11th-octave temperaments: Difference between revisions

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: Mapping generators: ~16/15, ~3
: Mapping generators: ~16/15, ~3


[[Optimal tuning]] ([[POTE]]): ~16/15 = 109.091, ~3/2 = 702.947
[[Optimal tuning]]s:
* [[CTE]]: ~16/15 = 109.091¢, ~3/2 = 702.794¢
* [[CWE]]: ~16/15 = 109.091¢, ~3/2 = 702.908¢


{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}
{{Optimal ET sequence|legend=1| 22, 55, 77, 99 }}


[[Badness]]: 0.454083
[[Badness]] (Sintel): 10.652


=== Undekapent ===
=== Undekapent ===
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: Mapping generators: ~648/625, ~3
: Mapping generators: ~648/625, ~3


[[Optimal tuning]] ([[POTE]]): ~648/625 = 109.091, ~3/2 = 703.829
[[Optimal tuning]]s:
* [[CTE]]: ~648/625 = 109.091¢, ~3/2 = 705.652¢
* [[CWE]]: ~648/625 = 109.091¢, ~3/2 = 704.698¢


{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}
{{Optimal ET sequence|legend=1| 22, 77c, 99c, 121c }}


[[Badness]]: 0.727539
[[Badness]] (Sintel): 17.067
 
=== Elven ===
{{see also| Sensibeta temperaments #Elven }}
This temperament has a period of 1/11 octave, which represents [[3125/2916]] in the 5-limit.
 
[[Subgroup]]: 2.3.5
 
[[Comma list]]: {{monzo|-23 -66 55}}
 
{{Mapping|legend=1| 11 2 7 | 0 5 6 }}
 
: Mapping generators: ~3125/2916, ~{{monzo| 10 29 -24 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.353¢
* [[CWE]]: ~3125/2916 = 109.091¢, ~5/3 = 882.336¢
 
{{Optimal ET sequence|legend=1| 121, 253, 374 }}
 
[[Badness]] (Sintel): 429.4


== Hendeca ==
== Hendeca ==
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{{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}
{{Optimal ET sequence|legend=1| 11, 22, 55d, 77d, 99dd }}


[[Badness]]: 0.172714
[[Badness]] (Sintel): 4.371


=== 11-limit ===
=== 11-limit ===
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{{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }}
{{Optimal ET sequence|legend=0| 11, 22, 55d, 77d, 99dd }}


Badness: 0.074543
Badness (Sintel): 2.464


== Undeka ==
== Undeka ==
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{{Optimal ET sequence|legend=1| 11c, 22 }}
{{Optimal ET sequence|legend=1| 11c, 22 }}


[[Badness]]: 0.141782
[[Badness]] (Sintel): 3.588


=== 11-limit ===
=== 11-limit ===
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{{Optimal ET sequence|legend=0| 11c, 22 }}
{{Optimal ET sequence|legend=0| 11c, 22 }}


Badness: 0.068672
Badness (Sintel): 2.270


=== 13-limit ===
=== 13-limit ===
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{{Optimal ET sequence|legend=0| 11cf, 22 }}
{{Optimal ET sequence|legend=0| 11cf, 22 }}


Badness: 0.056528
Badness (Sintel): 2.336


{{Navbox fractional-octave}}
{{Navbox fractional-octave}}