Xenharmonic Wiki

Very low accuracy temperaments: Difference between revisions

← Older editNewer edit →
VisualWikitext
Switch to Sintel's badness, WE & CWE tunings (1/2)
Switch to Sintel's badness, WE & CWE tunings (2/2). Complete missing data
Line 287: Line 287:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/4 = 354.664
* [[WE]]: ~2 = 1164.885{{c}}, ~5/4 = 374.162{{c}}
: [[error map]]: {{val| -35.115 +11.253 -82.382 +125.830 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 375.277{{c}}
: error map: {{val| 0.000 +48.600 -11.036 +231.174 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/4 = 354.664{{c}}
: [[error map]]: {{val| 0.000 +7.373 -31.649 +231.174 }}
: [[error map]]: {{val| 0.000 +7.373 -31.649 +231.174 }}
* [[POTE]]: ~2 = 1200.000, ~5/4 = 385.440
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/4 = 385.440{{c}}
: error map: {{val| 0.000 +68.926 -0.873 +231.174 }}
: error map: {{val| 0.000 +68.926 -0.873 +231.174 }} -->


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


[[Badness]] (Smith): 0.051009
[[Badness]] (Sintel): 1.29


== Malacoda ==
== Malacoda ==
Line 308: Line 312:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/4 = 938.796
* [[WE]]: ~2 = 1223.542{{c}}, ~7/4 = 941.838{{c}}
: [[error map]]: {{val| +23.542 -18.278 -57.528 +20.096 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/4 = 927.096{{c}}
: error map: {{val| 0.000 -47.763 -113.410 -41.730 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/4 = 938.796{{c}}
: [[error map]]: {{val| 0.000 -24.362 -125.110 -30.029 }}
: [[error map]]: {{val| 0.000 -24.362 -125.110 -30.029 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 923.717
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/4 = 923.717{{c}}
: error map: {{val| 0.000 -54.521 -110.031 -45.109 }}
: error map: {{val| 0.000 -54.521 -110.031 -45.109 }} -->


{{Optimal ET sequence|legend=1| 1, 3b, 4, 9c, 13bcc }}
{{Optimal ET sequence|legend=1| 1, 3b, 4, 9c, 13bcc }}


[[Badness]] (Smith): 0.037207
[[Badness]] (Sintel): 0.942


== Ugolino ==
== Ugolino ==
Line 327: Line 335:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~5/3 = 926.868
* [[WE]]: ~2 = 1206.628{{c}}, ~7/4 = 926.730{{c}}
: [[error map]]: {{val| +6.628 -48.494 -6.122 +58.198 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~7/4 = 923.776{{c}}
: error map: {{val| 0.000 -54.403 -14.986 +50.054 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 926.868{{c}}
: [[error map]]: {{val| 0.000 -48.218 -5.708 +65.517 }}
: [[error map]]: {{val| 0.000 -48.218 -5.708 +65.517 }}
* [[POTE]]: ~2 = 1200.000, ~5/3 = 921.640
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 921.640{{c}}
: error map: {{val| 0.000 -58.675 -21.394 +39.374 }}
: error map: {{val| 0.000 -58.675 -21.394 +39.374 }} -->


{{Optimal ET sequence|legend=1| 1cdd, 3bcdd, 4, 9d }}
{{Optimal ET sequence|legend=1| 1cdd, 3bcdd, 4, 9d }}


[[Badness]] (Smith): 0.043758
[[Badness]] (Sintel): 1.11


== Medusa ==
== Medusa ==
Line 346: Line 358:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 684.722
* [[WE]]: ~2 = 1200.960{{c}}, ~3/2 = 686.181{{c}}
: [[error map]]: {{val| +0.960 -14.814 -41.014 +62.655 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 685.511{{c}}
: error map: {{val| 0.000 -16.443 -42.849 +60.150 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 684.722{{c}}
: [[error map]]: {{val| 0.000 -17.233 -40.480 +61.730 }}
: [[error map]]: {{val| 0.000 -17.233 -40.480 +61.730 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 685.632
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 685.632{{c}}
: error map: {{val| 0.000 -16.323 -43.209 +59.911 }}
: error map: {{val| 0.000 -16.323 -43.209 +59.911 }} -->


{{Optimal ET sequence|legend=1| 2, 5c, 7 }}
{{Optimal ET sequence|legend=1| 2, 5c, 7 }}


[[Badness]] (Smith): 0.042712
[[Badness]] (Sintel): 1.08


=== 11-limit ===
=== 11-limit ===
Line 363: Line 379:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 683.589
* WE: ~2 = 1202.757{{c}}, ~3/2 = 687.384{{c}}
* POTE: ~2 = 1200.000, ~3/2 = 685.809
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 685.462{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 683.589{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 685.809{{c}} -->


{{Optimal ET sequence|legend=0| 2, 5c, 7 }}
{{Optimal ET sequence|legend=0| 2, 5c, 7 }}


