Xenharmonic Wiki

Trienstonic clan: Difference between revisions

← Older editNewer edit →
VisualWikitext
m Update linking
Switch to Sintel's badness, WE & CWE tunings, per community consensus
Line 23: Line 23:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 717.517
* [[WE]]: ~2 = 1196.254{{c}}, ~3/2 = 719.306{{c}}
: [[error map]]: {{val| -3.746 +13.604 -14.655 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 719.606{{c}}
: error map: {{val| 0.000 +17.651 -10.007 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 717.517{{c}}
: [[error map]]: {{val| 0.000 +15.562 -16.274 }}
: [[error map]]: {{val| 0.000 +15.562 -16.274 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 721.559
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 721.559{{c}}
: error map: {{val| 0.000 +19.604 -4.150 }}
: error map: {{val| 0.000 +19.604 -4.150 }} -->


{{Optimal ET sequence|legend=1| 2d, 3d, 5 }}
{{Optimal ET sequence|legend=1| 2d, 3d, 5 }}


[[Badness]] (Smith): 0.00685
[[Badness]] (Sintel): 0.235


== Father ==
== Father ==
Line 47: Line 51:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 731.394
* [[WE]]: ~2 = 1190.224{{c}}, ~3/2 = 725.221{{c}}
: [[error map]]: {{val| -9.776 +13.490 +3.707 -2.939 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 731.394{{c}}
: error map: {{val| 0.000 +29.439 +25.324 +25.355 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 732.223{{c}}
: [[error map]]: {{val| 0.000 +30.268 +20.350 +27.842 }}
: [[error map]]: {{val| 0.000 +30.268 +20.350 +27.842 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 731.177
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 731.177{{c}}
: error map: {{val| 0.000 +29.222 +26.622 +24.706 }}
: error map: {{val| 0.000 +29.222 +26.622 +24.706 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 58: Line 66:
{{Optimal ET sequence|legend=1| 5, 13d, 18, 23bc, 41bbcd }}
{{Optimal ET sequence|legend=1| 5, 13d, 18, 23bc, 41bbcd }}


[[Badness]] (Smith): 0.072653
[[Badness]] (Sintel): 1.84


== Octokaidecal ==
== Octokaidecal ==
Line 73: Line 81:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~27/20 = 600.000, ~3/2 = 723.608 (~10/9 = 123.608)
* [[WE]]: ~27/20 = 596.986{{c}}, ~3/2 = 725.434{{c}} (~10/9 = 128.448{{c}})
: [[error map]]: {{val| -6.029 +17.450 -13.027 }}
* [[CWE]]: ~27/20 = 600.000{{c}}, ~3/2 = 726.548{{c}} (~10/9 = 126.548{{c}})
: error map: {{val| 0.000 +24.593 -6.670 }}
<!-- * [[CTE]]: ~27/20 = 600.000{{c}}, ~3/2 = 723.608{{c}} (~10/9 = 123.608{{c}})
: [[error map]]: {{val| 0.000 +21.653 -15.490 }}
: [[error map]]: {{val| 0.000 +21.653 -15.490 }}
* [[POTE]]: ~27/20 = 600.000, ~3/2 = 729.097 (~10/9 = 129.097)
* [[POTE]]: ~27/20 = 600.000{{c}}, ~3/2 = 729.097{{c}} (~10/9 = 129.097{{c}})
: error map: {{val| 0.000 +27.142 +0.976 }}
: error map: {{val| 0.000 +27.142 +0.976 }} -->


{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}
{{Optimal ET sequence|legend=1| 8, 10, 18, 28b }}


[[Badness]] (Smith): 0.122848
[[Badness]] (Sintel): 2.88


=== 7-limit ===
=== 7-limit ===
Line 90: Line 102:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~7/5 = 600.000, ~3/2 = 723.371 (~15/14 = 123.371)
* [[WE]]: ~7/5 = 596.984{{c}}, ~3/2 = 725.210{{c}} (~15/14 = 128.226{{c}})
: [[error map]]: {{val| -6.031 +17.224 -13.699 +0.774 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~3/2 = 726.319{{c}} (~15/14 = 126.319{{c}})
: error map: {{val| 0.000 +24.364 -7.358 +10.130 }}
<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 723.371{{c}} (~15/14 = 123.371{{c}})
: [[error map]]: {{val| 0.000 +21.416 -16.201 +1.287 }}
: [[error map]]: {{val| 0.000 +21.416 -16.201 +1.287 }}
* [[POTE]]: ~7/5 = 600.000, ~3/2 = 728.874 (~15/14 = 128.874)
* [[POTE]]: ~7/5 = 600.000{{c}}, ~3/2 = 728.874{{c}} (~15/14 = 128.874{{c}})
: error map: {{val| 0.000 +26.919 +0.307 +17.795 }}
: error map: {{val| 0.000 +26.919 +0.307 +17.795 }} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 100: Line 116:
{{Optimal ET sequence|legend=1| 8d, 10, 18, 28b }}
{{Optimal ET sequence|legend=1| 8d, 10, 18, 28b }}


