Sensamagic family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus
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{{Mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }}
{{Mapping|legend=1| 1 0 0 0 | 0 1 1 2 | 0 0 2 -1 }}
: mapping generators: ~2, ~3, ~9/7
: mapping generators: ~2, ~3, ~9/7


Line 21: Line 20:
: Angle (3/2, 9/7) = 86.5288°
: Angle (3/2, 9/7) = 86.5288°


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 703.7414{{c}}, ~9/7 = 440.9014{{c}}
: [[error map]]: {{val| -0.002 +1.785 -0.771 -2.248 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}}
: error map: {{val| 0.000 +1.786 -0.769 -2.245 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 33: Line 37:
{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}
{{Optimal ET sequence|legend=1| 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283 }}


[[Badness]] (Smith): 0.129 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.570


[[Projection pair]]: 5 243/49 to 2.3.7
[[Projection pair]]: 5 243/49 to 2.3.7
Line 58: Line 62:
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }}
{{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 2 -2 | 0 0 2 -1 -1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9667{{c}}, ~3/2 = 703.7809{{c}}, ~9/7 = 440.9056{{c}}
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 21/13 6/13 -1/13 1/13 -3/13 }}, {{monzo| 35/13 10/13 7/13 -7/13 -5/13 }}, {{monzo| 35/13 10/13 -6/13 6/13 -5/13 }}, {{monzo| 42/13 -14/13 -2/13 2/13 7/13 }}]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 21/13 6/13 -1/13 1/13 -3/13 }}, {{monzo| 35/13 10/13 7/13 -7/13 -5/13 }}, {{monzo| 35/13 10/13 -6/13 6/13 -5/13 }}, {{monzo| 42/13 -14/13 -2/13 2/13 7/13 }}]
: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9
: [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/9


{{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283, 607bd, 694bd }}
{{Optimal ET sequence|legend=1| 17, 19, 22, 41, 68, 87, 196, 283 }}


[[Badness]] (Smith): 0.722 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.868


[[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7
[[Projection pair]]s: 5 243/49 11 896/81 to 2.3.7
Line 78: Line 87:
Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}
Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}


{{Optimal ET sequence|legend=0| 17, 22, 41, 46, 63, 87, 237, 283, 324d, 370bd, 411bd, 607bd, 694bd }}
Optimal tunings:
* WE: ~2 = 1199.9905{{c}}, ~3/2 = 703.7325{{c}}, ~9/7 = 440.9149{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.7381{{c}}, ~9/7 = 440.9184{{c}}


Badness (Smith): 1.20 × 10<sup>-3</sup>
{{Optimal ET sequence|legend=0| 17, 19f, 22, 41, 46, 63, 87, 237, 283 }}
 
Badness (Sintel): 1.12


== Sensawer ==
== Sensawer ==
Line 89: Line 102:
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }}
{{Mapping|legend=1| 1 0 0 0 -3 | 0 1 1 2 5 | 0 0 2 -1 -4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.1900{{c}}, ~9/7 = 441.1359{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.1654{{c}}, ~3/2 = 703.2870{{c}}, ~9/7 = 441.1967{{c}}
: [[error map]]: {{val| -0.033 +1.793 -0.755 -2.236 +0.048 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2917{{c}}, ~9/7 = 441.1849{{c}}
: error map: {{val| 0.000 +1.840 -0.683 -2.1554 +0.175 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.1900{{c}}, ~9/7 = 441.1359{{c}} -->


{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87, 302d, 389d, 476bd }}
{{Optimal ET sequence|legend=1| 14c, 19e, 27e, 41, 60e, 87 }}


[[Badness]] (Smith): 0.796 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.957


=== 13-limit ===
=== 13-limit ===
Line 101: Line 119:


Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}
Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}
Optimal tunings:
* WE: ~2 = 1199.9800{{c}}, ~3/2 = 703.4468{{c}}, ~9/7 = 441.3705{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.4494{{c}}, ~9/7 = 441.3758{{c}}


{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}
{{Optimal ET sequence|legend=0| 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd }}


Badness (Smith): 0.928 × 10<sup>-3</sup>
Badness (Sintel): 0.868


== Octarod ==
== Octarod ==
Line 113: Line 135:
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }}
{{Mapping|legend=1| 1 0 0 0 2 | 0 1 1 2 0 | 0 0 2 -1 4 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 705.0464{{c}}, ~9/7 = 439.5050{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.2854{{c}}, ~3/2 = 704.6266{{c}}, ~9/7 = 439.2433{{c}}
: [[error map]]: {{val| -0.715 +1.957 -3.915 -0.245 +4.226 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5246{{c}}, ~9/7 = 439.2798{{c}}
: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.0464{{c}}, ~9/7 = 439.5050{{c}} -->


