Lehmerismic temperaments: Difference between revisions
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These are rank-3 temperaments tempering out [[3025/3024]], | These are rank-3 temperaments tempering out [[3025/3024]]. Temperaments discussed elsewhere are: | ||
* ''[[Oxpecker]]'', {121/120, 126/125} → [[Starling family #Oxpecker|Starling family]] | |||
* ''[[Manwe]]'', {176/175, 1331/1323} → [[Valinorsmic temperaments #Manwe|Valinorsmic temperaments]] | |||
* ''[[Spectacle]]'', {225/224, 243/242} → [[Marvel family #Spectacle|Marvel family]] | |||
* ''[[Portent]]'', {385/384, 441/440} → [[Gamelismic family #Portent|Gamelismic family]] | |||
* ''[[Indra]]'', {540/539, 1375/1372} → [[Mirkwai family #Indra|Mirkwai family]] | |||
* ''[[Tolerant]]'', {896/891, 2200/2187} → [[Pentacircle temperaments #Tolerant|Pentacircle temperaments]] | |||
* ''[[Freya]]'', {2401/2400, 3025/3024} → [[Breed family #Freya|Breed family]] | |||
* ''[[Triglav]]'', {3025/3024, 3136/3125} → [[Hemimean family #Triglav|Hemimean family]] | |||
* ''[[Thor]]'', {3025/3024, 4375/4374} → [[Ragismic family #Thor|Ragismic family]] | |||
* ''[[Kapo]]'', {3025/3024, 5120/5103} → [[Hemifamity family #Kapo|Hemifamity family]] | |||
Considered below are tyr, skadi, ganesha, hanuman, lux, and galaxy, but we can begin by looking at the rank-4 temperament. | |||
== Lehmerismic == | == Lehmerismic == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
[[Comma list]]: 3025/3024 | [[Comma list]]: [[3025/3024]] | ||
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 1 2 }}, {{val| 0 0 1 0 -1 }}, {{val| 0 0 0 2 1 }}] | ||
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== Tyr == | == Tyr == | ||
{{ | {{See also| Landscape family }} | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== Skadi == | == Skadi == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== Ganesha == | == Ganesha == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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== Hanuman == | == Hanuman == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}] | Mapping: [{{val| 1 2 0 -8 1 -6 }}, {{val| 0 -3 0 11 1 3 }}, {{val| 0 0 1 4 1 4 }}] | ||
Vals: {{Val list| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }} | Vals: {{Val list| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }} | ||
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[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 4 -1 }}, {{val| 0 0 -5 -2 }}] | [[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 4 -1 }}, {{val| 0 0 -5 -2 }}] | ||
Mapping generators: ~2, ~3, ~40960/35721 | |||
{{Multival|legend=1|rank=3| 5 2 13 30 }} | {{Multival|legend=1|rank=3| 5 2 13 30 }} | ||
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{{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }} | {{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }} | ||
[[Badness]]: 1. | [[Badness]]: 1.71 × 10<sup>-3</sup> | ||
=== 11-limit === | === 11-limit === | ||
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{{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }} | {{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }} | ||
[[Badness]]: 0. | [[Badness]]: 0.508 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Vals: {{Val list| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }} | Vals: {{Val list| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }} | ||
Badness: 0. | Badness: 0.360 × 10<sup>-3</sup> | ||
== Galaxy == | == Galaxy == | ||
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{{Val list|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }} | {{Val list|legend=1| 46, 103, 121, 149, 167, 224, 270, 494, 764, 1631, 1901, 2395, 2665 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.841 × 10<sup>-3</sup> | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: [{{val| 1 0 5 -4 -5 -4 }}, {{val| 0 1 3 -3 -3 -4 }}, {{val| 0 0 -9 14 16 17 }}] | Mapping: [{{val| 1 0 5 -4 -5 -4 }}, {{val| 0 1 3 -3 -3 -4 }}, {{val| 0 0 -9 14 16 17 }}] | ||
POTE generators: ~3/2 = 701.9368, ~484/273 = 991.0597 | POTE generators: ~3/2 = 701.9368, ~484/273 = 991.0597 | ||
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Vals: {{val list| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }} | Vals: {{val list| 46, 75e, 103, 121, 149, 224, 270, 494, 764, 1137, 1258, 1361, 1631, 2125 }} | ||
Badness: 0. | Badness: 0.463 × 10<sup>-3</sup> | ||
=== 17-limit === | === 17-limit === | ||
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Mapping: [{{val| 1 0 5 -4 -5 -4 -1 }}, {{val| 0 1 3 -3 -3 -4 -2 }}, {{val| 0 0 -9 14 16 17 10 }}] | Mapping: [{{val| 1 0 5 -4 -5 -4 -1 }}, {{val| 0 1 3 -3 -3 -4 -2 }}, {{val| 0 0 -9 14 16 17 10 }}] | ||
POTE generators: ~3/2 = 702.1144, ~85/48 = 991.1035 | POTE generators: ~3/2 = 702.1144, ~85/48 = 991.1035 | ||
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Vals: {{val list| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }} | Vals: {{val list| 46, 75e, 103, 121, 149, 167, 224, 270, 494g }} | ||
Badness: 0. | Badness: 0.933 × 10<sup>-3</sup> | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||