila: Difference between revisions
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| Title = Mavila | | Title = Mavila | ||
| Subgroups = 2.3.5, 2.3.5.11 | | Subgroups = 2.3.5, 2.3.5.11 | ||
| Comma basis = [[135/128]] (2.3.5)<br>[[33/32]], [[45/44]] (2.3.5.11) | | Comma basis = [[135/128]] (2.3.5);<br>[[33/32]], [[45/44]] (2.3.5.11) | ||
| Mapping = 1; 1 -3 -1 | | Mapping = 1; 1 -3 -1 | ||
| Edo join 1 = 7 | Edo join 2 = 9 | | Edo join 1 = 7 | Edo join 2 = 9 | ||
| | | Generators = 3/2 | ||
| | | Generators tuning = 679.0 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| Pergen = (P8, P5) | | Pergen = (P8, P5) | ||
| Color name = Layobiti | | Color name = Layobiti | ||
| MOS scales = [[2L 3s]], [[2L 5s]], [[7L 2s]] | | MOS scales = [[2L 3s]], [[2L 5s]], [[7L 2s]] | ||
| Odd limit 1 = 5 | Mistuning 1 = 23.0 | Complexity 1 = | | Odd limit 1 = 5 | Mistuning 1 = 23.0 | Complexity 1 = 5 | ||
| Odd limit 2 = | | Odd limit 2 = 2.3.5.11 11 | Mistuning 2 = 36.9 | Complexity 2 = 7 | ||
}} | }} | ||
'''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly very flat ({{nowrap|~{{dash|670, 680}}}}{{c}} or so), flatter than even that of [[7edo]] (4\7). Consequently, stacking 7 of these fifths gives you an [[2L 5s|antidiatonic]] [[mos scale]], where in a certain sense, major and minor intervals get reversed. For example, stacking four fifths and octave-reducing now gets you a [[6/5]] ''minor'' third, whereas stacking three fourths and octave-reducing now gets you a [[5/4]] ''major'' third. Note that since we have a heptatonic scale, terms like ''fifths'', ''thirds'', etc. make perfect sense and really are the fifth, third, etc. steps in the antidiatonic scale. | '''Mavila''' is a [[regular temperament|temperament]] where the major chroma, [[135/128]], is [[tempering out|tempered out]]. Like [[meantone]], mavila is based on the [[chain of fifths]], but as a result of tempering out 135/128 rather than [[81/80]], the fifths are supposedly very flat ({{nowrap|~{{dash|670, 680}}}}{{c}} or so), flatter than even that of [[7edo]] (4\7). Consequently, stacking 7 of these fifths gives you an [[2L 5s|antidiatonic]] [[mos scale]], where in a certain sense, major and minor intervals get reversed. For example, stacking four fifths and octave-reducing now gets you a [[6/5]] ''minor'' third, whereas stacking three fourths and octave-reducing now gets you a [[5/4]] ''major'' third. Note that since we have a heptatonic scale, terms like ''fifths'', ''thirds'', etc. make perfect sense and really are the fifth, third, etc. steps in the antidiatonic scale. | ||
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| 600.000 | | 600.000 | ||
| Lower bound of 5-odd-limit diamond monotone | | Lower bound of 5-odd-limit diamond monotone | ||
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| 11/8 | |||
| 648.682 | |||
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| 6\11 | |||
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| 654.545 | |||
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| 655.866 | | 655.866 | ||
| 1/2 comma | | 1/2 comma | ||
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| 15/11 | |||
| 663.049 | |||
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|- | |- | ||
| 5\9 | | 5\9 | ||
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| 675.000 | | 675.000 | ||
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| 11/6 | |||
| 675.319 | |||
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| 678.910 | | 678.910 | ||
| 1/4 comma, 5-odd-limit minimax | | 1/4 comma, 5-odd-limit minimax | ||
|- | |||
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| 11/10 | |||
| 682.502 | |||
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| 683.519 | | 683.519 | ||
| 1/5 comma, 5-limit 9-odd-limit minimax | | 1/5 comma, 5-limit 9-odd-limit minimax | ||
|- | |||
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| 11/9 | |||
| 684.197 | |||
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|- | |- | ||
| 4\7 | | 4\7 | ||
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| 685.714 | | 685.714 | ||
| Upper bound of 5-odd-limit diamond monotone<br | | Upper bound of 5-odd-limit diamond monotone<br>5-limit 9-odd-limit and 2.3.5.11-subgroup 11-odd-limit diamond monotone (singleton) | ||
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