Ripple family: Difference between revisions

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== Ripple ==
== Ripple ==
The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered [[4/3|fourth]] reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice often even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often inconsistent, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]].
The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The ploidacot of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a [[dual-fifth temperament]] unless you use tunings close to [[12edo]].


Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]].
Reasonable [[patent val]] tunings not appearing in the optimal ET sequence are [[35edo]] and [[47edo]].
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~27/25 = 100.752
* [[WE]]: ~2 = 1200.2636{{c}}, ~27/25 = 100.8602{{c}}
: [[error map]]: {{val| 0.000 -5.717 +7.668 }}
: [[error map]]: {{val| +0.264 -5.729 +7.596 }}
* [[CWE]]: ~2 = 1200.000, ~27/25 = 100.798
* [[CWE]]: ~2 = 1200.0000{{c}}, ~27/25 = 100.7982{{c}}
: [[error map]]: {{val| 0.000 -5.946 +7.300 }}
: [[error map]]: {{val| 0.000 -5.946 +7.300 }}
* [[POTE]]: ~2 = 1200.000, ~27/25 = 100.838
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~27/25 = 100.752{{c}}
: error map: {{val| 0.000 -6.145 +6.982 }}
: error map: {{val| 0.000 -5.717 +7.668 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~27/25 = 100.838{{c}}
: error map: {{val| 0.000 -6.145 +6.982 }} -->


[[Tuning ranges]]:  
[[Tuning ranges]]:  
Line 29: Line 31:
{{Optimal ET sequence|legend=1| 11c, 12, 71b, 83b }}
{{Optimal ET sequence|legend=1| 11c, 12, 71b, 83b }}


[[Badness]]:
[[Badness]] (Sintel): 3.26
* Smith 0.139
* Dirichlet: 3.26


== Septimal ripple ==
== Septimal ripple ==
{{See also| Dual-fifth temperaments }}
{{See also| Dual-fifth temperaments }}
Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~(21/16)⋅(4/3) = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy.
Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~(21/16)⋅(4/3) = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy.


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{{Mapping|legend=1| 1 2 3 4 | 0 -5 -8 -14 }}
{{Mapping|legend=1| 1 2 3 4 | 0 -5 -8 -14 }}


[[Optimal tuning]]s:
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~15/14 = 101.538
* [[WE]]: ~2 = 1201.7546{{c}}, ~15/14 = 102.1309{{c}}
: [[error map]]: {{val| 0 -9.643 +1.385 +9.647 }}
: error map: {{val| +1.755 -9.100 +1.903 +8.360 }}
* [[CWE]]: ~2 = 1200.000, ~15/14 = 101.777
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/14 = 101.7772{{c}}
: error map: {{val| 0 -10.841 -0.531 +6.294 }}
: error map: {{val| 0.000 -10.841 -0.531 +6.294 }}
* [[CEE]]: ~2 = 1200.000, ~15/14 = 101.881
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 101.538{{c}}
: error map: {{val| 0 -11.361 -1.364 +4.837 }}
: error map: {{val| 0.000 -9.643 +1.385 +9.647 }}
* [[CEE]]: ~2 = 1200.000{{c}}, ~15/14 = 101.881{{c}}
: error map: {{val| 0.000 -11.361 -1.364 +4.837 }} -->


{{Optimal ET sequence|legend=1| 11cd, 12, 35, 47 }}
{{Optimal ET sequence|legend=1| 11cd, 12, 35, 47 }}


