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Whitewood family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 386.314{{c}} (~80/81 = 43.457{{c}})
* [[WE]]: ~9/8 = 172.1541{{c}}, ~5/4 = 376.0535{{c}} (~80/81 = 31.7453{{c}})
: [[error map]]: {{val| +5.079 -8.260 -0.102 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 378.3830{{c}} (~80/81 = 35.5258{{c}})
: error map: {{val| 0.000 -16.241 -7.931 }}
<!-- * [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 386.314{{c}} (~80/81 = 43.457{{c}})
: [[error map]]: {{val| 0.000 -16.241 0.000 }}
: [[error map]]: {{val| 0.000 -16.241 0.000 }}
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 374.469{{c}} (~80/81 = 31.612{{c}})
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 374.469{{c}} (~80/81 = 31.612{{c}})
: error map: {{val| 0.000 -16.241 -11.845 }}
: error map: {{val| 0.000 -16.241 -11.845 }} -->


{{Optimal ET sequence|legend=1| 7, 21, 28, 35, 77bb }}
{{Optimal ET sequence|legend=1| 7, 21, 28, 35, 77bbc }}


[[Badness]] (Smith): 0.154651
[[Badness]] (Sintel): 3.63


== Septimal whitewood ==
== Septimal whitewood ==
Line 37: Line 41:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.930{{c}} (~64/63 = 50.073{{c}})
* [[WE]]: ~9/8 = 171.5524{{c}}, ~5/4 = 392.9834{{c}} (~64/63 = 49.8786{{c}})
: [[error map]]: {{val| +0.867 -14.879 +8.403 +12.343 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 392.7412{{c}} (~64/63 = 49.8841{{c}})
: error map: {{val| 0.000 -16.241 +6.428 +9.861 }}
<!-- * [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.930{{c}} (~64/63 = 50.073{{c}})
: [[error map]]: {{val| 0.000 -16.241 +6.617 +9.672 }}
: [[error map]]: {{val| 0.000 -16.241 +6.617 +9.672 }}
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.700{{c}} (~64/63 = 49.843{{c}})
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 392.700{{c}} (~64/63 = 49.843{{c}})
: error map: {{val| 0.000 -16.241 +6.386 +9.903 }}
: error map: {{val| 0.000 -16.241 +6.386 +9.903 }} -->


{{Optimal ET sequence|legend=1| 7, 14, 21, 28, 49b }}
{{Optimal ET sequence|legend=1| 7, 14, 21, 28, 49b }}


[[Badness]] (Smith): 0.113987
[[Badness]] (Sintel): 2.88


=== 11-limit ===
=== 11-limit ===
Line 54: Line 62:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~5/4 = 390.178{{c}} (~64/63 = 47.321{{c}})
* WE: ~11/10 = 171.4451{{c}}, ~5/4 = 390.0053{{c}} (~64/63 = 47.1151{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~5/4 = 389.968{{c}} (~64/63 = 47.111{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 389.9864{{c}} (~64/63 = 47.1293{{c}})
<!-- * CTE: ~11/10 = 171.429{{c}}, ~5/4 = 390.178{{c}} (~64/63 = 47.321{{c}})
* POTE: ~11/10 = 171.429{{c}}, ~5/4 = 389.968{{c}} (~64/63 = 47.111{{c}}) -->


{{Optimal ET sequence|legend=0| 7, 14e, 21, 28, 49b }}
{{Optimal ET sequence|legend=0| 7, 14e, 21, 28 }}


Badness (Smith): 0.060908
Badness (Sintel): 2.01


=== 13-limit ===
=== 13-limit ===
Line 69: Line 79:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~5/4 = 390.178{{c}} (~64/63 = 47.321{{c}})
* WE: ~11/10 = 171.3236{{c}}, ~5/4 = 390.4957{{c}} (~64/63 = 47.8484{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~5/4 = 390.735{{c}} (~64/63 = 47.878{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 390.6336{{c}} (~64/63 = 47.7765{{c}})
<!-- * CTE: ~11/10 = 171.429{{c}}, ~5/4 = 390.178{{c}} (~64/63 = 47.321{{c}})
* POTE: ~11/10 = 171.429{{c}}, ~5/4 = 390.735{{c}} (~64/63 = 47.878{{c}}) -->


{{Optimal ET sequence|legend=0| 7, 14e, 21, 28, 49bf }}
{{Optimal ET sequence|legend=0| 7, 14e, 21, 28 }}


