Diminished 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]]: ~6/5 = 300.000, ~3/2 = 696.983 (~25/24 = 96.983)
* [[WE]]: ~6/5 = 299.6476{{c}}, ~3/2 = 698.6854{{c}} (~25/24 = 99.3903{{c}})
: [[error map]]: {{val| -1.410 -4.679 +9.905 }}
* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 698.2660{{c}} (~25/24 = 98.2660{{c}})
: error map: {{val| 0.000 -3.689 +11.952 }}
<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 696.983{{c}} (~25/24 = 96.983{{c}})
: [[error map]]: {{val| 0.000 -4.972 +10.670 }}
: [[error map]]: {{val| 0.000 -4.972 +10.670 }}
* [[POTE]]: ~6/5 = 300.000, ~3/2 = 699.507 (~25/24 = 99.507)
* [[POTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 699.507{{c}} (~25/24 = 99.507{{c}})
: error map: {{val| 0.000 -2.448 +13.193 }}
: error map: {{val| 0.000 -2.448 +13.193 }} -->


{{Optimal ET sequence|legend=1| 4, 8, 12 }}
{{Optimal ET sequence|legend=1| 4, 8, 12 }}


[[Badness]] (Smith): 0.047231
[[Badness]] (Sintel): 1.11


== Diminished ==
== Diminished ==
Line 33: Line 37:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~6/5 = 300.000, ~3/2 = 691.955 (~21/20 = 91.955)
* [[WE]]: ~6/5 = 299.0347{{c}}, ~3/2 = 697.2727{{c}} (~21/20 = 99.2032{{c}})
: [[error map]]: {{val| -3.861 -8.543 +4.202 +19.759 }}
* [[CWE]]: ~6/5 = 300.0000{{c}}, ~3/2 = 695.9619{{c}} (~21/20 = 95.9619{{c}})
: error map: {{val| 0.000 -5.993 +9.648 +27.136 }}
<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 691.955{{c}} (~21/20 = 91.955{{c}})
: [[error map]]: {{val| 0.000 -10.000 +5.641 +23.129 }}
: [[error map]]: {{val| 0.000 -10.000 +5.641 +23.129 }}
* [[POTE]]: ~6/5 = 300.000, ~3/2 = 699.523 (~21/20 = 99.523)
* [[POTE]]: ~6/5 = 300.000{{c}}, ~3/2 = 699.523{{c}} (~21/20 = 99.523{{c}})
: error map: {{val| 0.000 -2.432 +13.210 +30.698 }}
: error map: {{val| 0.000 -2.432 +13.210 +30.698 }} -->


{{Optimal ET sequence|legend=1| 4, 8d, 12 }}
{{Optimal ET sequence|legend=1| 4, 8d, 12 }}


[[Badness]] (Smith): 0.022401
[[Badness]] (Sintel): 0.567


=== 11-limit ===
=== 11-limit ===
Line 50: Line 58:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~3/2 = 691.955 (~21/20 = 91.955)
* WE: ~6/5 = 297.8458{{c}}, ~3/2 = 703.9277{{c}} (~15/14 = 108.2361{{c}})
* POTE: ~6/5 = 300.000, ~3/2 = 709.109 (~15/14 = 109.109)
* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 703.5558{{c}} (~15/14 = 103.5558{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 691.955{{c}} (~21/20 = 91.955{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 709.109{{c}} (~15/14 = 109.109{{c}}) -->


{{Optimal ET sequence|legend=0| 4, 8d, 12, 32cddee, 44cddeee }}
{{Optimal ET sequence|legend=0| 4, 8d, 12, 32cddee, 44cddeee }}


Badness (Smith): 0.022132
Badness (Sintel): 0.732


==== 13-limit ====
==== 13-limit ====
Line 65: Line 75:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~3/2 = 691.954 (~21/20 = 91.954)
* WE: ~6/5 = 297.2520{{c}}, ~3/2 = 707.2352{{c}} (~15/14 = 112.7312{{c}})
* POTE: ~6/5 = 300.000, ~3/2 = 713.773 (~15/14 = 113.773)
* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 708.4648{{c}} (~15/14 = 108.4648{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 691.954{{c}} (~21/20 = 91.954{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 713.773{{c}} (~15/14 = 113.773{{c}}) -->


{{Optimal ET sequence|legend=0| 4, 8d, 12f, 20cdef }}
{{Optimal ET sequence|legend=0| 4, 8d, 12f, 20cdef, 32cddeefff }}


