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Kleismic rank-3 family: Difference between revisions

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m Units & misc. cleanup
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{{Mapping|legend=1| 1 0 1 0 | 0 6 5 0 | 0 0 0 1 }}
{{Mapping|legend=1| 1 0 1 0 | 0 6 5 0 | 0 0 0 1 }}
: mapping generators: ~2, ~6/5, ~7
: mapping generators: ~2, ~6/5, ~7


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 317.0586, ~7/4 = 968.8259
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0586{{c}}, ~7/4 = 968.8259{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{Optimal ET sequence|legend=1| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}
{{Optimal ET sequence|legend=1| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}


[[Badness]]: 0.363 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.363 × 10<sup>-3</sup>


=== 2.3.5.7.13 subgroup ===
=== 2.3.5.7.13 subgroup ===
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Comma list: 325/324, 625/624
Comma list: 325/324, 625/624


Sval mapping: {{mapping| 1 0 1 0 0 | 0 6 5 0 14 | 0 0 0 1 0 }}
Subgroup-val mapping: {{mapping| 1 0 1 0 0 | 0 6 5 0 14 | 0 0 0 1 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~6/5 = 317.1110, ~7/4 = 968.8259
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1110{{c}}, ~7/4 = 968.8259{{c}}


{{Optimal ET sequence|legend=1| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}
{{Optimal ET sequence|legend=0| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}


Badness: 0.290 × 10<sup>-3</sup>
Badness (Smith): 0.290 × 10<sup>-3</sup>


== Enlil ==
== Enlil ==
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{{Mapping|legend=1| 1 0 1 0 6 | 0 6 5 0 1 | 0 0 0 1 -1 }}
{{Mapping|legend=1| 1 0 1 0 6 | 0 6 5 0 1 | 0 0 0 1 -1 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 317.0667, ~7/4 = 967.6041
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0667{{c}}, ~7/4 = 967.6041{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{Optimal ET sequence|legend=1| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}
{{Optimal ET sequence|legend=1| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}


[[Badness]]: 0.798 × 10<sup>-3</sup>
[[Badness]] (Smith): 0.798 × 10<sup>-3</sup>


=== 13-limit (sumatra) ===
=== 13-limit (sumatra) ===
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Mapping: {{mapping| 1 0 1 0 6 0 | 0 6 5 0 1 14 | 0 0 0 1 -1 0 }}
Mapping: {{mapping| 1 0 1 0 6 0 | 0 6 5 0 1 14 | 0 0 0 1 -1 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~6/5 = 317.1156, ~7/4 = 967.6235
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1156{{c}}, ~7/4 = 967.6235{{c}}


Minimax tuning:  
Minimax tuning:  
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: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7
: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7


{{Optimal ET sequence|legend=1| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}
{{Optimal ET sequence|legend=0| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}


Badness: 0.680 × 10<sup>-3</sup>
Badness (Smith): 0.680 × 10<sup>-3</sup>


Complexity spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 8/7, 11/8, 11/10, 7/5, 12/11, 7/6, 16/13, 15/11, 15/14, 11/9, 9/7, 13/11, 14/13, 14/11
Complexity spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 8/7, 11/8, 11/10, 7/5, 12/11, 7/6, 16/13, 15/11, 15/14, 11/9, 9/7, 13/11, 14/13, 14/11
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{{Mapping|legend=1| 1 0 1 0 9 | 0 6 5 0 -21 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 0 1 0 9 | 0 6 5 0 -21 | 0 0 0 1 0 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 316.7584, ~7/4 = 968.8259
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 316.7584{{c}}, ~7/4 = 968.8259{{c}}


{{Optimal ET sequence|legend=1| 19, 34e, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}
{{Optimal ET sequence|legend=1| 19, 34e, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}


[[Badness]]: 3.690 × 10<sup>-3</sup>
[[Badness]] (Smith): 3.690 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 1 0 9 0 | 0 6 5 0 -21 14 | 0 0 0 1 0 0 }}
Mapping: {{mapping| 1 0 1 0 9 0 | 0 6 5 0 -21 14 | 0 0 0 1 0 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~6/5 = 316.8446, ~7/4 = 968.8259
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 316.8446{{c}}, ~7/4 = 968.8259{{c}}


{{Optimal ET sequence|legend=1| 19, 34e, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeeff }}
{{Optimal ET sequence|legend=0| 19, 34e, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeeff }}


Badness: 2.273 × 10<sup>-3</sup>
Badness (Smith): 2.273 × 10<sup>-3</sup>


== Enki ==
== Enki ==
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{{Mapping|legend=1| 1 0 1 0 1 | 0 6 5 0 4 | 0 0 0 2 1 }}
{{Mapping|legend=1| 1 0 1 0 1 | 0 6 5 0 4 | 0 0 0 2 1 }}
: mapping generators: ~2, ~6/5, ~66/25
: mapping generators: ~2, ~6/5, ~66/25


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 317.0396, ~33/25 = 484.2358
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0396{{c}}, ~33/25 = 484.2358{{c}}


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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{{Optimal ET sequence|legend=1| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}
{{Optimal ET sequence|legend=1| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}


[[Badness]]: 1.09 × 10<sup>-3</sup>
[[Badness]] (Smith): 1.09 × 10<sup>-3</sup>


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 0 1 0 1 0 | 0 6 5 0 4 14 | 0 0 0 2 1 0 }}
Mapping: {{mapping| 1 0 1 0 1 0 | 0 6 5 0 4 14 | 0 0 0 2 1 0 }}


Optimal tuning (CTE): ~2 = 1\1, ~6/5 = 317.1387, ~33/25 = 483.3828
Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1387{{c}}, ~33/25 = 483.3828{{c}}


Minimax tuning:  
Minimax tuning:  
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: unchanged-interval (eigenmonzo) basis: 2.7.13/5
: unchanged-interval (eigenmonzo) basis: 2.7.13/5


{{Optimal ET sequence|legend=1| 34d, 49f, 72, 87, 159, 193, 280 }}
{{Optimal ET sequence|legend=0| 34d, 49f, 72, 87, 159, 193, 280 }}


Badness: 0.874 × 10<sup>-3</sup>
Badness (Smith): 0.874 × 10<sup>-3</sup>


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Kleismic rank-3 family| ]] <!-- main article -->
[[Category:Kleismic rank-3 family| ]] <!-- main article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Kleismic_rank-3_family"