Orwellismic family: Difference between revisions
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The '''orwellismic family''' of rank-3 temperaments tempers out the orwellisma, [[1728/1715]]. | The '''orwellismic family''' of rank-3 temperaments tempers out the orwellisma, [[1728/1715]]. | ||
== Orwellismic | == Orwellismic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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[[Badness]]: 0.187 × 10<sup>-3</sup> | [[Badness]]: 0.187 × 10<sup>-3</sup> | ||
[[Projection pair]]: 5 1728/343 to 2.3.7 | [[Projection pair]]: ~5 = 1728/343 to 2.3.7 | ||
Scales: [[orwellismic9]] | Scales: [[orwellismic9]] | ||
== Orwellian | == Orwellian == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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[[Badness]]: 0.715 × 10<sup>-3</sup> | [[Badness]]: 0.715 × 10<sup>-3</sup> | ||
== Guanyin | == Guanyin == | ||
[[Comma list]]: 176/175, 540/539 | [[Comma list]]: 176/175, 540/539 | ||
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[[Badness]]: 0.411 × 10<sup>-3</sup> | [[Badness]]: 0.411 × 10<sup>-3</sup> | ||
[[Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7 | [[Projection pair]]s: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7 | ||
Scales: [[guanyin22]] | Scales: [[guanyin22]] | ||
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* [http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 Trio for SoftSaturn, NebulaSing and TromBonehead] [http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] by [[Gene Ward Smith]] | * [http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 Trio for SoftSaturn, NebulaSing and TromBonehead] [http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] by [[Gene Ward Smith]] | ||
=== 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 0 0 2 -2 3 }}, {{val| 0 1 0 1 1 -2 }}, {{val| 0 0 3 -1 5 5 }}] | Mapping: [{{val| 1 0 0 2 -2 3 }}, {{val| 0 1 0 1 1 -2 }}, {{val| 0 0 3 -1 5 5 }}] | ||
Optimal GPV sequence: {{Val list| 22, 31, 53, 58, 80, 111, 280cdf, 391cdf }} | |||
Badness: 0.758 × 10<sup>-3</sup> | Badness: 0.758 × 10<sup>-3</sup> | ||
Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7 | Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7 | ||
=== Georgian === | |||
This temperament is also called as '''avalokita'''. | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Mapping: [{{val| 1 0 0 2 -2 6 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 -1 5 -5 }}] | Mapping: [{{val| 1 0 0 2 -2 6 }}, {{val| 0 1 0 1 1 1 }}, {{val| 0 0 3 -1 5 -5 }}] | ||
Optimal GPV sequence: {{Val list| 9, 31, 46, 48, 58 }} | |||
Badness: 0.904 × 10<sup>-3</sup> | Badness: 0.904 × 10<sup>-3</sup> | ||
Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7 | Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||