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Marveltwin: Difference between revisions

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== Rank-4 temperaments ==
== Rank-4 temperaments ==
=== 225/224 ===
=== 225/224 ===
[[Subgroup]]: 2.3.5.7.11.13


13-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.11/5.13/5
[[Comma list]]: 225/224, 325/324


15-limit eigenmonzo subgroup (unchanged-interval basis): 2.7.15/11.15/13
{{Mapping|legend=1| 1 0 0 -5 0 2 | 0 1 0 2 0 4 | 0 0 1 2 0 -2 | 0 0 0 0 1 0 }}


[[Spectrum_of_a_temperament|Spectrum]]: 4/3, 5/4, 6/5, 16/15, 15/14, 9/8, 10/9, 7/5, 9/7, 7/6, 18/13, 8/7, 13/12, 16/13, 11/8, 12/11, 15/13, 11/10, 15/11, 11/9, 13/10, 14/13, 14/11, 13/11
[[Minimax tuning]]s:  
* 13-limit eigenmonzo (unchanged-interval) basis: 2.7.11/5.13/5
* 15-limit eigenmonzo (unchanged-interval) basis: 2.7.15/11.15/13


Mapping:
{{Optimal ET sequence|legend=1| 12, 19, 41, 53, 72, 166 }}


{| class="wikitable"
[[Complexity spectrum]]: 4/3, 5/4, 6/5, 16/15, 15/14, 9/8, 10/9, 7/5, 9/7, 7/6, 18/13, 8/7, 13/12, 16/13, 11/8, 12/11, 15/13, 11/10, 15/11, 11/9, 13/10, 14/13, 14/11, 13/11
|-
| | <1 0 0 -5 0 2]
|-
| | <0 1 0 2 0 4]
|-
| | <0 0 1 2 0 -2]
|-
| | <0 0 0 0 1 0]
|}
Edos: 12, 19, 41, 53, 72, 166


10^6 * Badness: 3.668
[[Badness]]: 3.668 × 10<sup>-6</sup>


=== 385/384 ===
=== 385/384 ===
[[Subgroup]]: 2.3.5.7.11.13


Spectrum: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 11/8, 7/6, 12/11, 16/15, 18/13, 13/12, 9/7, 7/5, 16/13, 11/9, 11/10, 13/11, 14/13, 15/14, 15/11, 13/10, 15/13, 14/11
[[Comma list]]: 325/324, 385/384


Edos: 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212, 299
[[Complexity spectrum]]: 4/3, 6/5, 10/9, 5/4, 9/8, 8/7, 11/8, 7/6, 12/11, 16/15, 18/13, 13/12, 9/7, 7/5, 16/13, 11/9, 11/10, 13/11, 14/13, 15/14, 15/11, 13/10, 15/13, 14/11


10^6 * Badness: 2.206
{{Optimal ET sequence|legend=1| 7, 15, 19, 26, 34, 41, 46, 53, 72, 87, 140, 159, 212, 299 }}
 
[[Badness]]: 2.206 × 10<sup>-6</sup>


=== 364/363 ===
=== 364/363 ===
[[Subgroup]]: 2.3.5.7.11.13
[[Comma list]]: 325/324, 364/363


Spectrum: 4/3, 6/5, 10/9, 11/8, 5/4, 12/11, 14/11, 9/8, 13/11, 11/9, 8/7, 13/12, 18/13, 16/15, 7/6, 11/10, 7/5, 16/13, 9/7, 15/11, 15/14, 13/10, 15/13, 14/13
[[Complexity spectrum]]: 4/3, 6/5, 10/9, 11/8, 5/4, 12/11, 14/11, 9/8, 13/11, 11/9, 8/7, 13/12, 18/13, 16/15, 7/6, 11/10, 7/5, 16/13, 9/7, 15/11, 15/14, 13/10, 15/13, 14/13


Edos: 15, 26, 41, 46, 72, 87, 121, 159, 193, 239, 280
{{Optimal ET sequence|legend=1| 15, 26, 41, 46, 72, 87, 121, 159, 193, 239, 280 }}


10^6 * Badness: 3.011
[[Badness]]: 3.011 × 10<sup>-6</sup>


=== 441/440 ===
=== 441/440 ===
[[Subgroup]]: 2.3.5.7.11.13
[[Comma list]]: 325/324, 441/440


Spectrum: 4/3, 6/5, 8/7, 10/9, 14/11, 5/4, 7/6, 9/8, 7/5, 16/15, 13/12, 18/13, 9/7, 11/8, 12/11, 15/14, 16/13, 11/9, 11/10, 13/11, 15/11, 14/13, 13/10, 15/13
[[Complexity spectrum]]: 4/3, 6/5, 8/7, 10/9, 14/11, 5/4, 7/6, 9/8, 7/5, 16/15, 13/12, 18/13, 9/7, 11/8, 12/11, 15/14, 16/13, 11/9, 11/10, 13/11, 15/11, 14/13, 13/10, 15/13


