Orwellismic family: Difference between revisions

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== Orwellismic ==
== Orwellismic ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 1728/1715
[[Comma list]]: 1728/1715


[[Mapping]]: [{{val| 1 0 0 2 }}, {{val| 0 1 0 1 }}, {{val| 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


[[Mapping to lattice]]: [{{val| 0 0 -3 1 }}, {{val| 0 1 0 1 }}]
[[Mapping to lattice]]: {{mapping| 0 0 -3 1 | 0 1 0 1 }}


Lattice basis:  
Lattice basis:  
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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| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 3/2 3/4 3/4 -3/4 }}, {{monzo| 3/2 3/4 -1/4 1/4 }}]
: {{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]]s (unchanged-intervals): 2, 4/3, 7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.3.7/5


{{Optimal ET sequence|legend=1| 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd }}
{{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]]: 0.187 × 10<sup>-3</sup>
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Scales: [[orwellismic9]]
Scales: [[orwellismic9]]
== Orwellian ==
Subgroup: 2.3.5.7.11
[[Comma list]]: 99/98, 385/384
[[Mapping]]: [{{val| 1 0 0 2 5 }}, {{val| 0 1 0 1 0 }}, {{val| 0 0 3 -1 -2 }}]
{{Optimal ET sequence|legend=1| 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee }}
[[Badness]]: 0.715 × 10<sup>-3</sup>


== Guanyin ==
== Guanyin ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 176/175, 540/539
[[Comma list]]: 176/175, 540/539


[[Mapping]]: [{{val| 1 0 0 2 -2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 -1 5 }}]
{{Mapping|legend=1| 1 0 0 2 -2 | 0 1 0 1 1 | 0 0 3 -1 5 }}


Mapping to lattice: [{{val| 0 0 -3 1 -5 }}, {{val| 0 1 0 1 1 }}]
Mapping to lattice: {{mapping| 0 0 -3 1 -5 | 0 1 0 1 1 }}


Lattice basis:  
Lattice basis:  
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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]]s (unchanged-intervals): 2, 11/8, 7/5
: [[Eigenmonzo basis|Eigenmonzo (unchanged-interval) basis]]: 2.11.7/5


{{Optimal ET sequence|legend=1| 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd }}
{{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cd }}


[[Badness]]: 0.411 × 10<sup>-3</sup>
[[Badness]]: 0.411 × 10<sup>-3</sup>
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; Music:  
; Music:  
* [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 ===
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Comma list: 176/175, 351/350, 540/539
Comma list: 176/175, 351/350, 540/539


Mapping: [{{val| 1 0 0 2 -2 3 }}, {{val| 0 1 0 1 1 -2 }}, {{val| 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=1| 22, 31, 53, 58, 80, 111, 280cdf, 391cdf }}
{{Optimal ET sequence|legend=1| 22, 27e, 31, 53, 58, 80, 111, 280cdf }}


Badness: 0.758 × 10<sup>-3</sup>
Badness: 0.758 × 10<sup>-3</sup>
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=== Georgian ===
=== Georgian ===
This temperament is also called as '''avalokita'''.
This temperament is also known as '''avalokita'''.


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Comma list: 144/143, 176/175, 196/195
Comma list: 144/143, 176/175, 196/195


Mapping: [{{val| 1 0 0 2 -2 6 }}, {{val| 0 1 0 1 1 1 }}, {{val| 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=1| 9, 31, 46, 48, 58 }}
{{Optimal ET sequence|legend=1| 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff }}


Badness: 0.904 × 10<sup>-3</sup>
Badness: 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
== Orwellian ==
[[Subgroup]]: 2.3.5.7.11
[[Comma list]]: 99/98, 385/384
{{Mapping|legend=1| 1 0 0 2 5 | 0 1 0 1 0 | 0 0 3 -1 -2 }}
{{Optimal ET sequence|legend=1| 4, 5, 9, 17, 22, 31, 53, 84e }}
[[Badness]]: 0.715 × 10<sup>-3</sup>


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 09:20, 29 June 2023

The orwellismic family of rank-3 temperaments tempers out the orwellisma, 1728/1715.

Orwellismic

Subgroup: 2.3.5.7

Comma list: 1728/1715

Mapping: [⟨1 0 0 2], ⟨0 1 0 1], ⟨0 0 3 -1]]

mapping generators: ~2, ~3, ~12/7

Mapping to lattice: [⟨0 0 -3 1], ⟨0 1 0 1]]

Lattice basis:

7/6 length = 0.7526, 3/2 length = 1.3931
Angle (7/6, 3/2) = 97.5081

Minimax tuning:

[[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 (unchanged-interval) basis: 2.3.7/5

Optimal ET sequence: 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d

Badness: 0.187 × 10-3

Projection pair: ~5 = 1728/343 to 2.3.7

Scales: orwellismic9

Guanyin

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539

Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 1 1], ⟨0 0 3 -1 5]]

Mapping to lattice: [⟨0 0 -3 1 -5], ⟨0 1 0 1 1]]

Lattice basis:

7/6 length = 0.5167, 3/2 length = 1.3055
Angle (7/6, 3/2) = 79.0940

Minimax tuning:

[[1 0 0 0 0⟩, [-2/9 0 -5/9 5/9 4/9⟩, [4/3 0 1/3 -1/3 1/3⟩, [4/3 0 -2/3 2/3 1/3⟩, [0 0 0 0 1⟩]
Eigenmonzo (unchanged-interval) basis: 2.11.7/5

Optimal ET sequence: 22, 27e, 31, 53, 58, 80, 111, 280cd

Badness: 0.411 × 10-3

Projection pairs: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7

Scales: guanyin22

Music

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 540/539

Mapping: [⟨1 0 0 2 -2 3], ⟨0 1 0 1 1 -2], ⟨0 0 3 -1 5 5]]

Optimal ET sequence: 22, 27e, 31, 53, 58, 80, 111, 280cdf

Badness: 0.758 × 10-3

Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7

Georgian

This temperament is also known as avalokita.

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 196/195

Mapping: [⟨1 0 0 2 -2 6], ⟨0 1 0 1 1 1], ⟨0 0 3 -1 5 -5]]

Optimal ET sequence: 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff

Badness: 0.904 × 10-3

Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7

Orwellian

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384

Mapping: [⟨1 0 0 2 5], ⟨0 1 0 1 0], ⟨0 0 3 -1 -2]]

Optimal ET sequence: 4, 5, 9, 17, 22, 31, 53, 84e

Badness: 0.715 × 10-3

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