Badness (Smith): 0.039956
Badness (Sintel): 1.65


== Redwood ==
== Redwood ==
Line 84: Line 96:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 376.366{{c}} (~36/35 = 33.509{{c}})
* [[WE]]: ~9/8 = 171.5524{{c}}, ~5/4 = 392.9834{{c}} (~36/35 = 49.8786{{c}})
: [[error map]]: {{val| +0.867 -14.879 +8.403 +12.343 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 392.7412{{c}} (~36/35 = 49.8841{{c}})
: error map: {{val| 0.000 -16.241 +6.428 +9.861 }}
<!-- * [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 376.366{{c}} (~36/35 = 33.509{{c}})
: [[error map]]: {{val| 0.000 -16.241 -9.948 -7.271 }}
: [[error map]]: {{val| 0.000 -16.241 -9.948 -7.271 }}
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 378.152{{c}} (~36/35 = 35.295{{c}})
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 378.152{{c}} (~36/35 = 35.295{{c}})
: error map: {{val| 0.000 -16.241 -8.162 -10.845 }}
: error map: {{val| 0.000 -16.241 -8.162 -10.845 }} -->


{{Optimal ET sequence|legend=1| 7, 28d, 35 }}
{{Optimal ET sequence|legend=1| 7, 28d, 35 }}


[[Badness]] (Smith): 0.165257
[[Badness]] (Sintel): 4.18


=== 11-limit ===
=== 11-limit ===
Line 101: Line 117:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~5/4 = 376.745{{c}} (~36/35 = 33.888{{c}})
* WE: ~11/10 = 171.9390{{c}}, ~5/4 = 377.8321{{c}} (~36/35 = 33.9542{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~5/4 = 376.711{{c}} (~36/35 = 33.854{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 376.7162{{c}} (~36/35 = 33.8590{{c}})
<!-- * CTE: ~11/10 = 171.429{{c}}, ~5/4 = 376.745{{c}} (~36/35 = 33.888{{c}})
* POTE: ~11/10 = 171.429{{c}}, ~5/4 = 376.711{{c}} (~36/35 = 33.854{{c}}) -->


{{Optimal ET sequence|legend=0| 7, 28d, 35 }}
{{Optimal ET sequence|legend=0| 7, 28d, 35 }}


Badness (Smith): 0.078193
Badness (Sintel): 2.59


== Mujannab ==
== Mujannab ==
Line 116: Line 134:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 386.314{{c}} (~80/81 = 43.457{{c}})
* [[WE]]: ~9/8 = 170.8233{{c}}, ~5/4 = 393.7921{{c}} (~15/14 = 52.1453{{c}})
: [[error map]]: {{val| -4.236 -22.898 -0.994 +47.642 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~5/4 = 392.7194{{c}} (~15/14 = 49.8622{{c}})
: error map: {{val| 0.000 -16.241 +6.406 +59.746 }}
<!-- * [[CTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 386.314{{c}} (~80/81 = 43.457{{c}})
: [[error map]]: {{val| 0.000 -16.241 0.000 +59.746 }}
: [[error map]]: {{val| 0.000 -16.241 0.000 +59.746 }}
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 395.187{{c}} (~15/14 = 52.330{{c}})
* [[POTE]]: ~9/8 = 171.429{{c}}, ~5/4 = 395.187{{c}} (~15/14 = 52.330{{c}})
: error map: {{val| 0.000 -16.241 +8.873 +59.746 }}
: error map: {{val| 0.000 -16.241 +8.873 +59.746 }} -->


{{Optimal ET sequence|legend=1| 7, 14d }}
{{Optimal ET sequence|legend=1| 7, 14d }}


[[Badness]] (Smith): 0.105820
[[Badness]] (Sintel): 2.68


=== 11-limit ===
=== 11-limit ===
Line 133: Line 155:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~5/4 = 384.318{{c}} (~33/32 = 41.461{{c}})
* WE: ~11/10 = 170.8171{{c}}, ~5/4 = 393.2529{{c}} (~33/32 = 51.6187{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~5/4 = 394.661{{c}} (~33/32 = 51.804{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 391.8401{{c}} (~33/32 = 48.9830{{c}})
<!-- * CTE: ~11/10 = 171.429{{c}}, ~5/4 = 384.318{{c}} (~33/32 = 41.461{{c}})
* POTE: ~11/10 = 171.429{{c}}, ~5/4 = 394.661{{c}} (~33/32 = 51.804{{c}}) -->


{{Optimal ET sequence|legend=0| 7, 14de }}
{{Optimal ET sequence|legend=0| 7, 14de }}


