Horwell temperaments: Difference between revisions
→Oquatonic: normalize mappings and generators |
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Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
Comma list: 65625/65536, 250047/250000 | [[Comma list]]: 65625/65536, 250047/250000 | ||
Mapping: [{{val|3 5 7 8}}, {{val|0 -7 -1 12}}] | [[Mapping]]: [{{val|3 5 7 8}}, {{val|0 -7 -1 12}}] | ||
{{Multival|legend=1|21 3 -36 -44 -116 -92}} | {{Multival|legend=1|21 3 -36 -44 -116 -92}} | ||
POTE generator: ~5/4 = 385.964 | [[POTE generator]]: ~5/4 = 385.964 | ||
{{Val list|legend=1| 3, 84, 87, 171 }} | |||
Badness: 0.028406 | [[Badness]]: 0.028406 | ||
=== 11-limit === | === 11-limit === | ||
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POTE generator: ~5/4 = 386.020 | POTE generator: ~5/4 = 386.020 | ||
Optimal GPV sequence: {{Val list| 3, 84, 87, 171, 258, 429e }} | |||
Badness: 0.058344 | Badness: 0.058344 | ||
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POTE generator: ~5/4 = 386.022 | POTE generator: ~5/4 = 386.022 | ||
Optimal GPV sequence: {{Val list| 3, 84, 87, 171, 258, 429ef }} | |||
Badness: 0.029089 | Badness: 0.029089 | ||
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== Fifthplus == | == Fifthplus == | ||
Fifthplus (22&171) tempers out the sesesix comma, {{monzo|-74 13 23}} in the 5-limit. The name "fifthplus" means using a sharp fifth interval (such as [[superpyth]] fifth) as a generator. | Fifthplus (22&171) tempers out the sesesix comma, {{monzo|-74 13 23}} in the 5-limit. The name "fifthplus" means using a sharp fifth interval (such as [[superpyth]] fifth) as a generator. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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== Emkay == | == Emkay == | ||
[[Emkay]] (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out. | [[Emkay]] (87&224) tempers out the same 5-limit comma as the [[Hemimean clan #Emka|emka temperament]] (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~11/8 = 551.7746 | POTE generator: ~11/8 = 551.7746 | ||
Optimal GPV sequence: {{Val list| 87, 137, 224, 311, 535, 1381ce, 1916ce }} | |||
Badness: 0.035586 | Badness: 0.035586 | ||
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POTE generator: ~11/8 = 551.7749 | POTE generator: ~11/8 = 551.7749 | ||
Optimal GPV sequence: {{Val list| 87, 137, 224, 311, 535, 1916cef, 2451cceff, 2986cceeff }} | |||
Badness: 0.017853 | Badness: 0.017853 | ||
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POTE generator: ~121/112 = 132.1864 | POTE generator: ~121/112 = 132.1864 | ||
Optimal GPV sequence: {{Val list| 109, 118, 345de, 463de, 581dde }} | |||
Badness: 0.052693 | Badness: 0.052693 | ||
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POTE generator: ~13/12 = 132.1789 | POTE generator: ~13/12 = 132.1789 | ||
Optimal GPV sequence: {{Val list| 109, 118f, 227f }} | |||
Badness: 0.046695 | Badness: 0.046695 | ||
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== Oquatonic == | == Oquatonic == | ||
The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28. | The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the [[Hemfiness temperaments|hemfiness]] (4096000/4084101, saquinru-atriyo). In this temperament, major third of [[5/4]] is mapped into 9\28. | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~3/2 = 702.0186 | POTE generator: ~3/2 = 702.0186 | ||
Optimal GPV sequence: {{Val list| 84, 140, 224, 364, 588, 1400cd, 1988cd, 2576ccdd }} | |||
Badness: 0.047853 | Badness: 0.047853 | ||
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POTE generator: ~3/2 = 702.0288 | POTE generator: ~3/2 = 702.0288 | ||
Optimal GPV sequence: {{Val list| 84, 140, 224, 364, 588 }} | |||
Badness: 0.021968 | Badness: 0.021968 | ||