Whitewood family: Difference between revisions

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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]]

Revision as of 15:06, 10 September 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The whitewood family of temperaments tempers out the apotome, 2187/2048. Consequently the fifths are always 4/7 of an octave, a distinctly flat 685.714 cents. While quite flat, this is close enough to a just fifth to serve as one, and some people are fond of it.

The 5-limit version of this temperament is called whitewood, to serve in contrast with the blackwood temperament which tempers out 256/243, the pythagorean limma. Whereas blackwood temperament can be thought of as a closed chain of 5 fifths and a major third generator, whitewood is a closed chain of 7 fifths and a major third generator. This means that blackwood is generally supported by 5n-edos, and whitewood is supported by 7n-edos, and the mos of both scales follow a similar pattern.

The 14-note mos of whitewood, like the 10-note mos of blackwood, shares a number of interesting properties which derive from the relatively small circle of fifths common to both. From any major or minor triad in the scale, one can always move away by ~3/2 or ~4/3 to reach another triad of the same type. This contrasts with the diatonic scale, in which one will eventually "hit a wall" if one moves by perfect fifth for long enough; the chain of fifths will eventually "stop" and make the next fifth a diminished fifth. This means that this scale is, in a sense, "pantonal", since resolutions that work in one key will work in all other keys in the scale, at least keys that share the same chord quality.

Another interesting property is that it becomes possible to construct "super-linked" 5-limit chords. In Whitewood[14], or Blackwood[10], if one stacks alternating major and minor thirds on top of one another, one will eventually come back to the root without ever hitting a wall, and hence the pattern can continue forever. Since all of the diatonic modes can be thought of as a stacked chain of 7 alternating thirds, placed in inversion, this means that Whitewood[14] and Blackwood[10] also make for excellent "panmodal" scales, in which you can construct "modal" sounding sonorities in one key that will work in all keys.

Lastly, while blackwood fifths are sharp and thus necessitate the tuning as a whole to be sharp-leaning, whitewood fifths are flat and thus this tuning is generally flat-leaning.

Whitewood

Subgroup: 2.3.5

Comma list: 2187/2048

Mapping: [⟨7 11 0], ⟨0 0 1]]

mapping generators: ~9/8, ~5

Optimal tunings:

  • WE: ~9/8 = 172.1541 ¢, ~5/4 = 376.0535 ¢ (~80/81 = 31.7453 ¢)
error map: ⟨+5.079 -8.260 -0.102]
  • CWE: ~9/8 = 171.4286 ¢, ~5/4 = 378.3830 ¢ (~80/81 = 35.5258 ¢)
error map: ⟨0.000 -16.241 -7.931]

Optimal ET sequence: 7, 21, 28, 35, 77bbc

Badness (Sintel): 3.63

Septimal whitewood

Subgroup: 2.3.5.7

Comma list: 36/35, 2187/2048

Mapping: [⟨7 11 0 36], ⟨0 0 1 -1]]

Optimal tunings:

  • WE: ~9/8 = 171.5524 ¢, ~5/4 = 392.9834 ¢ (~64/63 = 49.8786 ¢)
error map: ⟨+0.867 -14.879 +8.403 +12.343]
  • CWE: ~9/8 = 171.4286 ¢, ~5/4 = 392.7412 ¢ (~64/63 = 49.8841 ¢)
error map: ⟨0.000 -16.241 +6.428 +9.861]

Optimal ET sequence: 7, 14, 21, 28, 49b

Badness (Sintel): 2.88

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 2079/2048

Mapping: [⟨7 11 0 36 8], ⟨0 0 1 -1 1]]

Optimal tunings:

  • WE: ~11/10 = 171.4451 ¢, ~5/4 = 390.0053 ¢ (~64/63 = 47.1151 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~5/4 = 389.9864 ¢ (~64/63 = 47.1293 ¢)

Optimal ET sequence: 7, 14e, 21, 28

Badness (Sintel): 2.01

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 512/507

Mapping: [⟨7 11 0 36 8 26], ⟨0 0 1 -1 1 0]]

Optimal tunings:

  • WE: ~11/10 = 171.3236 ¢, ~5/4 = 390.4957 ¢ (~64/63 = 47.8484 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~5/4 = 390.6336 ¢ (~64/63 = 47.7765 ¢)

Optimal ET sequence: 7, 14e, 21, 28

Badness (Sintel): 1.65

Redwood

Subgroup: 2.3.5.7

Comma list: 525/512, 729/700

Mapping: [⟨7 11 0 52], ⟨0 0 1 -2]]

