Keemic temperaments: Difference between revisions

Move pentadecal here
Move undeka here
Line 12: Line 12:
* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]]
* [[Superkleismic]] (+1029/1024) → [[Gamelismic clan #Superkleismic|Gamelismic clan]]
* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]]
* ''[[Sycamore]]'' (+686/675) → [[Sycamore family #Septimal sycamore|Sycamore family]]
* ''[[Undeka]]'' (+3200/3087) → [[11th-octave temperaments #Undeka|11th-octave temperaments]]


Discussed below are quasitemp, chromo, barbad, pentadecal, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].
Discussed below are quasitemp, chromo, barbad, pentadecal, undeka, hyperkleismic, and sevond, in the order of increasing [[TE logflat badness]].


== Quasitemp ==
== Quasitemp ==
Line 255: Line 254:


Badness (Sintel): 2.29
Badness (Sintel): 2.29
== Undeka ==
[[Subgroup]]: 2.3.5.7
[[Comma list]]: 875/864, 3200/3087
{{Mapping|legend=1| 11 0 8 31 | 0 1 1 0 }}
: mapping generators: ~21/20, ~3
[[Optimal tuning]]s:
* [[WE]]: ~21/20 = 108.9318{{c}}, ~3/2 = 707.7579{{c}}
: [[error map]]: {{val| -1.750 +4.053 -8.852 +8.059 }}
* [[CWE]]: ~21/20 = 109.0909{{c}}, ~3/2 = 707.7526{{c}}
: error map: {{val| 0.000 +5.798 -5.834 +12.992 }}
{{Optimal ET sequence|legend=1| 11b, 22 }}
[[Badness]] (Sintel): 3.59
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 100/99, 352/343, 385/384
Mapping: {{mapping| 11 0 8 31 38 | 0 1 1 0 0 }}
Optimal tunings:
* WE: ~21/20 = 109.0321{{c}}, ~3/2 = 706.3870{{c}}
* CWE: ~21/20 = 109.0909{{c}}, ~3/2 = 706.4785{{c}}
{{Optimal ET sequence|legend=0| 11c, 22 }}
Badness (Sintel): 2.27
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 65/63, 100/99, 169/165, 352/343
Mapping: {{mapping| 11 0 8 31 38 23 | 0 1 1 0 0 1 }}
Optimal tunings:
* WE: ~13/12 = 109.1184{{c}}, ~3/2 = 707.9422{{c}}
* CWE: ~13/12 = 109.0909{{c}}, ~3/2 = 707.9065{{c}}
{{Optimal ET sequence|legend=0| 11cf, 22 }}
Badness (Sintel): 2.34


== Hyperkleismic ==
== Hyperkleismic ==