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


Line 25: Line 25:
[[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


Line 60: Line 60:
[[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 }}]


Vals: {{Val list| 22, 31, 53, 58, 80, 111, 280cdf, 391cdf }}
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'''.


=== Georgian  ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 87: Line 89:
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 }}]


Vals: {{Val list| 9, 31, 46, 48, 58 }}
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]]