Jubilismic clan: Difference between revisions

Revision as of 09:11, 13 March 2023

The jubilismic clan tempers out the jubilisma, 50/49, which means 7/5 and 10/7 are identified and the octave is divided in two.

Jubilic

The head of this clan, jubilic, is generated by ~5/4. That and a semioctave gives ~7/4.

Subgroup: 2.5.7

Comma list: 50/49

Sval mapping: [⟨2 0 1], ⟨0 1 1]]

Sval mapping generators: ~7/5, ~5

Gencom mapping: [⟨2 0 0 1], ⟨0 0 1 1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.840

Template:Val list

Overview to extensions

Lemba finds the perfect fifth three steps away by tempering out 1029/1024. Astrology, five steps away by tempering out 3125/3072. Decimal, two steps away by tempering out 25/24 and 49/48. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.

Lemba, doublewide, and diminished are discussed below; others in the clan are

which are discussed elsewhere.

Lemba

Main article: Lemba

Subgroup: 2.3.5.7

Comma list: 50/49, 525/512

Mapping: [⟨2 2 5 6], ⟨0 3 -1 -1]]

Mapping generators: ~7/5, ~8/7

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 232.089

Template:Val list

Badness: 0.062208

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 385/384

Mapping: [⟨2 2 5 6 5], ⟨0 3 -1 -1 5]]

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974

Optimal GPV sequence: Template:Val list

Badness: 0.041563

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 65/64, 78/77

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

Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966

Optimal GPV sequence: Template:Val list

Badness: 0.025477

Diminished

Deutsch

See also: Dimipent family § Diminished

Subgroup: 2.3.5.7

Comma list: 36/35, 50/49

Mapping: [⟨4 0 3 5], ⟨0 1 1 1]]

Mapping generators: ~6/5, ~3

Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 699.523

Template:Val list

Badness: 0.022401

Scales: diminished12

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 tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109

Optimal GPV sequence: Template:Val list

Badness: 0.022132

Scales: diminished12

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 tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773

Optimal GPV sequence: Template:Val list

Badness: 0.019509

Scales: diminished12

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 tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881

Optimal GPV sequence: Template:Val list

Badness: 0.026574

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 tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679

Optimal GPV sequence: Template:Val list

Badness: 0.054965

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 tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299

Optimal GPV sequence: Template:Val list

Badness: 0.041707

Doublewide

Subgroup: 2.3.5.7

Comma list: 50/49, 875/864

Mapping: [⟨2 1 3 4], ⟨0 4 3 3]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.719

Template:Val list

Badness: 0.043462

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 875/864

Mapping: [⟨2 1 3 4 8], ⟨0 4 3 3 -2]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545

Optimal GPV sequence: Template:Val list

Badness: 0.032058

Fleetwood

Subgroup: 2.3.5.7.11

Comma list: 50/49, 55/54, 176/175

Mapping: [⟨2 1 3 4 2], ⟨0 4 3 3 9]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038

Optimal GPV sequence: Template:Val list

Badness: 0.035202

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 176/175

Mapping: [⟨2 1 3 4 2 3], ⟨0 4 3 3 9 8]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841

Optimal GPV sequence: Template:Val list

Badness: 0.031835

Cavalier

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 875/864

Mapping: [⟨2 1 3 4 1], ⟨0 4 3 3 11]]

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427

Optimal GPV sequence: Template:Val list

Badness: 0.052899

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 325/324

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

Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396

Optimal GPV sequence: Template:Val list

Badness: 0.035040

Elvis

For the 5-limit version of this temperament, see High badness temperaments #Elvis.