[[Badness]]:
[[Badness]] (Sintel): 1.52
* Smith: 0.0601
* Dirichlet: 1.52


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000, ~15/14 = 101.538
* WE: ~2 = 1202.5973{{c}}, ~15/14 = 102.7900{{c}}
: error map: {{val| 0 -11.785 -2.041 +3.651 +13.296 }}
: error map: {{val| +2.597 -10.710 -0.842 +2.504 +11.449 }}
* CWE: ~2 = 1200.000, ~15/14 = 102.297
* CWE: ~2 = 1200.0000{{c}}, ~15/14 = 102.2972{{c}}
: error map: {{val| 0 -13.441 -4.691 -0.986 +7.333 }}
: error map: {{val| 0.000 -13.441 -4.691 -0.986 +7.333 }}
* CEE: ~2 = 1200.000, ~15/14 = 102.319
<!-- * CTE: ~2 = 1200.0000{{c}}, ~15/14 = 101.538{{c}}
: error map: {{val| 0 -13.551 -4.868 -1.296 +6.935 }}
: error map: {{val| 0.000 -11.785 -2.041 +3.651 +13.296 }}
* CEE: ~2 = 1200.000{{c}}, ~15/14 = 102.319{{c}}
: error map: {{val| 0.000 -13.551 -4.868 -1.296 +6.935 }} -->


{{Optimal ET sequence|legend=0| 11cdee, 12, 23de, 35 }}
{{Optimal ET sequence|legend=0| 11cdee, 12, 23de, 35 }}


Badness:
Badness (Sintel): 1.33
* Smith: 0.0403
* Dirichlet: 1.33


== Rip ==
== Rip ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~21/20 = 101.089
* [[WE]]: ~2 = 1195.0347{{c}}, ~21/20 = 99.0710{{c}}
: [[error map]]: {{val| 0.000 -7.402 +4.970 +28.995 }}
: error map: {{val| -4.965 -7.240 +6.223 +18.136 }}
* [[CWE]]: ~2 = 1200.000, ~21/20 = 100.109
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 100.1093{{c}}
: error map: {{val| 0.000 -2.501 +12.812 +30.956 }}
: error map: {{val| 0.000 -2.501 +12.812 +30.956 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 99.483
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 101.089{{c}}
: error map: {{val| 0.000 +0.632 +17.825 +32.209 }}
: error map: {{val| 0.000 -7.402 +4.970 +28.995 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 99.483{{c}}
: error map: {{val| 0.000 +0.632 +17.825 +32.209 }} -->


{{Optimal ET sequence|legend=1| 11c, 12 }}
{{Optimal ET sequence|legend=1| 11c, 12 }}


[[Badness]] (Smith): 0.0597
[[Badness]] (Sintel): 1.51


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 101.923
* WE: ~2 = 1192.7877{{c}}, ~21/20 = 98.7876{{c}}
* CWE: ~2 = 1200.000, ~21/20 = 100.320
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 100.3202{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 99.385
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 101.923{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 99.385{{c}} -->


{{Optimal ET sequence|legend=0| 11c, 12 }}
{{Optimal ET sequence|legend=0| 11c, 12 }}


Badness (Smith): 0.0388
Badness (Sintel): 1.28


=== 13-limit ===
=== 13-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 102.376
* WE: ~2 = 1189.8521{{c}}, ~21/20 = 97.7384{{c}}
* CWE: ~2 = 1200.000, ~21/20 = 99.762
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 99.7618{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 98.572
<!-- * CTE: ~2 = 1200.000{{c}}, ~21/20 = 102.376{{c}}
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 98.572{{c}} -->


{{Optimal ET sequence|legend=0| 11c, 12f, 37ccddeeeeffff }}
{{Optimal ET sequence|legend=0| 11c, 12f, 37ccddeeeeffff }}


Badness (Smith): 0.0316
Badness (Sintel): 1.31


== Hemiripple ==
== Hemiripple ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~36/35 = 50.231
* [[WE]]: ~2 = 1203.5561{{c}}, ~36/35 = 50.9765{{c}}
: error map: {{val| +3.556 -4.608 +8.730 -13.040 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~36/35 = 50.5928{{c}}
: error map: {{val| 0.000 -7.883 +4.201 -21.790 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~36/35 = 50.231{{c}}
: [[error map]]: {{val| 0.000 -4.264 +9.991 -19.981 }}
: [[error map]]: {{val| 0.000 -4.264 +9.991 -19.981 }}
* [[CWE]]: ~2 = 1200.000, ~36/35 = 50.593
* [[POTE]]: ~2 = 1200.000{{c}}, ~36/35 = 50.826{{c}}
: error map: {{val| 0.000 -7.883 +4.201 -21.790 }}
: error map: {{val| 0.000 -10.214 +0.472 -22.956 }} -->
* [[POTE]]: ~2 = 1200.000, ~36/35 = 50.826
: error map: {{val| 0.000 -10.214 +0.472 -22.956 }}


