Orwellismic family: Difference between revisions
Cmloegcmluin (talk | contribs) link for mapping to lattice |
mNo edit summary |
||
| Line 1: | Line 1: | ||
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 | ||
| Line 40: | Line 40: | ||
[[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]] | ||
| Line 67: | Line 67: | ||
* [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 | ||
| Line 74: | Line 74: | ||
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 | ||
| 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 }}] | ||
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]] | ||
Revision as of 14:16, 30 January 2022
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
- 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 (unchanged intervals): 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]]
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
- [[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 (unchanged intervals): 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]]
Optimal GPV sequence: Template:Val list
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 called 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 GPV sequence: Template:Val list
Badness: 0.904 × 10-3
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7