Badness (Smith): 0.019509
Badness (Sintel): 0.806


=== Demolished ===
=== Demolished ===
Line 80: Line 92:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~3/2 = 687.747 (~21/20 = 87.747)
* WE: ~6/5 = 299.6308{{c}}, ~3/2 = 689.0322{{c}} (~21/20 = 89.7707{{c}})
* POTE: ~6/5 = 300.000, ~3/2 = 689.881 (~21/20 = 89.881)
* CWE: ~6/5 = 300.0000{{c}}, ~3/2 = 688.9304{{c}} (~21/20 = 88.9304{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~3/2 = 687.747{{c}} (~21/20 = 87.747{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~3/2 = 689.881{{c}} (~21/20 = 89.881{{c}}) -->


{{Optimal ET sequence|legend=0| 12, 28, 40de }}
{{Optimal ET sequence|legend=0| 4e, 8dee, 12, 28 }}


Badness (Smith): 0.026574
Badness (Smith): 0.879


=== Cohedim ===
=== Cohedim ===
This temperament has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[Dimipent family #Hemidim|11-limit 4e &amp; 24 and 13-limit 4ef &amp; 24]]. For 11-limit 8bce &amp; 12 temperament, ''cohedim'' arguably makes more sense.
This temperament has been documented in Graham Breed's temperament finder as ''hemidim'', the same name as [[Dimipent family #Hemidim|11-limit 4e &amp; 24 and 13-limit 4ef &amp; 24]]. For 11-limit 8bce & 12 temperament, ''cohedim'' arguably makes more sense.


Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11
Line 99: Line 113:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~11/7 = 793.423 (~12/11 = 106.577)
* WE: ~6/5 = 298.7799{{c}}, ~11/7 = 795.0744{{c}} (~12/11 = 101.2653{{c}})
* POTE: ~6/5 = 300.000, ~11/7 = 798.421 (~12/11 = 101.679)
* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 796.0102{{c}} (~12/11 = 103.9898{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~11/7 = 793.423{{c}} (~12/11 = 106.577{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~11/7 = 798.421{{c}} (~12/11 = 101.679{{c}}) -->


{{Optimal ET sequence|legend=0| 8bce, 12 }}
{{Optimal ET sequence|legend=0| 8bce, 12 }}


Badness (Smith): 0.054965
Badness (Sintel): 1.82


==== 13-limit ====
==== 13-limit ====
Line 114: Line 130:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~11/7 = 791.375 (~12/11 = 108.625)
* WE: ~6/5 = 298.4646{{c}}, ~11/7 = 793.6185{{c}} (~12/11 = 101.7754{{c}})
* POTE: ~6/5 = 300.000, ~11/7 = 797.701 (~12/11 = 102.299)
* CWE: ~6/5 = 300.0000{{c}}, ~11/7 = 794.7323{{c}} (~12/11 = 105.2677{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~11/7 = 791.375{{c}} (~12/11 = 108.625{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~11/7 = 797.701{{c}} (~12/11 = 102.299{{c}}) -->


{{Optimal ET sequence|legend=0| 8bcef, 12f }}
{{Optimal ET sequence|legend=0| 8bcef, 12f }}


Badness (Smith): 0.041707
Badness (Sintel): 1.72


== Hemidim ==
== Hemidim ==
Line 131: Line 149:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~6/5 = 300.000, ~7/4 = 949.540 (~36/35 = 49.540)
* [[WE]]: ~6/5 = 300.5053{{c}}, ~7/4 = 949.0409{{c}} (~36/35 = 47.5250{{c}})
: [[error map]]: {{val| +2.021 -3.873 +13.284 -15.743 }}
* [[CWE]]: ~6/5 = 300.0000{{c}}, ~7/4 = 948.2575{{c}} (~36/35 = 48.2575{{c}})
: error map: {{val| 0.000 -5.440 +10.201 -20.568 }}
<!-- * [[CTE]]: ~6/5 = 300.000{{c}}, ~7/4 = 949.540{{c}} (~36/35 = 49.540{{c}})
: [[error map]]: {{val| 0.000 -2.875 +12.766 -19.286 }}
: [[error map]]: {{val| 0.000 -2.875 +12.766 -19.286 }}
* [[POTE]]: ~6/5 = 300.000, ~7/4 = 947.445 (~36/35 = 47.445)
* [[POTE]]: ~6/5 = 300.000{{c}}, ~7/4 = 947.445{{c}} (~36/35 = 47.445{{c}})
: error map: {{val| 0.000 -7.065 +8.576 -21.381 }}
: error map: {{val| 0.000 -7.065 +8.576 -21.381 }} -->


