Canou family: Difference between revisions

Revision as of 08:33, 14 September 2023

The canou family of rank-3 temperaments tempers out the canousma, 4802000/4782969 = [4 -14 3 4⟩, a 7-limit comma measuring about 6.9 cents.

Canou

Main article: Canou temperament

The canou temperament features a period of an octave and generators of 3/2 and 81/70. The 81/70-generator is about 255 cents. Two of them make 980/729 at about 510 cents, an audibly off perfect fourth. Three make 14/9; four make 9/5. It therefore also features splitting the septimal diesis, 49/48, into three equal parts, making two distinct interseptimal intervals related to the 35th harmonic.

For tunings, a basic option would be 99edo, although 80edo is even simpler and distinctive. More intricate tunings are provided by 311edo and 410edo, whereas the optimal patent val goes up to 1131edo, relating it to the amicable temperament.

It has a neat extension to the 2.3.5.7.17.19 subgroup with virtually no additional errors. The comma basis is {1216/1215, 1225/1224, 1445/1444}. Otherwise, 11- and 13-limit extensions are somewhat less ideal.

Subgroup: 2.3.5.7

Comma list: 4802000/4782969

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

mapping generators: ~2, ~3, ~81/70

Lattice basis:

3/2 length = 0.8110, 81/70 length = 0.5135

Angle (3/2, 81/70) = 73.88 deg

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3175, ~81/70 = 254.6220

Minimax tuning:

7-odd-limit: 3 +c/14, 5 and 7 just

eigenmonzo (unchanged-interval) basis: 2.5.7

9-odd-limit: 3 just, 5 and 7 -c/7 to 3 +c/14, 5 and 7 just

eigenmonzo (unchanged-interval) basis: 2.7/5

Optimal ET sequence: 19, 56d, 61d, 75, 80, 94, 99, 212, 292, 311, 410, 1131, 1541b, 1659b

Badness: 1.122 × 10^-3

Complexity spectrum: 4/3, 9/7, 9/8, 7/6, 6/5, 10/9, 5/4, 8/7, 7/5

2.3.5.7.17 subgroup

Subgroup: 2.3.5.7.17

Comma list: 1225/1224, 295936/295245

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3458, ~81/70 = 254.6233

Optimal ET sequence: 94, 99, 193, 217, 292, 311, 410, 1131, 1541b

Badness: 0.775 × 10^-3

2.3.5.7.17.19 subgroup

Subgroup: 2.3.5.7.17.19

Comma list: 1216/1215, 1225/1224, 1445/1444

Mapping: [⟨1 0 0 -1 -5 -6], ⟨0 1 2 2 6 7], ⟨0 0 -4 3 -2 -4]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3233, ~81/70 = 254.6279

Optimal ET sequence: 94, 99, 118, 193, 217, 292h, 311, 410, 721

Badness: 0.548 × 10^-3

Synca

Synca, for symbiotic canou, adds the symbiotic comma and the wilschisma to the comma list.

Subgroup: 2.3.5.7.11

Comma list: 19712/19683, 42875/42768

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2115, ~81/70 = 254.6215

Optimal ET sequence: 94, 99e, 118, 193, 212, 311, 740, 1051d

Badness: 2.04 × 10^-3

Complexity spectrum: 4/3, 9/8, 9/7, 7/6, 5/4, 6/5, 10/9, 11/9, 8/7, 12/11, 11/10, 14/11, 11/8, 7/5

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 19712/19683, 42875/42768

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2075, ~81/70 = 254.6183

Optimal ET sequence: 94, 118f, 193f, 212, 217, 311, 740, 1051d

Badness: 2.56 × 10^-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 595/594, 833/832, 1156/1155, 19712/19683

Mapping: [⟨1 0 0 -1 -7 -13 -5], ⟨0 1 2 2 7 10 6], ⟨0 0 -4 3 -3 4 -2]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2296, ~51/44 = 254.6012