{{Optimal ET sequence|legend=1| 8d, 14c, 19, 22, 27e, 41, 104, 131e }}
{{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e }} *


[[Badness]] (Smith): 0.581 × 10<sup>-3</sup>
<nowiki/>[[optimal patent val]]: [[104edo|104]]
 
[[Badness]] (Sintel): 0.698


Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]]
Scales: [[octarod1]], [[octarod2]], [[octarod3]], [[octarod4]], [[octarod5]]
Line 128: Line 157:
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }}
{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 1 2 4 | 0 0 2 -1 3 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 706.3702{{c}}, ~9/7 = 442.1147{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.9114{{c}}, ~3/2 = 705.7294{{c}}, ~9/7 = 441.7137{{c}}
: [[error map]]: {{val| -1.089 +2.686 +1.754 -1.258 -3.259 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 705.8402{{c}}, ~9/7 = 442.1064{{c}}
: error map: {{val| 0.000 +3.885 +3.739 +0.748 -1.638 }}
<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 706.3702{{c}}, ~9/7 = 442.1147{{c}} -->


{{Optimal ET sequence|legend=1| 22, 46, 68, 95, 141bc, 163bc, 209bc, 350bc }}
{{Optimal ET sequence|legend=1| 19e, 22, 27e, 46, 68, 95, 141bc, 163bc }}


[[Badness]] (Smith): 0.877 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.05


=== Shrusic ===
=== Shrusic ===
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Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}
Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}


{{Optimal ET sequence|legend=0| 22, 46, 211bcf, 233bcf, 257bcf, 279bcf }}
Optimal tunings:
* WE: ~2 = 1199.7256{{c}}, ~3/2 = 704.9071{{c}}, ~9/7 = 443.1303{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.9572{{c}}, ~9/7 = 443.2018{{c}}
 
{{Optimal ET sequence|legend=0| 19e, 22, 27e, 46 }}


Badness (Smith): 1.125 × 10<sup>-3</sup>
Badness (Sintel): 1.05


== Bisector ==
== Bisector ==
Line 151: Line 189:


{{Mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }}
{{Mapping|legend=1| 2 0 0 0 3 | 0 1 1 2 1 | 0 0 2 -1 1 }}
: mapping generators: ~77/54, ~3, ~9/7
: mapping generators: ~77/54, ~3, ~9/7


[[Optimal tuning]] ([[POTE]]): ~77/54 = 600.0000{{c}}, ~3/2 = 703.0884{{c}}, ~9/7 = 441.1060{{c}}
[[Optimal tuning]]s:
* [[WE]]: ~2 = 600.3096{{c}}, ~3/2 = 703.4512{{c}}, ~9/7 = 441.3336{{c}}
: [[error map]]: {{val| +0.619 +2.115 +0.424 -2.019 -4.985 }}
* [[CWE]]: ~2 = 600.0000{{c}}, ~3/2 = 703.5671{{c}}, ~9/7 = 441.2436{{c}}
: error map: {{val| 0.000 +1.612 -0.259 -2.935 -6.507 }}
<!-- * [[POTE]]: ~77/54 = 600.0000{{c}}, ~3/2 = 703.0884{{c}}, ~9/7 = 441.1060{{c}} -->


{{Optimal ET sequence|legend=1| 22, 46, 68, 82e, 106de, 114, 128e }}
{{Optimal ET sequence|legend=1| 8d, 14c, 22, 38d, 46, 60e, 68, 106de, 128e, 174e }}


[[Badness]] (Smith): 1.089 × 10<sup>-3</sup>
[[Badness]] (Sintel): 1.31


== Sensigh ==
== Sensigh ==
Line 166: Line 208:


Mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 | 0 0 0 0 1 0 }}
Mapping: {{mapping| 1 6 8 11 0 10 | 0 -7 -9 -13 0 -10 | 0 0 0 0 1 0 }}
: mapping generators: ~2, ~9/7, ~11


: mapping generators: ~2, ~9/7, ~11
Optimal tunings:  
* WE: ~2 = 1200.0000{{c}}, ~9/7 = 443.4379{{c}}, ~11/8 = 550.3462{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3581{{c}}, ~11/8 = 550.7092{{c}}


{{Optimal ET sequence|legend=0| 19, 27, 46, 111df, 157df }}
{{Optimal ET sequence|legend=0| 27e, 38df, 46, 111df }}


Badness (Smith): 0.939 × 10<sup>-3</sup>
Badness (Sintel): 0.878


=== 17-limit ===
=== 17-limit ===
Line 180: Line 225:
Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }}
Mapping: {{mapping| 1 6 8 11 0 10 0 | 0 -7 -9 -13 0 -10 1 | 0 0 0 0 1 0 1 }}


{{Optimal ET sequence|legend=0| 19, 27, 46 }}
Optimal tunings:
* WE: ~2 = 1200.2286{{c}}, ~9/7 = 443.4291{{c}}, ~11/8 = 549.2790{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3707{{c}}, ~11/8 = 549.5775{{c}}
 
{{Optimal ET sequence|legend=0| 27eg, 38df, 46 }}
 
Badness (Sintel): 0.917


[[Category:Temperament families]]
[[Category:Temperament families]]

Revision as of 15:24, 11 October 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 sensamagic family of rank-3 temperaments tempers out the sensamagic comma, 245/243.