{{Optimal ET sequence|legend=1| 4, …, 20c, 24 }}
{{Optimal ET sequence|legend=1| 4, …, 20c, 24 }}


[[Badness]] (Smith): 0.086378
[[Badness]] (Sintel): 2.19


=== 11-limit ===
=== 11-limit ===
Line 148: Line 170:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~7/4 = 949.872 (~36/35 = 49.872)
* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.6958{{c}} (~36/35 = 48.4112{{c}})
* POTE: ~6/5 = 300.000, ~7/4 = 948.342 (~36/35 = 48.342)
* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.9065{{c}} (~36/35 = 48.9065{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~7/4 = 949.872{{c}} (~36/35 = 49.872{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~7/4 = 948.342{{c}} (~36/35 = 48.342{{c}}) -->


{{Optimal ET sequence|legend=0| 4e, 20ce, 24 }}
{{Optimal ET sequence|legend=0| 4e, 20ce, 24 }}


Badness (Smith): 0.056576
Badness (Sintel): 1.87


=== 13-limit ===
=== 13-limit ===
Line 163: Line 187:


Optimal tunings:  
Optimal tunings:  
* CTE: ~6/5 = 300.000, ~7/4 = 949.366 (~36/35 = 49.366)
* WE: ~6/5 = 300.4282{{c}}, ~7/4 = 949.2440{{c}} (~36/35 = 47.8487{{c}})
* POTE: ~6/5 = 300.000, ~7/4 = 947.775 (~36/35 = 47.775)
* CWE: ~6/5 = 300.0000{{c}}, ~7/4 = 948.3581{{c}} (~36/35 = 48.3581{{c}})
<!-- * CTE: ~6/5 = 300.000{{c}}, ~7/4 = 949.366{{c}} (~36/35 = 49.366{{c}})
* POTE: ~6/5 = 300.000{{c}}, ~7/4 = 947.775{{c}} (~36/35 = 47.775{{c}}) -->


{{Optimal ET sequence|legend=0| 4ef, 24 }}
{{Optimal ET sequence|legend=0| 4ef, 24 }}


Badness (Smith): 0.039030
Badness (Sintel): 1.61


== Octonion ==
== Octonion ==
Line 182: Line 208:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 150.000, ~3/2 = 702.765 (~36/35 = 47.235)
* [[WE]]: ~15/14 = 149.6673{{c}}, ~3/2 = 705.4455{{c}} (~36/35 = 42.8910{{c}})
* [[POTE]]: ~15/14 = 150.000, ~3/2 = 707.014 (~36/35 = 42.986)
: [[error map]]: {{val| -2.662 +0.828 +14.474 -12.260 }}
* [[CWE]]: ~15/14 = 150.0000{{c}}, ~3/2 = 704.9636{{c}} (~36/35 = 45.0364{{c}})
: error map: {{val| 0.000 +3.008 +18.650 -8.899 }}
<!-- * [[CTE]]: ~15/14 = 150.000{{c}}, ~3/2 = 702.765{{c}} (~36/35 = 47.235{{c}})
* [[POTE]]: ~15/14 = 150.000{{c}}, ~3/2 = 707.014{{c}} (~36/35 = 42.986{{c}}) -->


{{Optimal ET sequence|legend=1| 8d, 24, 32c }}
{{Optimal ET sequence|legend=1| 8d, 16d, 24, 32c }}


[[Badness]] (Smith): 0.107523
[[Badness]] (Sintel): 2.72


=== 11-limit ===
=== 11-limit ===
Line 197: Line 227:


Optimal tunings:  
Optimal tunings:  
* CTE: ~12/11 = 150.000, ~3/2 = 702.662 (~36/35 = 47.338)
* WE: ~12/11 = 149.7102{{c}}, ~3/2 = 705.2799{{c}} (~36/35 = 43.2712{{c}})
* POTE: ~12/11 = 150.000, ~3/2 = 706.645 (~36/35 = 43.355)
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 704.9285{{c}} (~36/35 = 45.0715{{c}})
<!-- * CTE: ~12/11 = 150.000{{c}}, ~3/2 = 702.662{{c}} (~36/35 = 47.338{{c}})
* POTE: ~12/11 = 150.000{{c}}, ~3/2 = 706.645{{c}} (~36/35 = 43.355{{c}}) -->


