4L 3s/Temperaments: Difference between revisions
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Mapping generators: ~2, ~5/3 | Mapping generators: ~2, ~5/3 | ||
[[POTE generator]]: ~6/5 = 310.146 | [[POTE generator]]: ~6/5 = 310.146 | ||
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* 7- and [[9-odd-limit]] | * 7- and [[9-odd-limit]] | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| 9/10 9/10 0 0 }}, {{monzo| 17/10 7/10 0 0 }}] | ||
: [[Eigenmonzo]]s: 2, 3 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 3 | ||
{{ | {{Optimal ET sequence|legend=1| 27, 31, 58, 89 }} | ||
[[Badness]]: 0.0270 | [[Badness]]: 0.0270 | ||
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[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[diamond monotone]] range: [300.000, 327.273] (4 to 11b) | * [[diamond monotone]] range: [300.000, 327.273] (4 to 11b) | ||
* [[diamond | * [[diamond tradeoff]] range: [315.641, 317.263] | ||
* | * diamond monotone and tradeoff range: [315.641, 317.263] | ||
{{ | {{Optimal ET sequence|legend=1| 15, 19, 34, 53, 458, 511c, …, 882c }} | ||
== Orgone == | == Orgone == | ||
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POTE generator: ~77/64 = 323.372 | POTE generator: ~77/64 = 323.372 | ||
Sval | Sval mapping: [<1 2 4|, <0 3 -2|] | ||
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc | EDOs: {{EDOs|7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc}} | ||
== Dual-3 Sixix == | == Dual-3 Sixix == | ||
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2.9.5 POTE generator: 335.8409 | 2.9.5 POTE generator: 335.8409 | ||
{{ | {{Optimal ET sequence|legend=1| 18, 25, 43 }} | ||
== Sixix == | == Sixix == | ||
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POTE generator: ~6/5 = 338.365 | POTE generator: ~6/5 = 338.365 | ||
{{ | {{Optimal ET sequence|legend=1| 7, 25, 32 }} | ||
Badness: 0.1531 | Badness: 0.1531 | ||
[[Category:Smitonic|T]] | [[Category:Smitonic|T]] | ||
[[Category: | [[Category:Lists of temperaments]] | ||
Latest revision as of 04:47, 12 June 2025
Myna
Subgroup: 2.3.5.7
Comma list: 126/125, 1728/1715
Mapping: [⟨1 9 9 8], ⟨0 -10 -9 -7]]
Mapping generators: ~2, ~5/3
POTE generator: ~6/5 = 310.146
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [9/10 9/10 0 0⟩, [17/10 7/10 0 0⟩]
- Eigenmonzos (unchanged-intervals): 2, 3
Optimal ET sequence: 27, 31, 58, 89
Badness: 0.0270
Kleismic
Subgroup: 2.3.5
Comma list: 15625/15552
Mapping: [⟨1 0 1], ⟨0 6 5]]
POTE generator: ~6/5 = 317.007
- diamond monotone range: [300.000, 327.273] (4 to 11b)
- diamond tradeoff range: [315.641, 317.263]
- diamond monotone and tradeoff range: [315.641, 317.263]
Optimal ET sequence: 15, 19, 34, 53, 458, 511c, …, 882c
Orgone
Commas:65536/65219
Subgroup: 2.7.11
POTE generator: ~77/64 = 323.372
Sval mapping: [<1 2 4|, <0 3 -2|]
EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc
Dual-3 Sixix
Subgroup: 2.3⁻.9.5
Comma list: 81/80, [2 -3 0 1⟩
Mapping: [⟨1 2 4 4], ⟨0 -2 -3 -6]]
2.9.5 POTE generator: 335.8409
Optimal ET sequence: 18, 25, 43
Sixix
Subgroup: 2.3.5
Comma list: 3125/2916
Mapping: [⟨1 3 4], ⟨0 -5 -6]]
POTE generator: ~6/5 = 338.365
Optimal ET sequence: 7, 25, 32
Badness: 0.1531