|
|
| Line 323: |
Line 323: |
|
| |
|
| [[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263 | | [[EDT]]s: 99, 17, 82, 116, 181, 65, 14[-5], 280, 48, 215, 31, 133, 314, 263 |
|
| |
| == Fomalhaut ==
| |
| The 23-limit version of Fomalhaut was created first, as an attempt to approximate the no-2s, no-7s 23-limit as accurately as possible using 25 to 35 notes per equave. Then the lower limit versions were created by simply extrapolating the temperament downwards.
| |
|
| |
| Fomalhaut follows the convention of naming no-twos temperaments after stars.
| |
|
| |
| <pre>
| |
| Reduced Mapping
| |
| 3 5 11
| |
| [ ⟨ 1 5 1 ]
| |
| ⟨ 0 -9 3 ] ⟩
| |
|
| |
| TE Generator Tunings (cents)
| |
| ⟨1903.7622, 748.1091]
| |
|
| |
| TE Step Tunings (cents)
| |
| ⟨61.30782, 5.67101]
| |
|
| |
| TE Tuning Map (cents)
| |
| ⟨1903.762, 2785.829, 4148.089]
| |
|
| |
| TE Mistunings (cents)
| |
| ⟨1.807, -0.485, -3.228]
| |
|
| |
| Complexity 1.299882
| |
| Adjusted Error 2.972273 cents
| |
| TE Error 0.859180 cents/octave
| |
|
| |
| Unison Vector
| |
| [-8, 1, 3⟩ (6655:6561)
| |
|
| |
| Subsets
| |
| b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff
| |
| </pre>
| |
|
| |
| === 3.5.11.13 ===
| |
| <pre>
| |
| Reduced Mapping
| |
| 3 5 11 13
| |
| [ ⟨ 1 5 1 -2 ]
| |
| ⟨ 0 -9 3 11 ] ⟩
| |
|
| |
| TE Generator Tunings (cents)
| |
| ⟨1905.7904, 749.5240]
| |
|
| |
| TE Step Tunings (cents)
| |
| ⟨40.98455, 22.97646]
| |
|
| |
| TE Tuning Map (cents)
| |
| ⟨1905.790, 2783.236, 4154.362, 4433.183]
| |
|
| |
| TE Mistunings (cents)
| |
| ⟨3.835, -3.077, 3.044, -7.345]
| |
|
| |
| Complexity 1.561892
| |
| Adjusted Error 6.495941 cents
| |
| TE Error 1.755451 cents/octave
| |
|
| |
| Unison Vectors
| |
| [-8, 1, 3, 0⟩ (6655:6561)
| |
| [1, 2, -5, 3⟩ (164775:161051)
| |
| [-7, 3, -2, 3⟩ (274625:264627)
| |
| [-15, 4, 1, 3⟩ (15104375:14348907)
| |
|
| |
| Subsets
| |
| b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ff
| |
| </pre>
| |
|
| |
| === 3.5.11.13.17 ===
| |
| <pre>
| |
| Reduced Mapping
| |
| 3 5 11 13 17
| |
| [ ⟨ 1 5 1 -2 1 ]
| |
| ⟨ 0 -9 3 11 4 ] ⟩
| |
|
| |
| TE Generator Tunings (cents)
| |
| ⟨1905.8711, 749.5638]
| |
|
| |
| TE Step Tunings (cents)
| |
| ⟨40.71768, 23.20533]
| |
|
| |
| TE Tuning Map (cents)
| |
| ⟨1905.871, 2783.281, 4154.563, 4433.460, 4904.126]
| |
|
| |
| TE Mistunings (cents)
| |
| ⟨3.916, -3.033, 3.245, -7.068, -0.829]
| |
|
| |
| Complexity 1.418914
| |
| Adjusted Error 6.431616 cents
