Orwellismic family: Difference between revisions
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Units & misc. cleanup |
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{{Technical data page}} | {{Technical data page}} | ||
The '''orwellismic family''' of rank-3 temperaments tempers out the orwellisma, [[1728/1715]]. | The '''orwellismic family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the orwellisma, [[1728/1715]]. | ||
== Orwellismic == | == Orwellismic == | ||
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{{Mapping|legend=1| 1 0 0 2 | 0 1 0 1 | 0 0 3 -1 }} | {{Mapping|legend=1| 1 0 0 2 | 0 1 0 1 | 0 0 3 -1 }} | ||
: mapping generators: ~2, ~3, ~12/7 | : mapping generators: ~2, ~3, ~12/7 | ||
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit|7-]] and [[9-odd-limit]] | * [[7-odd-limit|7-]] and [[9-odd-limit]] | ||
: {{ | : {{monzo list| 1 0 0 0 | 0 1 0 0 | 3/2 3/4 3/4 -3/4 | 3/2 3/4 -1/4 1/4 }} | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5 | ||
{{Optimal ET sequence|legend=1| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }} | {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d }} | ||
[[Badness]]: 0.187 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.187 × 10<sup>-3</sup> | ||
[[Projection pair]]: ~5 = 1728/343 to 2.3.7 | [[Projection pair]]: ~5 = 1728/343 to 2.3.7 | ||
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== Guanyin == | == Guanyin == | ||
Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]] | Guanyin is the most natural [[11-limit]] extension of orwellismic, where two ~7/6 generators make [[15/11]], tempering out [[540/539]], and two sharpened ~[[5/4]]'s make [[11/7]], tempering out [[176/175]]. | ||
[[Subgroup]]: 2.3.5.7.11 | [[Subgroup]]: 2.3.5.7.11 | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| -2/9 0 -5/9 5/9 4/9 }}, {{monzo| 4/3 0 1/3 -1/3 1/3 }}, {{monzo| 4/3 0 -2/3 2/3 1/3 }}, {{monzo| 0 0 0 0 1 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| -2/9 0 -5/9 5/9 4/9 }}, {{monzo| 4/3 0 1/3 -1/3 1/3 }}, {{monzo| 4/3 0 -2/3 2/3 1/3 }}, {{monzo| 0 0 0 0 1 }}] | ||
: [[ | : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.11.7/5 | ||
{{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cd }} | {{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cd }} | ||
[[Badness]]: 0.411 × 10<sup>-3</sup> | [[Badness]] (Smith): 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 | ||
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; Music | ; Music | ||
* ''Trio for SoftSaturn, NebulaSing and TromBonehead'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/trio-gorts SoundCloud] | [https://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 details] | [https://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] – | * ''Trio for SoftSaturn, NebulaSing and TromBonehead'' (archived 2010) by [[Gene Ward Smith]] – [https://soundcloud.com/genewardsmith/trio-gorts SoundCloud] | [https://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 details] | [https://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] – in Guanyin[22], 111edo tuning | ||
=== 13-limit === | === 13-limit === | ||
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Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }} | Mapping: {{mapping| 1 0 0 2 -2 3 | 0 1 0 1 1 -2 | 0 0 3 -1 5 5 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22, 27e, 31, 53, 58, 80, 111, 280cdf }} | ||
Badness: 0.758 × 10<sup>-3</sup> | Badness (Smith): 0.758 × 10<sup>-3</sup> | ||
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7 | Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7 | ||
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Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }} | Mapping: {{mapping| 1 0 0 2 -2 6 | 0 1 0 1 1 1 | 0 0 3 -1 5 -5 }} | ||
{{Optimal ET sequence|legend= | {{Optimal ET sequence|legend=0| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }} | ||
Badness: 0.904 × 10<sup>-3</sup> | Badness (Smith): 0.904 × 10<sup>-3</sup> | ||
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7 | Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7 | ||
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{{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }} | {{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }} | ||
[[Badness]]: 0.715 × 10<sup>-3</sup> | [[Badness]] (Smith): 0.715 × 10<sup>-3</sup> | ||
Scales: [[orwellian chromatic]] | Scales: [[orwellian chromatic]] | ||