Lehmerismic temperaments: Difference between revisions
+links to temperaments discussed elsewhere |
Edo lists reviewed |
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| Line 23: | Line 23: | ||
Mapping generators: ~2, ~3, ~5, ~55/36 | Mapping generators: ~2, ~3, ~5, ~55/36 | ||
{{Val list|legend=1| | {{Val list|legend=1| 7d, 8d, 10, 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }} | ||
= Tyr = | = Tyr = | ||
| Line 36: | Line 36: | ||
Mapping generators: ~63/50, ~400/231, ~5 | Mapping generators: ~63/50, ~400/231, ~5 | ||
{{Val list|legend=1| 15, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566 }} | {{Val list|legend=1| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }} | ||
[[Badness]]: 0.259 × 10<sup>-3</sup> | [[Badness]]: 0.259 × 10<sup>-3</sup> | ||
| Line 50: | Line 50: | ||
Mapping generators: ~2, ~3, ~18/11 | Mapping generators: ~2, ~3, ~18/11 | ||
{{Val list|legend=1| 31, | {{Val list|legend=1| 31, 90e, 114de, 121, 152, 311, 342, 836, 1178, 2014, 3192ce, 5206ce }} | ||
[[Badness]]: 0.349 × 10<sup>-3</sup> | [[Badness]]: 0.349 × 10<sup>-3</sup> | ||
| Line 64: | Line 64: | ||
Mapping generators: ~2, ~3, ~5 | Mapping generators: ~2, ~3, ~5 | ||
{{Val list|legend=1| 31, 87, 118, 152, 239, 270, 962, 1232, 1502 }} | {{Val list|legend=1| 31, 65d, 87, 118, 152, 239, 270, 962, 1232, 1502 }} | ||
[[Badness]]: 0.390 × 10<sup>-3</sup> | [[Badness]]: 0.390 × 10<sup>-3</sup> | ||
| Line 78: | Line 78: | ||
Mapping generators: ~2, ~11/10, ~5 | Mapping generators: ~2, ~11/10, ~5 | ||
{{Val list|legend=1| 15, 57, 72, 152, 224, 311, 463, 535, 998 | {{Val list|legend=1| 15, 42bc, 49bcde, 50d, 57, 65d, 72, 152, 224, 311, 463, 535, 998 }} | ||
[[Badness]]: 0.500 × 10<sup>-3</sup> | [[Badness]]: 0.500 × 10<sup>-3</sup> | ||
| Line 92: | Line 92: | ||
Mapping generators: ~2, ~11/10, ~5 | Mapping generators: ~2, ~11/10, ~5 | ||
Vals: {{Val list| 15, 72, 87, 137, | Vals: {{Val list| 15, 50d, 57f, 65d, 72, 87, 137, 152f, 224, 311, 535, 918c }} | ||
Badness: 0.653 × 10<sup>-3</sup> | Badness: 0.653 × 10<sup>-3</sup> | ||
Revision as of 11:31, 24 May 2021
These are rank-3 temperaments tempering out 3025/3024, but we can begin by looking at the rank-4 temperament.
Temperaments discussed elsewhere are:
Lehmerismic
Subgroup: 2.3.5.7.11
Comma list: 3025/3024
Mapping: [⟨1 0 0 0 2], ⟨0 1 0 1 2], ⟨0 0 1 0 -1], ⟨0 0 0 2 1]]
Mapping generators: ~2, ~3, ~5, ~55/36
Tyr
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 102487/102400
Mapping: [⟨3 0 0 4 8], ⟨0 2 0 -4 1], ⟨0 0 1 2 0]]
Mapping generators: ~63/50, ~400/231, ~5
Badness: 0.259 × 10-3
Skadi
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 703125/702464
Mapping: [⟨1 0 5 8 1], ⟨0 1 1 3 2], ⟨0 0 -6 -14 -1]]
Mapping generators: ~2, ~3, ~18/11
Badness: 0.349 × 10-3
Ganesha
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625
Mapping: [⟨1 0 0 -22 -9], ⟨0 1 0 1 2], ⟨0 0 1 10 4]]
Mapping generators: ~2, ~3, ~5
Badness: 0.390 × 10-3
Hanuman
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993
Mapping: [⟨1 2 0 -8 1], ⟨0 -3 0 11 1], ⟨0 0 1 4 1]]
Mapping generators: ~2, ~11/10, ~5
Badness: 0.500 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079
Mapping: [⟨1 2 0 -8 1 -6], ⟨0 -3 0 11 1 3], ⟨0 0 1 4 1 4]]
Mapping generators: ~2, ~11/10, ~5
Vals: Template:Val list
Badness: 0.653 × 10-3