Orwellismic family: Difference between revisions
m fix heading structure |
m Cleanup |
||
| Line 9: | Line 9: | ||
Mapping generators: ~2, ~3, ~12/7 | Mapping generators: ~2, ~3, ~12/7 | ||
Map to lattice: [{{val| 0 0 -3 1 }}, {{val| 0 1 0 1 }}] | Map to lattice: [{{val| 0 0 -3 1 }}, {{val| 0 1 0 1 }}] | ||
| Line 20: | Line 15: | ||
: 7/6 length = 0.7526, 3/2 length = 1.3931 | : 7/6 length = 0.7526, 3/2 length = 1.3931 | ||
: Angle (7/6, 3/2) = 97.5081 | : Angle (7/6, 3/2) = 97.5081 | ||
[[Minimax tuning]]: | |||
* [[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 }}] | |||
: [[Eigenmonzo]]s: 2, 4/3, 7/5 | |||
{{Val list|legend=1| 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd }} | {{Val list|legend=1| 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd }} | ||
| Line 44: | Line 44: | ||
[[Mapping]]: [{{val| 1 0 0 2 -2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 -1 5 }}] | [[Mapping]]: [{{val| 1 0 0 2 -2 }}, {{val| 0 1 0 1 1 }}, {{val| 0 0 3 -1 5 }}] | ||
Map to lattice: [{{val| 0 0 -3 1 -5 }}, {{val| 0 1 0 1 1 }}] | Map to lattice: [{{val| 0 0 -3 1 -5 }}, {{val| 0 1 0 1 1 }}] | ||
| Line 55: | Line 50: | ||
: 7/6 length = 0.5167, 3/2 length = 1.3055 | : 7/6 length = 0.5167, 3/2 length = 1.3055 | ||
: Angle (7/6, 3/2) = 79.0940 | : Angle (7/6, 3/2) = 79.0940 | ||
[[Minimax tuning]]: | |||
* [[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 }}] | |||
: [[Eigenmonzo]]s: 2, 11/8, 7/5 | |||
{{Val list|legend=1| 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd }} | {{Val list|legend=1| 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd }} | ||
| Line 64: | Line 64: | ||
Scales: [[guanyin22]] | Scales: [[guanyin22]] | ||
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]] | ||
| Line 96: | Line 95: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Orwellismic]] | [[Category:Orwellismic family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
[[Category:Guanyin]] | [[Category:Guanyin]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Revision as of 11:07, 11 June 2021
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
Map 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
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [3/2 3/4 3/4 -3/4⟩, [3/2 3/4 -1/4 1/4⟩]
- Eigenmonzos: 2, 4/3, 7/5
Badness: 0.187 × 10-3
Projection pair: 5 1728/343 to 2.3.7
Scales: orwellismic9
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]]
Badness: 0.715 × 10-3
Guanyin
Comma list: 176/175, 540/539
Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 1 1], ⟨0 0 3 -1 5]]
Map 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
- [[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⟩]
- Eigenmonzos: 2, 11/8, 7/5
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]]
Vals: Template:Val list
Badness: 0.758 × 10-3
Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7
Georgian
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]]
Vals: Template:Val list
Badness: 0.904 × 10-3
Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7