Edos: 12, 15, 26, 41, 46, 72, 87, 159
{{Optimal ET sequence|legend=1| 12, 15, 26, 41, 46, 72, 87, 159 }}


10^6 * Badness: 3.037
[[Badness]]: 3.037 × 10<sup>-6</sup>


=== 169/168 ===
=== 169/168 ===
[[Subgroup]]: 2.3.5.7.11.13


Spectrum: 10/9, 6/5, 4/3, 14/13, 13/12, 16/13, 5/4, 18/13, 9/8, 13/10, 8/7, 7/6, 15/13, 16/15, 9/7, 7/5, 11/8, 12/11, 13/11, 11/10, 15/14, 11/9, 14/11, 15/11
[[Comma list]]: 169/168, 325/324


Edos: 7, 19, 26, 46, 53, 72, 152
[[Complexity spectrum]]: 10/9, 6/5, 4/3, 14/13, 13/12, 16/13, 5/4, 18/13, 9/8, 13/10, 8/7, 7/6, 15/13, 16/15, 9/7, 7/5, 11/8, 12/11, 13/11, 11/10, 15/14, 11/9, 14/11, 15/11


10^6 * Badness: 2.975
{{Optimal ET sequence|legend=1| 7, 19, 26, 46, 53, 72, 152 }}
 
[[Badness]]: 2.975 × 10<sup>-6</sup>


=== 540/539 ===
=== 540/539 ===
[[Subgroup]]: 2.3.5.7.11.13


Spectrum: 4/3, 6/5, 7/6, 9/7, 10/9, 5/4, 7/5, 9/8, 15/14, 8/7, 16/15, 18/13, 13/12, 12/11, 11/9, 11/10, 11/8, 15/11, 16/13, 14/13, 15/13, 13/10, 13/11, 14/11
[[Comma list]]: 325/324, 540/539


Edos: 19, 41, 53, 72, 121, 166, 193
[[Complexity spectrum]]: 4/3, 6/5, 7/6, 9/7, 10/9, 5/4, 7/5, 9/8, 15/14, 8/7, 16/15, 18/13, 13/12, 12/11, 11/9, 11/10, 11/8, 15/11, 16/13, 14/13, 15/13, 13/10, 13/11, 14/11


10^6 * Badness: 3.281
{{Optimal ET sequence|legend=1| 19, 41, 53, 72, 121, 166, 193 }}
 
[[Badness]]: 3.281 × 10<sup>-6</sup>


=== 352/351 ===
=== 352/351 ===
[[Subgroup]]: 2.3.5.7.11.13


Spectrum: 4/3, 10/9, 6/5, 9/8, 5/4, 13/11, 16/13, 11/9, 13/12, 12/11, 16/15, 18/13, 8/7, 7/6, 11/8, 9/7, 15/11, 11/10, 7/5, 14/13, 13/10, 15/14, 14/11, 15/13
[[Comma list]]: 325/324, 352/351


Edos: 7, 34, 41, 46, 53, 80, 87, 121, 140, 261, 358, 401
[[Complexity spectrum]]: 4/3, 10/9, 6/5, 9/8, 5/4, 13/11, 16/13, 11/9, 13/12, 12/11, 16/15, 18/13, 8/7, 7/6, 11/8, 9/7, 15/11, 11/10, 7/5, 14/13, 13/10, 15/14, 14/11, 15/13


10^6 * Badness: 3.434
{{Optimal ET sequence|legend=1| 7, 34, 41, 46, 53, 80, 87, 121, 140, 261, 358, 401 }}
 
[[Badness]]: 3.434 × 10<sup>-6</sup>


=== 625/624 ===
=== 625/624 ===
[[Subgroup]]: 2.3.5.7.11.13
[[Comma list]]: 325/324, 625/624


Spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 16/13, 8/7, 7/5, 7/6, 15/14, 11/8, 9/7, 11/10, 12/11, 14/13, 15/11, 11/9, 13/11, 14/11
[[Complexity spectrum]]: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 16/13, 8/7, 7/5, 7/6, 15/14, 11/8, 9/7, 11/10, 12/11, 14/13, 15/11, 11/9, 13/11, 14/11


Edos: 15, 19, 34, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333
{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 72, 87, 121, 140, 159, 193, 212, 299, 333 }}


10^6 * Badness: 3.563
[[Badness]]: 3.563 × 10<sup>-6</sup>


== Rank-3 temperaments ==
== Rank-3 temperaments ==
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