Optimal ET sequence: 94, 118f, 193f, 212g, 217, 311, 740g, 1051dg

Badness: 1.49 × 10^-3

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215

Mapping: [⟨], ⟨1 0 0 -1 -7 -13 -5 -6], ⟨0 1 2 2 7 10 6 7], ⟨0 0 -4 3 -3 4 -2 -4]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2355, ~22/19 = 254.5930

Optimal ET sequence: 94, 118f, 193f, 212gh, 217, 311, 740g, 1051dgh

Badness: 1.00 × 10^-3

Canta

By adding 896/891, the pentacircle comma, 33/32 is equated with 28/27, so the scale is filled with this 33/32~28/27 mixture. This may be described as 75e & 80 & 99e, and 80edo makes the optimal. It has a natural extension to the 13-limit since 896/891 = (352/351)(364/363), named gentcanta in earlier materials.

Subgroup: 2.3.5.7.11

Comma list: 896/891, 472392/471625

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.8093, ~64/55 = 254.3378

Optimal ET sequence: 75e, 80, 99e, 179e

Badness: 4.523 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 472392/471625

Mapping: [⟨1 0 0 -1 6 11], ⟨0 1 2 2 -2 -5], ⟨0 0 4 -3 -3 -3]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 703.6228, ~64/55 = 254.3447

Optimal ET sequence: 75e, 80, 99ef, 179ef

Badness: 4.781 × 10^-3

Semicanou

Semicanou adds 9801/9800, the kalisma, to the comma list, and may be described as 80 & 94 & 118. It splits the octave into two equal parts, each representing 99/70~140/99. Note that 99/70 = (81/70)(11/9), this extension is more than natural.

The other comma necessary to define it is 14641/14580, the semicanousma, which is the difference between 121/120 and 243/242. By flattening the 11th harmonic by one cent, it identifies 20/11 by three 11/9's stacked, so an octave can be divided into 11/9-11/9-11/9-11/10.

Natural extensions arise up to the 19-limit, and 410edo provides a satisfactory tuning solution to all of them.

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 14641/14580

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

mapping generators: ~99/70, ~3, ~81/70

Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4262, ~81/70 = 254.6191

Optimal ET sequence: 80, 94, 118, 198, 212, 292, 330e, 410

Badness: 2.197 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 14641/14580

Mapping: [⟨2 0 0 -2 1 -11], ⟨0 1 2 2 2 5], ⟨0 0 -4 3 -1 6]]

Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4802, ~81/70 = 254.6526

Optimal ET sequence: 80f, 94, 118f, 198, 410

Badness: 2.974 × 10^-3

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 715/714, 1089/1088, 1225/1224, 14641/14580

Mapping: [⟨2 0 0 -2 1 -11 -10], ⟨0 1 2 2 2 5 6], ⟨0 0 -4 3 -1 6 -2]]

Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4415, ~81/70 = 254.6663

Optimal ET sequence: 94, 118f, 198g, 212g, 292, 410

Badness: 2.421 × 10^-3

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 715/714, 1089/1088, 1216/1215, 1225/1224, 1445/1444

Mapping: [⟨2 0 0 -2 1 -11 -10 -12], ⟨0 1 2 2 2 5 6 7], ⟨0 0 -4 3 -1 6 -2 -4]]

Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4030, ~81/70 = 254.6870

Optimal ET sequence: 94, 118f, 198gh, 212gh, 292h, 410, 622ef

Badness: 2.177 × 10^-3

Semicanoumint

This extension was named semicanou in the earlier materials. It adds 352/351, the minthma, to the comma list, so that the flat ~11/9 simultaneously represents ~39/32.

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 9801/9800, 14641/14580

Mapping: [⟨2 0 0 -2 1 11], ⟨0 1 2 2 2 -1], ⟨0 0 -4 3 -1 -1]]

Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.5374, ~81/70 = 254.6819

Optimal ET sequence: 80, 94, 118, 174d, 198, 490f

Badness: 2.701 × 10^-3

Semicanouwolf

This extension was named gentsemicanou in the earlier materials. It adds 351/350, the ratwolfsma, as wells as 364/363, the gentle comma, to the comma list. Since 351/350 = (81/70)/(15/13), the 81/70-generator simultaneously represents 15/13, adding a lot of fun to the scale.