Badness (Smith): 0.060985
Badness (Sintel): 2.02


=== 13-limit ===
=== 13-limit ===
Line 148: Line 172:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~5/4 = 384.318{{c}} (~33/32 = 41.461{{c}})
* WE: ~11/10 = 170.7953{{c}}, ~5/4 = 393.6112{{c}} (~33/32 = 52.0206{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~5/4 = 395.071{{c}} (~33/32 = 52.214{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~5/4 = 392.7250{{c}} (~33/32 = 49.8678{{c}})
<!-- * CTE: ~11/10 = 171.429{{c}}, ~5/4 = 384.318{{c}} (~33/32 = 41.461{{c}})
* POTE: ~11/10 = 171.429{{c}}, ~5/4 = 395.071{{c}} (~33/32 = 52.214{{c}}) -->


{{Optimal ET sequence|legend=0| 7, 14de }}
{{Optimal ET sequence|legend=0| 7, 14de }}


Badness (Smith): 0.042830
Badness (Sintel): 1.77


== Greenwood ==
== Greenwood ==
Line 165: Line 191:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~9/8 = 171.429{{c}}, ~15/14 = 108.062{{c}} (~21/20 = 63.367{{c}})
* [[WE]]: ~9/8 = 172.1073{{c}}, ~15/14 = 101.7681{{c}} (~21/20 = 70.3391{{c}})
: [[error map]]: {{val| +4.751 -8.775 -1.169 +2.980 }}
* [[CWE]]: ~9/8 = 171.4286{{c}}, ~15/14 = 103.3802{{c}} (~21/20 = 68.0484{{c}})
: error map: {{val| 0.000 -16.241 -8.125 -8.303 }}
<!-- * [[CTE]]: ~9/8 = 171.429{{c}}, ~15/14 = 108.062{{c}} (~21/20 = 63.367{{c}})
: [[error map]]: {{val| 0.000 -16.241 +1.239 -3.621 }}
: [[error map]]: {{val| 0.000 -16.241 +1.239 -3.621 }}
* [[POTE]]: ~9/8 = 171.429{{c}}, ~15/14 = 101.367{{c}} (~21/20 = 70.062{{c}})
* [[POTE]]: ~9/8 = 171.429{{c}}, ~15/14 = 101.367{{c}} (~21/20 = 70.062{{c}})
: error map: {{val| 0.000 -16.241 -12.152 -10.316 }}
: error map: {{val| 0.000 -16.241 -12.152 -10.316 }} -->


{{Optimal ET sequence|legend=1| 7c, 14c, 21, 35, 84bbccd }}
{{Optimal ET sequence|legend=1| 7c, 14c, 21, 35, 84bbccd }}


[[Badness]] (Smith): 0.121752
[[Badness]] (Sintel): 3.08


=== 11-limit ===
=== 11-limit ===
Line 182: Line 212:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~15/14 = 106.997{{c}} (~21/20 = 64.432{{c}})
* WE: ~11/10 = 172.0795{{c}}, ~15/14 = 100.5259{{c}} (~21/20 = 71.5536{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~15/14 = 100.046{{c}} (~21/20 = 71.383{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~15/14 = 102.1866{{c}} (~21/20 = 69.2419{{c}})
<!-- * CTE: ~9/8 = 171.429{{c}}, ~15/14 = 106.997{{c}} (~21/20 = 64.432{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~15/14 = 100.046{{c}} (~21/20 = 71.383{{c}}) -->


{{Optimal ET sequence|legend=0| 7ce, 14c, 21, 35, 49bcde }}
{{Optimal ET sequence|legend=0| 7ce, 14c, 21, 35, 49bcde }}


Badness (Smith): 0.057471
Badness (Sintel): 1.90


=== 13-limit ===
=== 13-limit ===
Line 197: Line 229:


Optimal tunings:  
Optimal tunings:  
* CTE: ~9/8 = 171.429{{c}}, ~15/14 = 106.997{{c}} (~21/20 = 64.432{{c}})
* WE: ~11/10 = 171.6777{{c}}, ~15/14 = 104.4016{{c}} (~21/20 = 67.2761{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~15/14 = 104.250{{c}} (~21/20 = 67.179{{c}})
* CWE: ~11/10 = 171.4286{{c}}, ~15/14 = 104.8518{{c}} (~21/20 = 66.5768{{c}})
<!-- * CTE: ~9/8 = 171.429{{c}}, ~15/14 = 106.997{{c}} (~21/20 = 64.432{{c}})
* POTE: ~9/8 = 171.429{{c}}, ~15/14 = 104.250{{c}} (~21/20 = 67.179{{c}}) -->


{{Optimal ET sequence|legend=0| 7ce, 14c, 21, 35 }}
{{Optimal ET sequence|legend=0| 7ce, 14c, 21, 35 }}


Badness (Smith): 0.054009
Badness (Sintel): 2.23


[[Category:Temperament families]]
[[Category:Temperament families]]
Retrieved from "https://en.xen.wiki/w/Whitewood_family"