{{Optimal ET sequence|legend=1| 23d, 24, 47d }}
{{Optimal ET sequence|legend=1| 23d, 24, 47d }}


[[Badness]] (Smith): 0.175
[[Badness]] (Sintel): 4.43


=== 11-limit ===
=== 11-limit ===
Line 162: Line 169:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 50.186
* WE: ~2 = 1203.5344{{c}}, ~36/35 = 50.9757{{c}}
* CWE: ~2 = 1200.000, ~36/35 = 50.587
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5870{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 50.826
<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 50.186{{c}}
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 50.826{{c}} -->


{{Optimal ET sequence|legend=0| 23de, 24, 47de }}
{{Optimal ET sequence|legend=0| 23de, 24, 47de }}


Badness (Smith): 0.0668
Badness (Sintel): 2.21


=== 13-limit ===
=== 13-limit ===
Line 178: Line 186:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~36/35 = 50.225
* WE: ~2 = 1202.0936{{c}}, ~36/35 = 50.7232{{c}}
* CWE: ~2 = 1200.000, ~36/35 = 50.505
* CWE: ~2 = 1200.0000{{c}}, ~36/35 = 50.5048{{c}}
* POTE: ~2 = 1200.000, ~36/35 = 50.635
<!-- * CTE: ~2 = 1200.000{{c}}, ~36/35 = 50.225{{c}}
* POTE: ~2 = 1200.000{{c}}, ~36/35 = 50.635{{c}} -->


{{Optimal ET sequence|legend=0| 23de, 24 }}
{{Optimal ET sequence|legend=0| 23de, 24 }}


Badness (Smith): 0.0466
Badness (Sintel): 1.93


== Cohemiripple ==
== Cohemiripple ==
Line 196: Line 205:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/5 = 550.063
* [[WE]]: ~2 = 1200.6977{{c}}, ~7/5 = 550.2638{{c}}
: [[error map]]: {{val| 0.000 -1.328 +14.690 -17.760 }}
: error map: {{val| +0.698 -1.410 +14.418 -17.830 }}
* [[CWE]]: ~2 = 1200.000, ~7/5 = 549.998
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/5 = 549.9979{{c}}
: error map: {{val| 0.000 -1.976 +13.653 -18.861 }}
: error map: {{val| 0.000 -1.976 +13.653 -18.861 }}
* [[POTE]]: ~2 = 1200.000, ~7/5 = 549.944
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~7/5 = 550.063{{c}}
: error map: {{val| 0.000 -2.515 +12.791 -19.777 }}
: error map: {{val| 0.000 -1.328 +14.690 -17.760 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/5 = 549.944{{c}}
: error map: {{val| 0.000 -2.515 +12.791 -19.777 }} -->


{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}
{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}


[[Badness]] (Smith): 0.190
[[Badness]] (Sintel): 4.81


=== 11-limit ===
=== 11-limit ===
Line 215: Line 226:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/5 = 550.060
* WE: ~2 = 1200.6959{{c}}, ~7/5 = 550.2641{{c}}
* CWE: ~2 = 1200.000, ~7/5 = 549.997
* CWE: ~2 = 1200.0000{{c}}, ~7/5 = 549.9969{{c}}
* POTE: ~2 = 1200.000, ~7/5 = 549.945
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/5 = 550.060{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/5 = 549.945{{c}} -->


{{Optimal ET sequence|legend=0| 11cdee, 13cdee, 24 }}
{{Optimal ET sequence|legend=0| 11cdee, 13cdee, 24 }}