Not supported by many patent vals, 80edo easily makes the optimal. Yet 104edo in 104c val and 118edo in 118f val are worth mentioning, and the temperament may be described as 80 & 104c & 118f.

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 11011/10935

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

Optimal tuning (CTE): ~3/2 = 702.7417, ~15/13 = 254.3382

Optimal ET sequence: 80, 104c, 118f, 198f, 420cff

Badness: 3.511 × 10^-3

@@ Line 1: / Line 1: @@
-The '''canou family''' of rank-3 temperaments tempers out the [[canousma]], 4802000/4782969 = {{monzo| 4 -14 3 4 }}, a 7-limit comma measuring about 6.9 cents.
+The '''canou family''' of [[Rank-3 temperament|rank-3]] [[temperament]]s [[Tempering out|tempers out]] the [[canousma]], 4802000/4782969 = {{monzo| 4 -14 3 4 }}, a 7-limit comma measuring about 6.9 [[cent]]s.
 == Canou ==
 {{Main| Canou temperament }}
-The canou temperament features a period of an octave and generators of [[3/2]] and [[81/70]]. The 81/70-generator is about 255 cents. Two of them interestingly make [[980/729]] at about 510 cents, an audibly off perfect fourth. Three make [[14/9]]; four make [[9/5]]. It therefore also features splitting the septimal diesis, [[49/48]], into three equal parts, making two distinct [[interseptimal]] intervals related to the 35th harmonic.
+The canou temperament features a [[period]] of an [[octave]] and [[generator]]s of [[3/2]] and [[81/70]]. The 81/70-generator is about 255 cents. Two of them make [[980/729]] at about 510 cents, an audibly off perfect fourth. Three make [[14/9]]; four make [[9/5]]. It therefore also features splitting the septimal diesis, [[49/48]], into three equal parts, making two distinct [[interseptimal interval]]s related to the 35th harmonic.
 For tunings, a basic option would be [[99edo]], although [[80edo]] is even simpler and distinctive. More intricate tunings are provided by [[311edo]] and [[410edo]], whereas the [[optimal patent val]] goes up to [[1131edo]], relating it to the [[amicable]] temperament.
-It has a neat extension to the 2.3.5.7.17.19 subgroup with virtually no additional errors. The [[comma basis]] is {1216/1215, 1225/1224, 1445/1444}. Otherwise, 11- and 13-limit extensions are somewhat less ideal.
+It has a neat extension to the 2.3.5.7.17.19 [[subgroup]] with virtually no additional errors. The [[comma basis]] is {1216/1215, 1225/1224, 1445/1444}. Otherwise, 11- and 13-limit extensions are somewhat less ideal.
 [[Subgroup]]: 2.3.5.7
@@ Line 14: / Line 14: @@
 [[Comma list]]: [[4802000/4782969]]
-[[Mapping]]: [{{val| 1 0 0 -1 }}, {{val| 0 1 2 2 }}, {{val| 0 0 -4 3 }}]
+{{Mapping|legend=1| 1 0 0 -1 | 0 1 2 2 | 0 0 -4 3 }}
+: mapping generators: ~2, ~3, ~81/70
