Keenanismic family: Difference between revisions
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The '''keenanismic family''' of rank-4 temperaments tempers out the [[keenanisma]], the 11-limit comma 385/384 = {{monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. | {{Technical data page}} | ||
The '''keenanismic family''' of [[Catalog of rank-4 temperaments|rank-4]] temperaments [[Tempering out|tempers out]] the [[keenanisma]], the 11-limit comma 385/384 = {{monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. | |||
== Keenanismic == | == Keenanismic == | ||
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* [[11-odd-limit]] | * [[11-odd-limit]] | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 0 1 0 0 0 }}, {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}, {{monzo| 7/3 1/3 -1/3 -1/3 2/3 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5 | ||
{{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }} | {{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }} | ||
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[[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament --> | [[Minimax tuning]]: {{confirm}} <!-- contradiction with the data in Rank-4 temperament --> | ||
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}] | : [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 0 1 0 0 0 0 }}, {{monzo| 2/3 4/3 1/3 0 0 -1/3 }}, {{monzo| 17/3 -5/3 1/3 0 -1 2/3 }}, {{monzo| 2/3 4/3 -2/3 0 1 -1/3 }}, {{monzo| 2/3 4/3 -2/3 0 0 2/3 }}] | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.11/5.13/5 | ||
{{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }} | {{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Keenanismic family| ]] <!-- main article --> | [[Category:Keenanismic family| ]] <!-- main article --> | ||
[[Category:Keenanismic| ]] <!-- key article --> | [[Category:Keenanismic| ]] <!-- key article --> | ||
[[Category:Rank 4]] | [[Category:Rank 4]] | ||
Latest revision as of 00:37, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The keenanismic family of rank-4 temperaments tempers out the keenanisma, the 11-limit comma 385/384 = [-7 -1 1 1 1⟩ of 4.503 cents.
Keenanismic
Subgroup: 2.3.5.7.11
Comma list: 385/384
Mapping: [⟨1 0 0 0 7], ⟨0 1 0 0 1], ⟨0 0 1 0 -1], ⟨0 0 0 1 -1]]
- mapping generators: ~2, ~3, ~5, ~7
Transpose: [2 3 5 7 385/35]
- [[1 0 0 0 0⟩, [0 1 0 0 0⟩, [7/3 1/3 2/3 -1/3 -1/3⟩, [7/3 1/3 -1/3 2/3 -1/3⟩, [7/3 1/3 -1/3 -1/3 2/3⟩]
- Unchanged-interval (eigenmonzo) basis: 2.3.7/5.11/5
Optimal ET sequence: 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de
Badness: 15.2 × 10-9
Martwin
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 385/384
Mapping: [⟨1 0 0 0 7 2], ⟨0 1 0 0 1 4], ⟨0 0 1 0 -1 -2], ⟨0 0 0 1 -1 0]]
Transpose: [2 3 5 7 385/35 324/25]
Minimax tuning: [to be confirmed]
- [[1 0 0 0 0 0⟩, [0 1 0 0 0 0⟩, [2/3 4/3 1/3 0 0 -1/3⟩, [17/3 -5/3 1/3 0 -1 2/3⟩, [2/3 4/3 -2/3 0 1 -1/3⟩, [2/3 4/3 -2/3 0 0 2/3⟩]
- Unchanged-interval (eigenmonzo) basis: 2.3.11/5.13/5
Optimal ET sequence: 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff
Badness: 2.21 × 10-6
Ancient
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 625/624
Mapping: [⟨1 0 0 0 7 -4], ⟨0 1 0 0 1 -1], ⟨0 0 1 0 -1 4], ⟨0 0 0 1 -1 0]]
Transpose: [2 3 5 7 385/35 625/48]
Optimal ET sequence: 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def
Badness: 2.57 × 10-6
Zaxa
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 385/384
Mapping: [⟨1 0 0 0 7 12], ⟨0 1 0 0 1 -2], ⟨0 0 1 0 -1 -1], ⟨0 0 0 1 -1 -1]]
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.657, ~5/4 = 385.632, ~7/4 = 967.829
Optimal ET sequence: 7, 10, 15f, 17, 19f, 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e
Badness: 3.35 × 10-6