Badness (Smith): 0.026828
Badness (Sintel): 0.887


== Wallaby ==
== Wallaby ==
Line 379: Line 397:
{{Mapping|legend=1| 1 0 7 -2 | 0 1 -3 3 }}
{{Mapping|legend=1| 1 0 7 -2 | 0 1 -3 3 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 691.757
* [[WE]]: ~2 = 1216.024{{c}}, ~3/2 = 700.583{{c}}
: [[error map]]: {{val| +16.024 +14.652 -23.967 -51.053 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 691.757{{c}}
: error map: {{val| 0.000 -10.198 -61.585 -93.555 }}
<!-- * [[CTE]]: ~2 = 1200.000, ~3/2 = 693.440{{c}}
: [[error map]]: {{val| 0.000 -8.515 -66.635 -88.505 }}
: [[error map]]: {{val| 0.000 -8.515 -66.635 -88.505 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 691.351
* [[POTE]]: ~2 = 1200.000, ~3/2 = 691.351{{c}}
: error map: {{val| 0.000 -10.604 -60.368 -94.772 }}
: error map: {{val| 0.000 -10.604 -60.368 -94.772 }} -->


{{Optimal ET sequence|legend=1| 2d, 5c, 7d, 19ccdd }}
{{Optimal ET sequence|legend=1| 2d, 5c, 7d, 19ccdd }}


[[Badness]] (Smith): 0.058468
[[Badness]] (Sintel): 1.48


== Plutus ==
== Plutus ==
Line 399: Line 421:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 685.837
* [[WE]]: ~2 = 1203.936{{c}}, ~3/2 = 685.135{{c}}
: [[error map]]: {{val| +3.936 -12.884 -45.774 +56.849 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 683.935{{c}}
: error map: {{val| 0.000 -18.020 -50.573 +50.850 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 685.837{{c}}
: [[error map]]: {{val| 0.000 -16.118 -42.965 +60.359 }}
: [[error map]]: {{val| 0.000 -16.118 -42.965 +60.359 }}
* [[POTE]]: ~2 = 1200.000, ~3/2 = 682.895
* [[POTE]]: ~2 = 1200.000{{c}}, ~3/2 = 682.895{{c}}
: error map: {{val| 0.000 -19.060 -54.734 +45.649 }}
: error map: {{val| 0.000 -19.060 -54.734 +45.649 }} -->


{{Optimal ET sequence|legend=1| 2cd, 5d, 7 }}
{{Optimal ET sequence|legend=1| 2cd, 5d, 7 }}


[[Badness]] (Smith): 0.045275
[[Badness]] (Sintel): 1.14


=== 11-limit ===
=== 11-limit ===
Line 416: Line 442:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 687.743
* WE: ~2 = 1203.293{{c}}, ~3/2 = 687.114{{c}}
* POTE: ~2 = 1200.000, ~3/2 = 685.234
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 686.078{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 687.743{{c}}
* POTE: ~2 = 1200.000{{c}}, ~3/2 = 685.234{{c}} -->


{{Optimal ET sequence|legend=0| 2cde, 5de, 7 }}
{{Optimal ET sequence|legend=0| 2cde, 5de, 7 }}


Badness (Smith): 0.032521
Badness (Sintel): 1.08


== Involution ==
== Involution ==
Line 435: Line 463:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~3/2 = 509.892
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 509.892{{c}}
: [[error map]]: {{val| 0.000 -192.063 -206.097 }}
: [[error map]]: {{val| 0.000 -192.063 -206.097 }} -->
* [[CWE]]: ~2 = 1200.000, ~3/2 = 520.625
* [[WE]]: ~2 = 1265.406{{c}}, ~3/2 = 552.346{{c}}
: error map: {{val| 0.000 -181.330 -227.565 }}
: error map: {{val| +65.405 -84.203 -94.789 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 520.626{{c}}
: error map: {{val| 0.000 -181.329 -227.565 }}


{{Optimal ET sequence|legend=1| 2c, 5bc, 7bbcc }}
{{Optimal ET sequence|legend=1| 2c, 5bc, 7bbcc }}


[[Badness]] (Smith): 0.133021
[[Badness]] (Sintel): 3.12


=== 7-limit ===
=== 7-limit ===
Line 452: Line 482:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~3/2 = 509.892
<!-- * CTE: ~2 = 1200.000{{c}}, ~3/2 = 509.892{{c}} -->
* CWE: ~2 = 1200.000, ~3/2 = 515.099
* WE: ~2 = 1205.230{{c}}, ~3/2 = 517.557{{c}}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 515.099{{c}}


Optimal ET sequence: none
Optimal ET sequence: none


Badness (Smith): 0.118764
Badness (Sintel): 3.01


== Devolution ==
== Devolution ==
Line 471: Line 502:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~3 = 1901.955, ~5/3 = 701.863
<!-- * [[CTE]]: ~3 = 1901.955{{c}}, ~5/3 = 701.863{{c}}
: [[error map]]: {{val| 0.000 -182.496 -266.779 }}
: [[error map]]: {{val| 0.000 -182.496 -266.779 }} -->
* [[CWE]]: ~3 = 1901.995, ~5/3 = 691.468
* [[WE]]: ~3 = 1988.549{{c}}, ~3/2 = 719.679{{c}}
: error map: {{val| +86.594 -78.085 -111.407 }}
* [[CWE]]: ~3 = 1901.995{{c}}, ~5/3 = 691.468{{c}}
: error map: {{val| 0.000 -192.891 -256.384 }}
: error map: {{val| 0.000 -192.891 -256.384 }}