 Lattice basis:
@@ Line 20: / Line 22: @@
 : Angle (3/2, 81/70) = 73.88 deg
-Optimal tuning ([[CTE]]): ~3/2 = 702.3175, ~81/70 = 254.6220
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.3175, ~81/70 = 254.6220
 [[Minimax tuning]]:
 * [[7-odd-limit]]: 3 +c/14, 5 and 7 just
-: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.5.7
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.7
 * [[9-odd-limit]]: 3 just, 5 and 7 -c/7 to 3 +c/14, 5 and 7 just
-: [[Eigenmonzo basis]] ([[unchanged-interval basis]]): 2.7/5
+: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
 {{Optimal ET sequence|legend=1| 19, 56d, 61d, 75, 80, 94, 99, 212, 292, 311, 410, 1131, 1541b, 1659b }}
@@ Line 39: / Line 41: @@
 Comma list: 1225/1224, 295936/295245
-Mapping: [{{val| 1 0 0 -1 -5 }}, {{val| 0 1 2 2 6 }}, {{val| 0 0 -4 3 -2 }}]
+Mapping: {{mapping| 1 0 0 -1 -5 | 0 1 2 2 6 | 0 0 -4 3 -2 }}
-Optimal tuning (CTE): ~3/2 = 702.3458, ~81/70 = 254.6233
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3458, ~81/70 = 254.6233
 {{Optimal ET sequence|legend=1| 94, 99, 193, 217, 292, 311, 410, 1131, 1541b }}
@@ Line 52: / Line 54: @@
 Comma list: 1216/1215, 1225/1224, 1445/1444
-Mapping: [{{val| 1 0 0 -1 -5 -6 }}, {{val| 0 1 2 2 6 7 }}, {{val| 0 0 -4 3 -2 -4 }}]
+Mapping: {{mapping| 1 0 0 -1 -5 -6 | 0 1 2 2 6 7 | 0 0 -4 3 -2 -4 }}
-Optimal tuning (CTE): ~3/2 = 702.3233, ~81/70 = 254.6279
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.3233, ~81/70 = 254.6279
 {{Optimal ET sequence|legend=1| 94, 99, 118, 193, 217, 292h, 311, 410, 721 }}
@@ Line 67: / Line 69: @@
 [[Comma list]]: 19712/19683, 42875/42768
-[[Mapping]]: [{{val| 1 0 0 -1 -7 }}, {{val| 0 1 2 2 7 }}, {{val| 0 0 -4 3 -3 }}]
+{{Mapping|legend=1| 1 0 0 -1 -7 | 0 1 2 2 7 | 0 0 -4 3 -3 }}
-Optimal tuning ([[CTE]]): ~3/2 = 702.2115, ~81/70 = 254.6215
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.2115, ~81/70 = 254.6215
 {{Optimal ET sequence|legend=1| 94, 99e, 118, 193, 212, 311, 740, 1051d }}
@@ Line 82: / Line 84: @@
 Comma list: 2080/2079, 19712/19683, 42875/42768
-Mapping: [{{val| 1 0 0 -1 -7 -13 }}, {{val| 0 1 2 2 7 10 }}, {{val| 0 0 -4 3 -3 4 }}]
+Mapping: {{mapping| 1 0 0 -1 -7 -13 | 0 1 2 2 7 10 | 0 0 -4 3 -3 4 }}
-Optimal tuning (CTE): ~3/2 = 702.2075, ~81/70 = 254.6183
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2075, ~81/70 = 254.6183
 {{Optimal ET sequence|legend=1| 94, 118f, 193f, 212, 217, 311, 740, 1051d }}
@@ Line 95: / Line 97: @@
 Comma list: 595/594, 833/832, 1156/1155, 19712/19683
-Mapping: [{{val| 1 0 0 -1 -7 -13 -5 }}, {{val| 0 1 2 2 7 10 6 }}, {{val| 0 0 -4 3 -3 4 -2 }}]
+Mapping: {{mapping| 1 0 0 -1 -7 -13 -5 | 0 1 2 2 7 10 6 | 0 0 -4 3 -3 4 -2 }}
-Optimal tuning (CTE): ~3/2 = 702.2296, ~51/44 = 254.6012