[[Badness]] (Smith): 0.036747
[[Badness]] (Sintel): 0.930


=== 11-limit ===
=== 11-limit ===
Line 110: Line 126:


Optimal tunings:
Optimal tunings:
* CTE: ~7/5 = 600.000, ~3/2 = 723.371 (~15/14 = 123.371)
* WE: ~7/5 = 595.139{{c}}, ~3/2 = 726.397{{c}} (~15/14 = 131.258{{c}})
* POTE: ~7/5 = 600.000, ~3/2 = 732.330 (~15/14 = 132.330)
* CWE: ~7/5 = 600.000{{c}}, ~3/2 = 729.485{{c}} (~15/14 = 129.485{{c}})
<!-- * CTE: ~7/5 = 600.000{{c}}, ~3/2 = 723.371{{c}} (~15/14 = 123.371{{c}})
* POTE: ~7/5 = 600.000{{c}}, ~3/2 = 732.330 (~15/14 = 132.330{{c}}) -->


{{Optimal ET sequence|legend=0| 8d, 10, 18e }}
{{Optimal ET sequence|legend=0| 8d, 10, 18e }}


Badness (Smith): 0.030235
Badness (Sintel): 1.00


== Parakangaroo ==
== Parakangaroo ==
Line 131: Line 149:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~10/7 = 638.863
* [[WE]]: ~2 = 596.984{{c}}, ~10/7 = 638.135{{c}}
: [[error map]]: {{val| -2.883 +12.450 +3.685 -19.845 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~10/7 = 639.302{{c}}
: error map: {{val| 0.000 +15.952 +6.710 -15.104 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~10/7 = 638.863{{c}}
: [[error map]]: {{val| 0.000 +14.633 +2.314 -19.061 }}
: [[error map]]: {{val| 0.000 +14.633 +2.314 -19.061 }}
* [[POTE]]: ~2 = 1200.000, ~10/7 = 639.672
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/7 = 639.672{{c}}
: error map: {{val| 0.000 +17.060 +10.404 -11.780 }}
: error map: {{val| 0.000 +17.060 +10.404 -11.780 }} -->


{{Optimal ET sequence|legend=1| 2cd, …, 13cd, 15 }}
{{Optimal ET sequence|legend=1| 2cd, …, 13cd, 15 }}


[[Badness]] (Smith): 0.077857
[[Badness]] (Sintel): 1.97


=== 11-limit ===
=== 11-limit ===
Line 147: Line 169:
Mapping: {{mapping| 1 0 -3 -2 -4 | 0 3 10 9 14 }}
Mapping: {{mapping| 1 0 -3 -2 -4 | 0 3 10 9 14 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~10/7 = 639.036
* WE: ~2 = 1196.971{{c}}, ~10/7 = 638.230{{c}}
* POTE: ~2 = 1200.000, ~10/7 = 639.845
* CWE: ~2 = 1200.000{{c}}, ~10/7 = 639.480{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~10/7 = 639.036{{c}}
* POTE: ~2 = 1200.000{{c}}, ~10/7 = 639.845{{c}} -->


{{Optimal ET sequence|legend=0| 15 }}
{{Optimal ET sequence|legend=0| 15 }}


Badness (Smith): 0.043195
Badness (Sintel): 1.43


=== 13-limit ===
=== 13-limit ===
Line 162: Line 186:
Mapping: {{mapping| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}
Mapping: {{mapping| 1 0 -3 -2 -4 0 | 0 3 10 9 14 7 }}


Optimal tunings:
Optimal tunings:  
* CTE: ~2 = 1200.000, ~10/7 = 638.717
* WE: ~2 = 1194.720{{c}}, ~10/7 = 637.413{{c}}
* POTE: ~2 = 1200.000, ~10/7 = 640.230
* CWE: ~2 = 1200.000{{c}}, ~10/7 = 639.609{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~10/7 = 638.717{{c}}
* POTE: ~2 = 1200.000{{c}}, ~10/7 = 640.230{{c}} -->


{{Optimal ET sequence|legend=0| 15 }}
{{Optimal ET sequence|legend=0| 15 }}


Badness (Smith): 0.032653
Badness (Sintel): 1.35


[[Category:Temperament clans]]
[[Category:Temperament clans]]
Retrieved from "https://en.xen.wiki/w/Trienstonic_clan"