For a list of rank-2 temperaments, see Sensamagic clan.

Sensamagic

Main article: Sensamagic

Subgroup: 2.3.5.7

Comma list: 245/243

Mapping: [⟨1 0 0 0], ⟨0 1 1 2], ⟨0 0 2 -1]]

mapping generators: ~2, ~3, ~9/7

Mapping to lattice: [⟨0 1 1 2], ⟨0 0 2 -1]]

Lattice basis:

3/2 length = 0.9644, 9/7 length = 1.0807
Angle (3/2, 9/7) = 86.5288°

Optimal tunings:

  • WE: ~2 = 1199.9983 ¢, ~3/2 = 703.7414 ¢, ~9/7 = 440.9014 ¢
error map: ⟨-0.002 +1.785 -0.771 -2.248]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.7411 ¢, ~9/7 = 440.9017 ¢
error map: ⟨0.000 +1.786 -0.769 -2.245]

Minimax tuning:

[[1 0 0 0⟩, [0 0 1/5 2/5⟩, [0 0 1 0⟩, [0 0 0 1⟩]
unchanged-interval (eigenmonzo) basis: 2.5.7
[[1 0 0 0⟩, [0 1 0 0⟩, [0 5/3 2/3 -2/3⟩, [0 5/3 -1/3 1/3⟩]
unchanged-interval (eigenmonzo) basis: 2.3.7/5

Optimal ET sequence: 5, 8d, 14c, 17, 19, 27, 41, 68, 87, 128, 196, 283

Badness (Sintel): 0.570

Projection pair: 5 243/49 to 2.3.7

Minkowski blocks

2.3.7 subgroup

  • 12: 729/686, 64/63
  • 17: 64/63, 19683/19208
  • 19: 49/48, 177147/175616
  • 22: 64/63, 537824/531441
  • 24: 64/63, 15059072/14348907

Overview to extensions

Temperaments discussed elsewhere include supernatural (→ Keemic family). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, bisector and sensigh.

Undecimal sensamagic

Main article: Sensamagic

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384

Mapping: [⟨1 0 0 0 7], ⟨0 1 1 2 -2], ⟨0 0 2 -1 -1]]

Optimal tunings:

  • WE: ~2 = 1199.9667 ¢, ~3/2 = 703.7809 ¢, ~9/7 = 440.9056 ¢
error map: ⟨-0.033 +1.793 -0.755 -2.236 +0.048]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.7948 ¢, ~9/7 = 440.9180 ¢
error map: ⟨0.000 +1.840 -0.683 -2.1554 +0.175]

Minimax tuning:

[[1 0 0 0 0⟩, [21/13 6/13 -1/13 1/13 -3/13⟩, [35/13 10/13 7/13 -7/13 -5/13⟩, [35/13 10/13 -6/13 6/13 -5/13⟩, [42/13 -14/13 -2/13 2/13 7/13⟩]
unchanged-interval (eigenmonzo) basis: 2.7/5.11/9

Optimal ET sequence: 17, 19, 22, 41, 68, 87, 196, 283

Badness (Sintel): 0.868

Projection pairs: 5 243/49 11 896/81 to 2.3.7

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 245/243, 352/351, 364/363

Mapping: [⟨1 0 0 0 7 12], ⟨0 1 1 2 -2 -5], ⟨0 0 2 -1 -1 -1]]

Optimal tunings:

  • WE: ~2 = 1199.9905 ¢, ~3/2 = 703.7325 ¢, ~9/7 = 440.9149 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.7381 ¢, ~9/7 = 440.9184 ¢

Optimal ET sequence: 17, 19f, 22, 41, 46, 63, 87, 237, 283

Badness (Sintel): 1.12

Sensawer

Subgroup: 2.3.5.7.11

Comma list: 245/243, 441/440

Mapping: [⟨1 0 0 0 -3], ⟨0 1 1 2 5], ⟨0 0 2 -1 -4]]

Optimal tunings:

  • WE: ~2 = 1200.1654 ¢, ~3/2 = 703.2870 ¢, ~9/7 = 441.1967 ¢
error map: ⟨-0.033 +1.793 -0.755 -2.236 +0.048]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.2917 ¢, ~9/7 = 441.1849 ¢
error map: ⟨0.000 +1.840 -0.683 -2.1554 +0.175]