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2296, ~51/44 = 254.6012
 {{Optimal ET sequence|legend=1| 94, 118f, 193f, 212g, 217, 311, 740g, 1051dg }}
@@ Line 108: / Line 110: @@
 Comma list: 595/594, 833/832, 969/968, 1156/1155, 1216/1215
-Mapping: [{{val| 1 0 0 -1 -7 -13 -5 -6 }}, {{val| 0 1 2 2 7 10 6 7 }}, {{val| 0 0 -4 3 -3 4 -2 -4 }}]
+Mapping: {{mapping|| 1 0 0 -1 -7 -13 -5 -6 | 0 1 2 2 7 10 6 7 | 0 0 -4 3 -3 4 -2 -4 }}
-Optimal tuning (CTE): ~3/2 = 702.2355, ~22/19 = 254.5930
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.2355, ~22/19 = 254.5930
 {{Optimal ET sequence|legend=1| 94, 118f, 193f, 212gh, 217, 311, 740g, 1051dgh }}
@@ Line 123: / Line 125: @@
 [[Comma list]]: 896/891, 472392/471625
-[[Mapping]]: [{{val| 1 0 0 -1 6 }}, {{val| 0 1 2 2 -2 }}, {{val| 0 0 4 -3 -3 }}]
+{{Mapping|legend=1| 1 0 0 -1 6 | 0 1 2 2 -2 | 0 0 4 -3 -3 }}
-Optimal tuning ([[CTE]]): ~3/2 = 702.8093, ~64/55 = 254.3378
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.8093, ~64/55 = 254.3378
 {{Optimal ET sequence|legend=1| 75e, 80, 99e, 179e }}
@@ Line 136: / Line 138: @@
 Comma list: 352/351, 364/363, 472392/471625
-Mapping: [{{val| 1 0 0 -1 6 11 }}, {{val| 0 1 2 2 -2 -5 }}, {{val| 0 0 4 -3 -3 -3 }}]
+Mapping: {{mapping| 1 0 0 -1 6 11 | 0 1 2 2 -2 -5 | 0 0 4 -3 -3 -3 }}
-Optimal tuning (CTE): ~3/2 = 703.6228, ~64/55 = 254.3447
+Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 703.6228, ~64/55 = 254.3447
 {{Optimal ET sequence|legend=1| 75e, 80, 99ef, 179ef }}
@@ Line 149: / Line 151: @@
 The other comma necessary to define it is 14641/14580, the [[semicanousma]], which is the difference between [[121/120]] and [[243/242]]. By flattening the 11th harmonic by one cent, it identifies [[20/11]] by three [[11/9]]'s stacked, so an octave can be divided into 11/9-11/9-11/9-11/10.
-Natural extensions arise up to the 19-limit, and 410edo provides a satisfactory tuning solution to any of them.
+Natural extensions arise up to the 19-limit, and 410edo provides a satisfactory tuning solution to all of them.
 [[Subgroup]]: 2.3.5.7.11
@@ Line 155: / Line 157: @@
 [[Comma list]]: 9801/9800, 14641/14580
-[[Mapping]]: [{{val| 2 0 0 -2 1 }}, {{val| 0 1 2 2 2 }}, {{val| 0 0 -4 3 -1 }}]
+{{Mapping|legend=1| 2 0 0 -2 1 | 0 1 2 2 2 | 0 0 -4 3 -1 }}
-Mapping generators: ~99/70, ~3, ~81/70
+: mapping generators: ~99/70, ~3, ~81/70
-Optimal tuning ([[CTE]]): ~3/2 = 702.4262, ~81/70 = 254.6191
+[[Optimal tuning]] ([[CTE]]): ~99/70 = 1\2, ~3/2 = 702.4262, ~81/70 = 254.6191
 {{Optimal ET sequence|legend=1| 80, 94, 118, 198, 212, 292, 330e, 410 }}
@@ Line 170: / Line 172: @@
 Comma list: 1716/1715, 2080/2079, 14641/14580
-Mapping: [{{val| 2 0 0 -2 1 -11 }}, {{val| 0 1 2 2 2 5 }}, {{val| 0 0 -4 3 -1 6 }}]