{{Optimal ET sequence|legend=0| 8d, 24, 32c }}
{{Optimal ET sequence|legend=0| 8d, 16d, 24, 32c }}


Badness (Smith): 0.047598
Badness (Sintel): 1.57


=== 13-limit ===
=== 13-limit ===
Line 212: Line 244:


Optimal tunings:  
Optimal tunings:  
* CTE: ~12/11 = 150.000, ~3/2 = 701.952 (~36/35 = 48.048)
* WE: ~12/11 = 149.6311{{c}}, ~3/2 = 705.6367{{c}} (~36/35 = 42.5188{{c}})
* POTE: ~12/11 = 150.000, ~3/2 = 707.376 (~36/35 = 42.624)
* CWE: ~12/11 = 150.0000{{c}}, ~3/2 = 705.2777{{c}} (~36/35 = 44.7223{{c}})
<!-- * CTE: ~12/11 = 150.000{{c}}, ~3/2 = 701.952{{c}} (~36/35 = 48.048{{c}})
* POTE: ~12/11 = 150.000{{c}}, ~3/2 = 707.376{{c}} (~36/35 = 42.624{{c}}) -->


{{Optimal ET sequence|legend=0| 8d, 24, 32cf }}
{{Optimal ET sequence|legend=0| 8d, 16d, 24, 32cf }}


Badness (Smith): 0.030597
Badness (Sintel): 1.26


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

Revision as of 15:10, 18 August 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 dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo.

Dimipent

Main article: Diminished (temperament)

Subgroup: 2.3.5

Comma list: 648/625

Mapping: [⟨4 0 3], ⟨0 1 1]]

Optimal tunings:

  • WE: ~6/5 = 299.6476 ¢, ~3/2 = 698.6854 ¢ (~25/24 = 99.3903 ¢)
error map: ⟨-1.410 -4.679 +9.905]
  • CWE: ~6/5 = 300.0000 ¢, ~3/2 = 698.2660 ¢ (~25/24 = 98.2660 ¢)
error map: ⟨0.000 -3.689 +11.952]

Optimal ET sequence: 4, 8, 12

Badness (Sintel): 1.11

Diminished

Deutsch
Main article: Diminished (temperament)

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Optimal tunings:

  • WE: ~6/5 = 299.0347 ¢, ~3/2 = 697.2727 ¢ (~21/20 = 99.2032 ¢)
error map: ⟨-3.861 -8.543 +4.202 +19.759]
  • CWE: ~6/5 = 300.0000 ¢, ~3/2 = 695.9619 ¢ (~21/20 = 95.9619 ¢)
error map: ⟨0.000 -5.993 +9.648 +27.136]

Optimal ET sequence: 4, 8d, 12

Badness (Sintel): 0.567

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 56/55

Mapping: [⟨4 0 3 5 14], ⟨0 1 1 1 0]]

Optimal tunings:

  • WE: ~6/5 = 297.8458 ¢, ~3/2 = 703.9277 ¢ (~15/14 = 108.2361 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~3/2 = 703.5558 ¢ (~15/14 = 103.5558 ¢)

Optimal ET sequence: 4, 8d, 12, 32cddee, 44cddeee

Badness (Sintel): 0.732

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 50/49, 66/65

Mapping: [⟨4 0 3 5 14 15], ⟨0 1 1 1 0 0]]

Optimal tunings:

  • WE: ~6/5 = 297.2520 ¢, ~3/2 = 707.2352 ¢ (~15/14 = 112.7312 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~3/2 = 708.4648 ¢ (~15/14 = 108.4648 ¢)

Optimal ET sequence: 4, 8d, 12f, 20cdef, 32cddeefff

Badness (Sintel): 0.806

Demolished

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 50/49

Mapping: [⟨4 0 3 5 -5], ⟨0 1 1 1 3]]

Optimal tunings:

  • WE: ~6/5 = 299.6308 ¢, ~3/2 = 689.0322 ¢ (~21/20 = 89.7707 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~3/2 = 688.9304 ¢ (~21/20 = 88.9304 ¢)

Optimal ET sequence: 4e, 8dee, 12, 28

Badness (Smith): 0.879

Cohedim

This temperament has been documented in Graham Breed's temperament finder as hemidim, the same name as 11-limit 4e & 24 and 13-limit 4ef & 24. For 11-limit 8bce & 12 temperament, cohedim arguably makes more sense.