Optimal ET sequence: 14c, 19e, 27e, 41, 60e, 87

Badness (Sintel): 0.957

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 352/351

Mapping: [⟨1 0 0 0 -3 2], ⟨0 1 1 2 5 2], ⟨0 0 2 -1 -4 -4]]

Optimal tunings:

  • WE: ~2 = 1199.9800 ¢, ~3/2 = 703.4468 ¢, ~9/7 = 441.3705 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 703.4494 ¢, ~9/7 = 441.3758 ¢

Optimal ET sequence: 14c, 19e, 27e, 41, 46, 60e, 68e, 87, 522bd

Badness (Sintel): 0.868

Octarod

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243

Mapping: [⟨1 0 0 0 2], ⟨0 1 1 2 0], ⟨0 0 2 -1 4]]

Optimal tunings:

  • WE: ~2 = 1199.2854 ¢, ~3/2 = 704.6266 ¢, ~9/7 = 439.2433 ¢
error map: ⟨-0.715 +1.957 -3.915 -0.245 +4.226]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.5246 ¢, ~9/7 = 439.2798 ¢
error map: ⟨0.000 +2.570 -3.230 +0.944 +5.801]

Optimal ET sequence: 14c, 19, 22, 27e, 41, 90e, 131e *

optimal patent val: 104

Badness (Sintel): 0.698

Scales: octarod1, octarod2, octarod3, octarod4, octarod5

Shrusus

Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243

Mapping: [⟨1 0 0 0 -4], ⟨0 1 1 2 4], ⟨0 0 2 -1 3]]

Optimal tunings:

  • WE: ~2 = 1198.9114 ¢, ~3/2 = 705.7294 ¢, ~9/7 = 441.7137 ¢
error map: ⟨-1.089 +2.686 +1.754 -1.258 -3.259]
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 705.8402 ¢, ~9/7 = 442.1064 ¢
error map: ⟨0.000 +3.885 +3.739 +0.748 -1.638]

Optimal ET sequence: 19e, 22, 27e, 46, 68, 95, 141bc, 163bc

Badness (Sintel): 1.05

Shrusic

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 176/175, 245/243

Mapping: [⟨1 0 0 0 -4 1], ⟨0 1 1 2 4 1], ⟨0 0 2 -1 3 3]]

Optimal tunings:

  • WE: ~2 = 1199.7256 ¢, ~3/2 = 704.9071 ¢, ~9/7 = 443.1303 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 704.9572 ¢, ~9/7 = 443.2018 ¢

Optimal ET sequence: 19e, 22, 27e, 46

Badness (Sintel): 1.05

Bisector

Subgroup: 2.3.5.7.11

Comma list: 121/120, 245/243

Mapping: [⟨2 0 0 0 3], ⟨0 1 1 2 1], ⟨0 0 2 -1 1]]

mapping generators: ~77/54, ~3, ~9/7

Optimal tunings:

  • WE: ~2 = 600.3096 ¢, ~3/2 = 703.4512 ¢, ~9/7 = 441.3336 ¢
error map: ⟨+0.619 +2.115 +0.424 -2.019 -4.985]
  • CWE: ~2 = 600.0000 ¢, ~3/2 = 703.5671 ¢, ~9/7 = 441.2436 ¢
error map: ⟨0.000 +1.612 -0.259 -2.935 -6.507]

Optimal ET sequence: 8d, 14c, 22, 38d, 46, 60e, 68, 106de, 128e, 174e

Badness (Sintel): 1.31

Sensigh

Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 126/125, 169/168

Mapping: [⟨1 6 8 11 0 10], ⟨0 -7 -9 -13 0 -10], ⟨0 0 0 0 1 0]]

mapping generators: ~2, ~9/7, ~11

Optimal tunings:

  • WE: ~2 = 1200.0000 ¢, ~9/7 = 443.4379 ¢, ~11/8 = 550.3462 ¢
  • CWE: ~2 = 1200.0000 ¢, ~9/7 = 443.3581 ¢, ~11/8 = 550.7092 ¢

Optimal ET sequence: 27e, 38df, 46, 111df

Badness (Sintel): 0.878

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 91/90, 126/125, 154/153, 169/168

Mapping: [⟨1 6 8 11 0 10 0], ⟨0 -7 -9 -13 0 -10 1], ⟨0 0 0 0 1 0 1]]

Optimal tunings:

  • WE: ~2 = 1200.2286 ¢, ~9/7 = 443.4291 ¢, ~11/8 = 549.2790 ¢
  • CWE: ~2 = 1200.0000 ¢, ~9/7 = 443.3707 ¢, ~11/8 = 549.5775 ¢

Optimal ET sequence: 27eg, 38df, 46

Badness (Sintel): 0.917

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