Badness (Smith): 0.0827
Badness (Sintel): 2.73


=== 13-limit ===
=== 13-limit ===
Line 231: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/5 = 549.987
* WE: ~2 = 1200.1161{{c}}, ~7/5 = 550.0107{{c}}
* CWE: ~2 = 1200.000, ~7/5 = 549.966
* CWE: ~2 = 1200.000{{c}}, ~7/5 = 549.9663{{c}}
* POTE: ~2 = 1200.000, ~7/5 = 549.958
<!-- * CTE: ~2 = 1200.000{{c}}, ~7/5 = 549.987{{c}}
* POTE: ~2 = 1200.000{{c}}, ~7/5 = 549.958{{c}} -->


{{Optimal ET sequence|legend=0| 11cdeef, 13cdeef, 24 }}
{{Optimal ET sequence|legend=0| 11cdeef, 13cdeef, 24 }}


Badness (Smith): 0.0499
Badness (Sintel): 2.06


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

Revision as of 14:36, 22 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 ripple family of temperaments tempers out the ripple comma (ratio: 6561/6250, monzo: [-1 8 -5⟩), which equates a stack of five 27/25's with 4/3.

Ripple

The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. The ploidacot of ripple is omega-pentacot. This means that 27/25 is severely flattened, so that the characteristic damage is a strongly flat-tempered fourth reached at 5 semitones. Interestingly, in optimal tunings, the major third of ~5/4 does not tend to be damaged much sharpwards as one might expect from the equivalence, and is in practice sometimes even flat, so that prime 3 takes on practically the whole damage of the 5-limit equivalence, for which it has the advantage of being the simplest so still having a good chance at psychoacoustic viability. As a result though, the mapping of ~9/8 is often very flat, so that ripple can in practice be thought of as a dual-fifth temperament unless you use tunings close to 12edo.

Reasonable patent val tunings not appearing in the optimal ET sequence are 35edo and 47edo.

Subgroup: 2.3.5

Comma list: 6561/6250

Mapping: [⟨1 2 3], ⟨0 -5 -8]]

mapping generators: ~2, ~27/25

Optimal tunings:

  • WE: ~2 = 1200.2636 ¢, ~27/25 = 100.8602 ¢
error map: ⟨+0.264 -5.729 +7.596]
  • CWE: ~2 = 1200.0000 ¢, ~27/25 = 100.7982 ¢
error map: ⟨0.000 -5.946 +7.300]

Tuning ranges:

Optimal ET sequence: 11c, 12, 71b, 83b

Badness (Sintel): 3.26

Septimal ripple

See also: Dual-fifth temperaments

Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~(21/16)⋅(4/3) = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy.

If you are looking for the former canonical extension, see #Rip.

Subgroup: 2.3.5.7

Comma list: 126/125, 405/392

Mapping: [⟨1 2 3 4], ⟨0 -5 -8 -14]]

Optimal tunings:

  • WE: ~2 = 1201.7546 ¢, ~15/14 = 102.1309 ¢
error map: ⟨+1.755 -9.100 +1.903 +8.360]
  • CWE: ~2 = 1200.0000 ¢, ~15/14 = 101.7772 ¢
error map: ⟨0.000 -10.841 -0.531 +6.294]

Optimal ET sequence: 11cd, 12, 35, 47

Badness (Sintel): 1.52

11-limit

A notable patent val tuning of 11-limit ripple not appearing in the optimal ET sequence is 47edo.

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 126/125

Mapping: [⟨1 2 3 4 5], ⟨0 -5 -8 -14 -18]]

Optimal tunings:

  • WE: ~2 = 1202.5973 ¢, ~15/14 = 102.7900 ¢
error map: ⟨+2.597 -10.710 -0.842 +2.504 +11.449]
  • CWE: ~2 = 1200.0000 ¢, ~15/14 = 102.2972 ¢
error map: ⟨0.000 -13.441 -4.691 -0.986 +7.333]

Optimal ET sequence: 11cdee, 12, 23de, 35

Badness (Sintel): 1.33

Rip

Formerly known as septimal ripple, but de-canonized in favour of canonizing a significantly more accurate extension of similar efficiency so that #Ripple admits nontrivial edo tunings of interest. The reason for de-canonization is not coming close to preserving the damage level of 5-limit ripple to the 7-limit or even of this 7-limit damage level to the 11-limit.

