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.
The '''keenanismic family''' of rank four temperaments tempers out the [[keenanisma|keenanisma (385/384)]], the 11-limit comma 385/384 = {{Monzo| -7 -1 1 1 1 }} of 4.503 cents.


== Keenanismic ==
== Keenanismic ==


Comma: 385/384
[[Comma list]]: 385/384


Minimax tuning
[[Mapping]]: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]


[|1 0 0 0 0>, |0 1 0 0 0>, |7/3 1/3 2/3 -1/3 -1/3>,
Transpose: [2 3 5 7 385/35]
|7/3 1/3 -1/3 2/3 -1/3>, |7/3 1/3 -1/3 -1/3 2/3>]
 
Eigenmonzos: 2, 3, 7/5, 11/5
 
Map: [<1 0 0 0 7|, <0 1 0 0 1|, <0 0 1 0 -1|, <0 0 0 1 -1|]


Transpose: [2 3 5 7 385/35]
[[Minimax tuning]]:
: [|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>]
: Eigenmonzos: 2, 3, 7/5, 11/5


EDOs: {{EDOs| 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212 and 284 }}
{{Val list|legend=1| 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284 }}


10^9*Badness: 15.159
[[Badness]]: 15.159 × 10<sup>-9</sup>


== Martwin ==
== Martwin ==


Commas: 385/384, 325/324
[[Comma list]]: 385/384, 325/324


Minimax tuning
[[Mapping]]: [&lt;1 0 0 0 7 2|, &lt;0 1 0 0 1 4|, &lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 -1 0|]
||1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, |2/3 4/3 1/3 0 0 -1/3&gt;,
|17/3 -5/3 1/3 0 -1 2/3&gt;, |2/3 4/3 -2/3 0 1 -1/3&gt;, |2/3 4/3 -2/3 0 0 2/3&gt;]


Eigenmonzos: 2, 3, 11/5, 13/5
Transpose: [2 3 5 7 385/35 324/25]


Map: [&lt;1 0 0 0 7 2|, &lt;0 1 0 0 1 4|, &lt;0 0 1 0 -1 -2|, &lt;0 0 0 1 -1 0|]
[[Minimax tuning]]:  
 
: ||1 0 0 0 0 0&gt;, |0 1 0 0 0 0&gt;, |2/3 4/3 1/3 0 0 -1/3&gt;, |17/3 -5/3 1/3 0 -1 2/3&gt;, |2/3 4/3 -2/3 0 1 -1/3&gt;, |2/3 4/3 -2/3 0 0 2/3&gt;]
Transpose: [2 3 5 7 385/35 324/25]
: Eigenmonzos: 2, 3, 11/5, 13/5


EDOs: {{EDOs| 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212 and 299 }}
{{Val list|legend=1| 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212, 299 }}


10^6*Badness: 2.206
[[Badness]]: 2.206 × 10<sup>-6</sup>


== Ancient ==
== Ancient ==


Commas: 385/384, 625/624
[[Comma list]]: 385/384, 625/624


Map: [&lt;1 0 0 0 7 -4|, &lt;0 1 0 0 1 -1|, &lt;0 0 1 0 -1 4|, &lt;0 0 0 1 -1 0|]
[[Mapping]]: [&lt;1 0 0 0 7 -4|, &lt;0 1 0 0 1 -1|, &lt;0 0 1 0 -1 4|, &lt;0 0 0 1 -1 0|]


Transpose: [2 3 5 7 385/35 625/48]
Transpose: [2 3 5 7 385/35 625/48]


EDOs: {{EDOs| 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190 }}
{{Val list|legend=1| 6, 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190 }}


10^6*Badness: 2.573
[[Badness]]: 2.573 × 10<sup>-6</sup>


[[Category:Temperament]]
[[Category:Regular temperament theory]]
[[Category:Temperament family]]
[[Category:Keenanismic family| ]] <!-- main article -->
[[Category:Rank 4]]
[[Category:Rank 4]]
[[Category:Keenanismic]]
[[Category:Keenanismic]]

Revision as of 07:22, 1 August 2021

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

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|]

Transpose: [2 3 5 7 385/35]

Minimax tuning:

[|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>]
Eigenmonzos: 2, 3, 7/5, 11/5

Template:Val list

Badness: 15.159 × 10-9

Martwin

Comma list: 385/384, 325/324

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:

||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>]
Eigenmonzos: 2, 3, 11/5, 13/5

Template:Val list

Badness: 2.206 × 10-6

Ancient

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]

Template:Val list

Badness: 2.573 × 10-6

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