Optimal tunings:

  • WE: ~9/8 = 171.5524 ¢, ~5/4 = 392.9834 ¢ (~36/35 = 49.8786 ¢)
error map: ⟨+0.867 -14.879 +8.403 +12.343]
  • CWE: ~9/8 = 171.4286 ¢, ~5/4 = 392.7412 ¢ (~36/35 = 49.8841 ¢)
error map: ⟨0.000 -16.241 +6.428 +9.861]

Optimal ET sequence: 7, 28d, 35

Badness (Sintel): 4.18

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 385/384, 729/700

Mapping: [⟨7 11 0 52 8], ⟨0 0 1 -2 1]]

Optimal tunings:

  • WE: ~11/10 = 171.9390 ¢, ~5/4 = 377.8321 ¢ (~36/35 = 33.9542 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~5/4 = 376.7162 ¢ (~36/35 = 33.8590 ¢)

Optimal ET sequence: 7, 28d, 35

Badness (Sintel): 2.59

Mujannab

Subgroup: 2.3.5.7

Comma list: 54/49, 64/63

Mapping: [⟨7 11 0 20], ⟨0 0 1 0]]

Optimal tunings:

  • WE: ~9/8 = 170.8233 ¢, ~5/4 = 393.7921 ¢ (~15/14 = 52.1453 ¢)
error map: ⟨-4.236 -22.898 -0.994 +47.642]
  • CWE: ~9/8 = 171.4286 ¢, ~5/4 = 392.7194 ¢ (~15/14 = 49.8622 ¢)
error map: ⟨0.000 -16.241 +6.406 +59.746]

Optimal ET sequence: 7, 14d

Badness (Sintel): 2.68

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 54/49, 64/63

Mapping: [⟨7 11 0 20 8], ⟨0 0 1 0 1]]

Optimal tunings:

  • WE: ~11/10 = 170.8171 ¢, ~5/4 = 393.2529 ¢ (~33/32 = 51.6187 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~5/4 = 391.8401 ¢ (~33/32 = 48.9830 ¢)

Optimal ET sequence: 7, 14de

Badness (Sintel): 2.02

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 45/44, 52/49, 64/63

Mapping: [⟨7 11 0 20 8 26], ⟨0 0 1 0 1 0]]

Optimal tunings:

  • WE: ~11/10 = 170.7953 ¢, ~5/4 = 393.6112 ¢ (~33/32 = 52.0206 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~5/4 = 392.7250 ¢ (~33/32 = 49.8678 ¢)

Optimal ET sequence: 7, 14de

Badness (Sintel): 1.77

Greenwood

Subgroup: 2.3.5.7

Comma list: 405/392, 1323/1280

Mapping: [⟨7 11 1 12], ⟨0 0 2 1]]

mapping generators: ~9/8, ~15/7

Optimal tunings:

  • WE: ~9/8 = 172.1073 ¢, ~15/14 = 101.7681 ¢ (~21/20 = 70.3391 ¢)
error map: ⟨+4.751 -8.775 -1.169 +2.980]
  • CWE: ~9/8 = 171.4286 ¢, ~15/14 = 103.3802 ¢ (~21/20 = 68.0484 ¢)
error map: ⟨0.000 -16.241 -8.125 -8.303]

Optimal ET sequence: 7c, 14c, 21, 35, 84bbccd

Badness (Sintel): 3.08

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 1323/1280

Mapping: [⟨7 11 1 12 9], ⟨0 0 2 1 2]]

Optimal tunings:

  • WE: ~11/10 = 172.0795 ¢, ~15/14 = 100.5259 ¢ (~21/20 = 71.5536 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~15/14 = 102.1866 ¢ (~21/20 = 69.2419 ¢)

Optimal ET sequence: 7ce, 14c, 21, 35, 49bcde

Badness (Sintel): 1.90

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 45/44, 99/98, 640/637

Mapping: [⟨7 11 1 12 9 26], ⟨0 0 2 1 2 0]]

Optimal tunings:

  • WE: ~11/10 = 171.6777 ¢, ~15/14 = 104.4016 ¢ (~21/20 = 67.2761 ¢)
  • CWE: ~11/10 = 171.4286 ¢, ~15/14 = 104.8518 ¢ (~21/20 = 66.5768 ¢)

Optimal ET sequence: 7ce, 14c, 21, 35

Badness (Sintel): 2.23

Retrieved from "https://en.xen.wiki/index.php?title=Whitewood_family&oldid=209696"