+Mapping: {{mapping| 2 0 0 -2 1 -11 | 0 1 2 2 2 5 | 0 0 -4 3 -1 6 }}
-Optimal tuning (CTE): ~3/2 = 702.4802, ~81/70 = 254.6526
+Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4802, ~81/70 = 254.6526
 {{Optimal ET sequence|legend=1| 80f, 94, 118f, 198, 410 }}
@@ Line 183: / Line 185: @@
 Comma list: 715/714, 1089/1088, 1225/1224, 14641/14580
-Mapping: [{{val| 2 0 0 -2 1 -11 -10 }}, {{val| 0 1 2 2 2 5 6 }}, {{val| 0 0 -4 3 -1 6 -2 }}]
+Mapping: {{mapping| 2 0 0 -2 1 -11 -10 | 0 1 2 2 2 5 6 | 0 0 -4 3 -1 6 -2 }}
-Optimal tuning (CTE): ~3/2 = 702.4415, ~81/70 = 254.6663
+Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4415, ~81/70 = 254.6663
 {{Optimal ET sequence|legend=1| 94, 118f, 198g, 212g, 292, 410 }}
@@ Line 196: / Line 198: @@
 Comma list: 715/714, 1089/1088, 1216/1215, 1225/1224, 1445/1444
-Mapping: [{{val| 2 0 0 -2 1 -11 -10 -12 }}, {{val| 0 1 2 2 2 5 6 7 }}, {{val| 0 0 -4 3 -1 6 -2 -4 }}]
+Mapping: {{mapping| 2 0 0 -2 1 -11 -10 -12 | 0 1 2 2 2 5 6 7 | 0 0 -4 3 -1 6 -2 -4 }}
-Optimal tuning (CTE): ~3/2 = 702.4030, ~81/70 = 254.6870
+Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.4030, ~81/70 = 254.6870
 {{Optimal ET sequence|legend=1| 94, 118f, 198gh, 212gh, 292h, 410, 622ef }}
@@ Line 211: / Line 213: @@
 Comma list: 352/351, 9801/9800, 14641/14580
-Mapping: [{{val| 2 0 0 -2 1 11 }}, {{val| 0 1 2 2 2 -1 }}, {{val| 0 0 -4 3 -1 -1 }}]
+Mapping: {{mapping| 2 0 0 -2 1 11 | 0 1 2 2 2 -1 | 0 0 -4 3 -1 -1 }}
-Optimal tuning (CTE): ~3/2 = 702.5374, ~81/70 = 254.6819
+Optimal tuning (CTE): ~99/70 = 1\2, ~3/2 = 702.5374, ~81/70 = 254.6819
 {{Optimal ET sequence|legend=1| 80, 94, 118, 174d, 198, 490f }}
@@ Line 228: / Line 230: @@
 Comma list: 351/350, 364/363, 11011/10935
-Mapping: [{{val| 2 0 0 -2 1 0 }}, {{val| 0 1 2 2 2 3 }}, {{val| 0 0 -4 3 -1 -5 }}]
+Mapping: {{mapping| 2 0 0 -2 1 0 | 0 1 2 2 2 3 | 0 0 -4 3 -1 -5 }}
 Optimal tuning (CTE): ~3/2 = 702.7417, ~15/13 = 254.3382
@@ Line 238: / Line 240: @@
 [[Category:Temperament families]]
 [[Category:Canou family| ]] <!-- main article -->
+[[Category:Canou| ]] <!-- key article -->
 [[Category:Rank 3]]

Canou family: Difference between revisions

Revision as of 08:33, 14 September 2023

Contents

Canou

2.3.5.7.17 subgroup

2.3.5.7.17.19 subgroup

Synca

13-limit

17-limit

19-limit

Canta

13-limit

Semicanou

13-limit

17-limit

19-limit

Semicanoumint

Semicanouwolf

Navigation menu

Canou family: Difference between revisions

Revision as of 08:33, 14 September 2023

Canou

2.3.5.7.17 subgroup

2.3.5.7.17.19 subgroup

Synca

13-limit

17-limit

19-limit

Canta

13-limit

Semicanou

13-limit

17-limit

19-limit

Semicanoumint

Semicanouwolf

Navigation menu

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