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 125/121

Mapping: [⟨4 1 4 6 6], ⟨0 2 2 2 3]]

mapping generators: ~6/5, ~11/7

Optimal tunings:

  • WE: ~6/5 = 298.7799 ¢, ~11/7 = 795.0744 ¢ (~12/11 = 101.2653 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~11/7 = 796.0102 ¢ (~12/11 = 103.9898 ¢)

Optimal ET sequence: 8bce, 12

Badness (Sintel): 1.82

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 50/49, 66/65, 125/121

Mapping: [⟨4 1 4 6 6 7], ⟨0 2 2 2 3 3]]

Optimal tunings:

  • WE: ~6/5 = 298.4646 ¢, ~11/7 = 793.6185 ¢ (~12/11 = 101.7754 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~11/7 = 794.7323 ¢ (~12/11 = 105.2677 ¢)

Optimal ET sequence: 8bcef, 12f

Badness (Sintel): 1.72

Hemidim

Subgroup: 2.3.5.7

Comma list: 49/48, 648/625

Mapping: [⟨4 0 3 8], ⟨0 2 2 1]]

mapping generators: ~6/5, ~7/4

Optimal tunings:

  • WE: ~6/5 = 300.5053 ¢, ~7/4 = 949.0409 ¢ (~36/35 = 47.5250 ¢)
error map: ⟨+2.021 -3.873 +13.284 -15.743]
  • CWE: ~6/5 = 300.0000 ¢, ~7/4 = 948.2575 ¢ (~36/35 = 48.2575 ¢)
error map: ⟨0.000 -5.440 +10.201 -20.568]

Optimal ET sequence: 4, …, 20c, 24

Badness (Sintel): 2.19

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 77/75, 243/242

Mapping: [⟨4 0 3 8 -2], ⟨0 2 2 1 5]]

Optimal tunings:

  • WE: ~6/5 = 300.4282 ¢, ~7/4 = 949.6958 ¢ (~36/35 = 48.4112 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~7/4 = 948.9065 ¢ (~36/35 = 48.9065 ¢)

Optimal ET sequence: 4e, 20ce, 24

Badness (Sintel): 1.87

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 77/75, 243/242

Mapping: [⟨4 0 3 8 -2 -1], ⟨0 2 2 1 5 5]]

Optimal tunings:

  • WE: ~6/5 = 300.4282 ¢, ~7/4 = 949.2440 ¢ (~36/35 = 47.8487 ¢)
  • CWE: ~6/5 = 300.0000 ¢, ~7/4 = 948.3581 ¢ (~36/35 = 48.3581 ¢)

Optimal ET sequence: 4ef, 24

Badness (Sintel): 1.61

Octonion

It was formerly known as "semidim" but renamed to avoid confusion with another temperament of the same name.

Subgroup: 2.3.5.7

Comma list: 245/243, 392/375

Mapping: [⟨8 0 6 -3], ⟨0 1 1 2]]

mapping generators: ~15/14, ~3

Optimal tunings:

  • WE: ~15/14 = 149.6673 ¢, ~3/2 = 705.4455 ¢ (~36/35 = 42.8910 ¢)
error map: ⟨-2.662 +0.828 +14.474 -12.260]
  • CWE: ~15/14 = 150.0000 ¢, ~3/2 = 704.9636 ¢ (~36/35 = 45.0364 ¢)
error map: ⟨0.000 +3.008 +18.650 -8.899]

Optimal ET sequence: 8d, 16d, 24, 32c

Badness (Sintel): 2.72

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 77/75, 245/243

Mapping: [⟨8 0 6 -3 15], ⟨0 1 1 2 1]]

Optimal tunings:

  • WE: ~12/11 = 149.7102 ¢, ~3/2 = 705.2799 ¢ (~36/35 = 43.2712 ¢)
  • CWE: ~12/11 = 150.0000 ¢, ~3/2 = 704.9285 ¢ (~36/35 = 45.0715 ¢)

Optimal ET sequence: 8d, 16d, 24, 32c

Badness (Sintel): 1.57

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 66/65, 77/75, 507/500

Mapping: [⟨8 0 6 -3 15 17], ⟨0 1 1 2 1 1]]

Optimal tunings:

  • WE: ~12/11 = 149.6311 ¢, ~3/2 = 705.6367 ¢ (~36/35 = 42.5188 ¢)
  • CWE: ~12/11 = 150.0000 ¢, ~3/2 = 705.2777 ¢ (~36/35 = 44.7223 ¢)

Optimal ET sequence: 8d, 16d, 24, 32cf

Badness (Sintel): 1.26

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