| |
| TE Error 1.573498 cents/octave
| |
|
| |
| Unison Vectors
| |
| [-2, 1, -2, 1, 1⟩ (1105:1089)
| |
| [-5, 0, 1, -1, 2⟩ (3179:3159)
| |
| [-5, 2, 0, 2, -1⟩ (4225:4131)
| |
| [-8, 1, 3, 0, 0⟩ (6655:6561)
| |
| [-3, 1, 2, 1, -2⟩ (7865:7803)
| |
| [1, 0, -4, 0, 3⟩ (14739:14641)
| |
|
| |
| Subsets
| |
| b28, b5p, b33, b23f, b61, b56f, b38c, b10cf, b66c, b51ffg
| |
| </pre>
| |
|
| |
| === 3.5.11.13.17.19 ===
| |
| <pre>
| |
| Reduced Mapping
| |
| 3 5 11 13 17 19
| |
| [ ⟨ 1 5 1 -2 1 7 ]
| |
| ⟨ 0 -9 3 11 4 -11 ] ⟩
| |
|
| |
| TE Generator Tunings (cents)
| |
| ⟨1905.9598, 749.5710]
| |
|
| |
| TE Step Tunings (cents)
| |
| ⟨41.63378, 22.43072]
| |
|
| |
| TE Tuning Map (cents)
| |
| ⟨1905.960, 2783.660, 4154.673, 4433.362, 4904.244, 5096.437]
| |
|
| |
| TE Mistunings (cents)
| |
| ⟨4.005, -2.654, 3.355, -7.166, -0.712, -1.076]
| |
|
| |
| Complexity 1.449992
| |
| Adjusted Error 6.125446 cents
| |
| TE Error 1.441985 cents/octave
| |
|
| |
| Unison Vectors
| |
| [-5, 0, 0, 1, 0, 1⟩ (247:243)
| |
| [0, 2, 0, 1, -1, -1⟩ (325:323)
| |
| [-2, 1, -2, 1, 1, 0⟩ (1105:1089)
| |
| [-3, -1, 2, 0, -1, 1⟩ (2299:2295)
| |
| [-5, 0, 1, -1, 2, 0⟩ (3179:3159)
| |
| [0, 0, -1, 2, -2, 1⟩ (3211:3179)
| |
| [-5, 2, 0, 2, -1, 0⟩ (4225:4131)
| |
| [-5, 2, 1, 0, 1, -1⟩ (4675:4617)
| |
|
| |
| Subsets
| |
| b28, b33, b5p, b61, b56f, b23f, b38ch, b66ch, b89fgh, b10cfh
| |
| </pre>
| |
|
| |
| === 3.5.11.13.17.19.23 ===
| |
| <pre>
| |
| Reduced Mapping
| |
| 3 5 11 13 17 19 23
| |
| [ ⟨ 1 5 1 -2 1 7 6 ]
| |
| ⟨ 0 -9 3 11 4 -11 -8 ] ⟩
| |
|
| |
| TE Generator Tunings (cents)
| |
| ⟨1905.4824, 749.4748]
| |
|
| |
| TE Step Tunings (cents)
| |
| ⟨38.60323, 24.98764]
| |
|
| |
| TE Tuning Map (cents)
| |
| ⟨1905.482, 2782.139, 4153.907, 4433.258, 4903.382, 5094.154, 5437.096]
| |
|
| |
| TE Mistunings (cents)
| |
| ⟨3.527, -4.175, 2.589, -7.270, -1.574, -3.359, 8.822]
| |
|
| |
| Complexity 1.382541
| |
| Adjusted Error 7.087107 cents
| |
| TE Error 1.566709 cents/octave
| |
|
| |
| Unison Vectors
| |
| [-2, 0, 1, 0, 0, 1, -1⟩ (209:207)
| |
| [1, 1, -1, 0, 1, 0, -1⟩ (255:253)
| |
| [-3, 0, -1, 1, 0, 0, 1⟩ (299:297)
| |
| [0, 2, 0, 1, -1, -1, 0⟩ (325:323)
| |
| [-5, 2, 1, 0, 1, -1, 0⟩ (4675:4617)
| |
| [0, -2, -1, 1, -1, 2, 0⟩ (4693:4675)
| |
|
| |
| Subsets
| |
| b28, b5p, b33, b23f, b61, b56f, b38ch, b10cfhi, b66ch, b51ffg
| |
| </pre>
| |
|
| |
|
| = 3.7.11 subgroup temperaments = | | = 3.7.11 subgroup temperaments = |