Lehmerismic temperaments: Difference between revisions
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Badness: 0.653 × 10<sup>-3</sup> | Badness: 0.653 × 10<sup>-3</sup> | ||
= Lux = | |||
== 7-limit == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 26843545600/26795786661 | |||
[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 4 -1 }}, {{val| 0 0 -5 -2 }}] | |||
{{Multival|legend=1|rank=3| 5 2 13 30 }} | |||
[[POTE generator]]s: ~3/2 = 702.1152, ~40960/35721 = 235.5941 | |||
{{Val list|legend=1| 41, 87, 128, 142, 178, 183, 224, 270, 494, 764, 1034, 1798, 6428bcdd, 8226bbcddd }} | |||
[[Badness]]: 1.709 × 10<sup>-3</sup> | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 3025/3024, 131072/130977 | |||
[[Mapping]]: [{{val| 1 0 0 6 5 }}, {{val| 0 1 4 -1 -3 }}, {{val| 0 0 -5 -2 4 }}] | |||
{{Multival|legend=1|rank=3| 5 2 -4 13 -1 10 30 25 34 71 }} | |||
[[POTE generator]]s: ~3/2 = 702.1117, ~55/48 = 235.5784 | |||
{{Val list|legend=1| 41, 87, 137, 178, 183, 224, 270, 494, 764, 1839, 2109, 2603, 3367d }} | |||
[[Badness]]: 0.5083 × 10<sup>-3</sup> | |||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 2080/2079, 3025/3024, 4096/4095 | |||
Mapping: [{{val| 1 0 0 6 5 6 }}, {{val| 0 1 4 -1 -3 -5 }}, {{val| 0 0 -5 -2 4 7 }}] | |||
POTE generators: ~3/2 = 702.0674, ~55/48 = 235.5870 | |||
Vals: {{Val list| 41, 46, 87, 137, 178, 183, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }} | |||
Badness: 0.3602 × 10<sup>-3</sup> | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 07:46, 28 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
Lux
7-limit
Subgroup: 2.3.5.7
Comma list: 26843545600/26795786661
Mapping: [⟨1 0 0 6], ⟨0 1 4 -1], ⟨0 0 -5 -2]]
Wedgie: ⟨⟨⟨ 5 2 13 30 ]]]
POTE generators: ~3/2 = 702.1152, ~40960/35721 = 235.5941
Badness: 1.709 × 10-3
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 131072/130977
Mapping: [⟨1 0 0 6 5], ⟨0 1 4 -1 -3], ⟨0 0 -5 -2 4]]
Wedgie: ⟨⟨⟨ 5 2 -4 13 -1 10 30 25 34 71 ]]]
POTE generators: ~3/2 = 702.1117, ~55/48 = 235.5784
Badness: 0.5083 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095
Mapping: [⟨1 0 0 6 5 6], ⟨0 1 4 -1 -3 -5], ⟨0 0 -5 -2 4 7]]
POTE generators: ~3/2 = 702.0674, ~55/48 = 235.5870
Vals: Template:Val list
Badness: 0.3602 × 10-3