Subgroup: 2.3.5.7

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Optimal tunings:

  • WE: ~2 = 1195.0347 ¢, ~21/20 = 99.0710 ¢
error map: ⟨-4.965 -7.240 +6.223 +18.136]
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 100.1093 ¢
error map: ⟨0.000 -2.501 +12.812 +30.956]

Optimal ET sequence: 11c, 12

Badness (Sintel): 1.51

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 80/77, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]

Optimal tunings:

  • WE: ~2 = 1192.7877 ¢, ~21/20 = 98.7876 ¢
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 100.3202 ¢

Optimal ET sequence: 11c, 12

Badness (Sintel): 1.28

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]

Optimal tunings:

  • WE: ~2 = 1189.8521 ¢, ~21/20 = 97.7384 ¢
  • CWE: ~2 = 1200.0000 ¢, ~21/20 = 99.7618 ¢

Optimal ET sequence: 11c, 12f, 37ccddeeeeffff

Badness (Sintel): 1.31

Hemiripple

Subgroup: 2.3.5.7

Comma list: 49/48, 6561/6250

Mapping: [⟨1 2 3 3], ⟨0 -10 -16 -5]]

Optimal tunings:

  • WE: ~2 = 1203.5561 ¢, ~36/35 = 50.9765 ¢
error map: ⟨+3.556 -4.608 +8.730 -13.040]
  • CWE: ~2 = 1200.000 ¢, ~36/35 = 50.5928 ¢
error map: ⟨0.000 -7.883 +4.201 -21.790]

Optimal ET sequence: 23d, 24, 47d

Badness (Sintel): 4.43

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 121/120, 567/550

Mapping: [⟨1 2 3 3 4], ⟨0 -10 -16 -5 -13]]

Optimal tunings:

  • WE: ~2 = 1203.5344 ¢, ~36/35 = 50.9757 ¢
  • CWE: ~2 = 1200.0000 ¢, ~36/35 = 50.5870 ¢

Optimal ET sequence: 23de, 24, 47de

Badness (Sintel): 2.21

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 66/65, 121/120, 351/350

Mapping: [⟨1 2 3 3 4 4], ⟨0 -10 -16 -5 -13 -7]]

Optimal tunings:

  • WE: ~2 = 1202.0936 ¢, ~36/35 = 50.7232 ¢
  • CWE: ~2 = 1200.0000 ¢, ~36/35 = 50.5048 ¢

Optimal ET sequence: 23de, 24

Badness (Sintel): 1.93

Cohemiripple

See also: Sensamagic clan

Subgroup: 2.3.5.7

Comma list: 245/243, 1323/1250

Mapping: [⟨1 7 11 12], ⟨0 -10 -16 -17]]

Optimal tunings:

  • WE: ~2 = 1200.6977 ¢, ~7/5 = 550.2638 ¢
error map: ⟨+0.698 -1.410 +14.418 -17.830]
  • CWE: ~2 = 1200.0000 ¢, ~7/5 = 549.9979 ¢
error map: ⟨0.000 -1.976 +13.653 -18.861]

Optimal ET sequence: 11cd, 13cd, 24

Badness (Sintel): 4.81

11-limit

Subgroup: 2.3.5.7.11

Comma list: 77/75, 243/242, 245/242

Mapping: [⟨1 7 11 12 17], ⟨0 -10 -16 -17 -25]]

Optimal tunings:

  • WE: ~2 = 1200.6959 ¢, ~7/5 = 550.2641 ¢
  • CWE: ~2 = 1200.0000 ¢, ~7/5 = 549.9969 ¢

Optimal ET sequence: 11cdee, 13cdee, 24

Badness (Sintel): 2.73

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 77/75, 147/143, 243/242

Mapping: [⟨1 7 11 12 17 14], ⟨0 -10 -16 -17 -25 -19]]

Optimal tunings:

  • WE: ~2 = 1200.1161 ¢, ~7/5 = 550.0107 ¢
  • CWE: ~2 = 1200.000 ¢, ~7/5 = 549.9663 ¢

Optimal ET sequence: 11cdeef, 13cdeef, 24

Badness (Sintel): 2.06

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