Canopic clan: Difference between revisions
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== Gaster == | == Gaster == | ||
{{main| Gaster temperament }} | |||
The ''gaster'' temperament (111&113) tempers out {{monzo|-70 72 -19}} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[skeetsma]] (14348907/14336000) in the 7-limit. The word "[[Wiktionary:gaster|gaster]]" means [[Wiktionary:abdomen|abdomen]] or [[Wiktionary:stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is enough to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit. | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Mapping]]: [{{val|1 11 38 37}}, {{val|0 -19 -72 -69}}] | [[Mapping]]: [{{val|1 11 38 37}}, {{val|0 -19 -72 -69}}] | ||
[[POTE generator]]: ~800/567 = 594. | {{Multival|legend=1|19 72 69 70 56 -42}} | ||
[[POTE generator]]: ~800/567 = 594.641 | |||
{{Optimal GPV sequence|legend=1| 111, 224 }} | {{Optimal GPV sequence|legend=1| 111, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1}}, {{val|0 -19 -72 -69 9}}] | Mapping: [{{val|1 11 38 37 -1}}, {{val|0 -19 -72 -69 9}}] | ||
POTE generator: ~512/363 = 594. | POTE generator: ~512/363 = 594.639 | ||
Optimal GPV sequence: {{Val list| 111, 224, 783d, 1007d, 1231dd }} | Optimal GPV sequence: {{Val list| 111, 224, 783d, 1007d, 1231dd }} | ||
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Mapping: [{{val|1 11 38 37 -1 26}}, {{val|0 -19 -72 -69 9 -45}}] | Mapping: [{{val|1 11 38 37 -1 26}}, {{val|0 -19 -72 -69 9 -45}}] | ||
POTE generator: ~55/39 = 594. | POTE generator: ~55/39 = 594.639 | ||
Optimal GPV sequence: {{Val list| 111, 224, 783df, 1007df, 1231ddf }} | Optimal GPV sequence: {{Val list| 111, 224, 783df, 1007df, 1231ddf }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14}}, {{val|0 -19 -72 -69 9 -45 -20}}] | Mapping: [{{val|1 11 38 37 -1 26 14}}, {{val|0 -19 -72 -69 9 -45 -20}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.636 | ||
Optimal GPV sequence: {{Val list| 111, 224, 559dgg }} | Optimal GPV sequence: {{Val list| 111, 224, 559dgg }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32}}, {{val|0 -19 -72 -69 9 -45 -20 -56}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32}}, {{val|0 -19 -72 -69 9 -45 -20 -56}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.636 | ||
Optimal GPV sequence: {{Val list| 111, 224 }} | Optimal GPV sequence: {{Val list| 111, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32 7}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32 7}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.641 | ||
Optimal GPV sequence: {{Val list| 111, 224 }} | Optimal GPV sequence: {{Val list| 111, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.646 | ||
Optimal GPV sequence: {{Val list| 111, 113, 224 }} | Optimal GPV sequence: {{Val list| 111, 113, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.644 | ||
Optimal GPV sequence: {{Val list| 111, 113, 224 }} | Optimal GPV sequence: {{Val list| 111, 113, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.644 | ||
Optimal GPV sequence: {{Val list| 111, 113, 224 }} | Optimal GPV sequence: {{Val list| 111, 113, 224 }} | ||
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Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27 45}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80}}] | Mapping: [{{val|1 11 38 37 -1 26 14 32 7 -11 0 -27 45}}, {{val|0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80}}] | ||
POTE generator: ~24/17 = 594. | POTE generator: ~24/17 = 594.643 | ||
Optimal GPV sequence: {{Val list| 111, 113, 224 }} | Optimal GPV sequence: {{Val list| 111, 113, 224 }} | ||