[[Optimal ET sequence]]: [[1edt|b1]], [[2edt|b2d]], [[3edt|b3]], [[8edt|b8cdd]]
[[Optimal ET sequence]]: [[1edt|b1]], [[2edt|b2d]], [[3edt|b3]], [[8edt|b8cdd]]


[[Badness]]:
[[Badness]] (Sintel): 0.751
* Smith: 0.00406
* Dirichlet: 0.751


== Codex ==
== Codex ==
Line 494: Line 525:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~7/5 = 600.000, ~5/3 = 935.289
<!-- * [[CTE]]: ~7/5 = 600.000{{c}}, ~5/3 = 935.289{{c}}
: [[error map]]: {{val| 0.000 -31.377 +19.554 +37.041 }}
: [[error map]]: {{val| 0.000 -31.377 +19.554 +37.041 }} -->
* [[CWE]]: ~7/5 = 600.000, ~5/3 = 936.030
* [[WE]]: ~7/5 = 598.589{{c}}, ~5/3 = 934.978{{c}}
: error map: {{val| -2.821 -31.998 +18.621 +34.699 }}
* [[CWE]]: ~7/5 = 600.000{{c}}, ~5/3 = 936.030{{c}}
: error map: {{val| 0.000 -29.895 +21.776 +39.264 }}
: error map: {{val| 0.000 -29.895 +21.776 +39.264 }}


{{Optimal ET sequence|legend=1| 4, 10cd, 14d }}
{{Optimal ET sequence|legend=1| 4, 10cd, 14d }}


[[Badness]] (Smith): 0.077065
[[Badness]] (Sintel): 1.95


== Oxygen ==
== Oxygen ==
Line 513: Line 546:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~10/9 = 161.341
* [[WE]]: ~2 = 1213.695{{c}}, ~10/9 = 171.042{{c}}
: error map: {{val| +13.695 +12.309 -0.438 -69.825 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~10/9 = 166.042{{c}}
: error map: {{val| 0.000 -0.083 -16.526 -100.911 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~10/9 = 161.341{{c}}
: [[error map]]: {{val| 0.000 +14.023 +6.982 -91.507 }}
: [[error map]]: {{val| 0.000 +14.023 +6.982 -91.507 }}
* [[POTE]]: ~2 = 1200.000, ~10/9 = 169.112
* [[POTE]]: ~2 = 1200.000{{c}}, ~10/9 = 169.112{{c}}
: error map: {{val| 0.000 -9.291 -31.873 -107.050 }}
: error map: {{val| 0.000 -9.291 -31.873 -107.050 }} -->


{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}
{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}


[[Badness]] (Smith): 0.059866
[[Badness]] (Sintel): 1.52


== Bixby ==
== Bixby ==
''Main article: [[Bixby]]''
{{Main| Bixby }}
 
''See also: [[Circular temperament]]''


[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5
Line 531: Line 566:
[[Comma list]]: [[4/3]]
[[Comma list]]: [[4/3]]


[[Mapping]]: [[1 2 2][0 0 1]]
{{Mapping|legend=1| 1 2 0 | 0 0 1 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1020.058{{c}}, ~5/4 = 674.394{{c}}
: [[error map]]: {{val| -179.942 +138.161 -71.803 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 629.521{{c}}
: error map: {{val| 0.000 +498.045 +243.208 }}


[[Optimal tuning|Optimal tunings]]:
{{Optimal ET sequence|legend=1| 1c, 2b, 3bbcc }}


* CWE: ~2 = 1200.000, ~5/4 = 629.521
[[Badness]] (Sintel): 0.424


== Archon ==
== Archon ==
[[Subgroup]]: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 5/4
[[Comma list]]: [[5/4]]


[[Mapping]]: [[1 1 2][0 1 0]]
{{Mapping|legend=1| 1 0 2 | 0 1 0 }}
 
[[Optimal tuning]]s:
* WE: ~2 = 1268.274{{c}}, ~3/2 = 612.921{{c}}
: error map: {{val| +68.274 -20.760 -249.765 }}
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 614.055{{c}}
: error map: {{val| 0.000 -87.900 -386.314 }}


[[Optimal tuning|Optimal tunings]]:
{{Optimal ET sequence|legend=1| 2c }}


* WE: ~2 = 1268.274, ~3/2 = 612.921
[[Badness]] (Sintel): 0.474
** Error map: (68.274, -20.760, -249.765)  
* CWE: ~2 = 1200.000, ~3/2 = 614.055
** Error map: (0.000, -87.900, -386.314)


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Pages with mostly numerical content]]
Retrieved from "https://en.xen.wiki/w/Very_low_accuracy_temperaments"