Subgroup: 2.3.5.7

Comma list: 50/49, 8505/8192

Mapping: [⟨2 1 10 11], ⟨0 2 -5 -5]]

Wedgie: ⟨⟨ 4 -10 -10 -25 -27 5 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~45/32 = 553.721

Template:Val list

Badness: 0.141473

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 50/49, 1344/1331

Mapping: [⟨2 1 10 11 8], ⟨0 2 -5 -5 -1]]

Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882

Optimal GPV sequence: Template:Val list

Badness: 0.063212

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 50/49, 78/77, 1053/1024

Mapping: [⟨2 1 10 11 8 16], ⟨0 2 -5 -5 -1 -8]]

Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892

Optimal GPV sequence: Template:Val list

Badness: 0.043997

Crepuscular

See also: Fifive family § Crepuscular

Subgroup: 2.3.5.7

Comma list: 50/49, 4375/4374

Mapping: [⟨2 2 3 4], ⟨0 5 7 7]]

Wedgie: ⟨⟨ 10 14 14 -1 -6 -7 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~27/25 = 140.349

Template:Val list

Badness: 0.086669

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 864/847

Mapping: [⟨2 2 3 4 6], ⟨0 5 7 7 4]]

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587

Optimal GPV sequence: Template:Val list

Badness: 0.040758

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 78/77, 99/98, 144/143

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

Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554

Optimal GPV sequence: Template:Val list

Badness: 0.024368

Comic

For the 5-limit version of this temperament, see High badness temperaments #Comic.

Subgroup: 2.3.5.7

Comma list: 50/49, 2240/2187

Mapping: [⟨2 1 -3 -2], ⟨0 2 7 7]]

Wedgie: ⟨⟨ 4 14 14 13 11 -7 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.699

Template:Val list

Badness: 0.084395

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 99/98, 2662/2625

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

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184

Optimal GPV sequence: Template:Val list

Badness: 0.045052

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/63, 99/98, 968/945

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

Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435

Optimal GPV sequence: Template:Val list

Badness: 0.041470

Bipyth

See also: Archytas clan § Superpyth

Subgroup: 2.3.5.7

Comma list: 50/49, 20480/19683

Mapping: [⟨2 0 -24 -23], ⟨0 1 9 9]]

Wedgie: ⟨⟨ 2 18 18 24 23 -9 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.437

Template:Val list

Badness: 0.165033

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 896/891

Mapping: [⟨2 0 -24 -23 -9], ⟨0 1 9 9 5]]

Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310

Optimal GPV sequence: Template:Val list

Badness: 0.070910

Sedecic

Subgroup: 2.3.5.7

Comma list: 50/49, 546875/524288

Mapping: [⟨16 0 37 45], ⟨0 1 0 0]]

Wedgie: ⟨⟨ 16 0 0 -37 -45 0 ]]

Optimal tuning (POTE): ~128/125 = 1\16, ~3/2 = 700.554

Template:Val list

Badness: 0.265972

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 385/384, 1331/1323

Mapping: [⟨16 0 37 45 30], ⟨0 1 0 0 1]]

Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331

Optimal GPV sequence: Template:Val list

Badness: 0.092774

Duodecim

See also: Compton family § Duodecim

Subgroup: 2.3.5.7.11

Comma list: 36/35, 50/49, 64/63

Mapping: [⟨12 19 28 34 0], ⟨0 0 0 0 1]]

Optimal tuning (POTE): ~16/15 = 1\12, ~11/8 = 565.023

Template:Val list

Badness: 0.030536

Vigintiduo

Subgroup: 2.3.5.7.11

Comma list: 50/49, 64/63, 245/243

Mapping: [⟨22 35 51 62 0], ⟨0 0 0 0 1]]

Optimal tuning (POTE): ~36/35 = 1\22, ~11/8 = 557.563

Template:Val list

Badness: 0.048372

Vigin

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 64/63, 99/98

Mapping: [⟨22 35 51 62 76 0], ⟨0 0 0 0 0 1]]

Optimal tuning (POTE): ~33/32 = 1\22, ~13/8 = 844.624

Template:Val list

Badness: 0.029849

Jubilismic clan: Difference between revisions

Revision as of 09:11, 13 March 2023

Contents

Jubilic

Overview to extensions

Lemba

11-limit

13-limit

Diminished

11-limit

13-limit

Demolished

Cohedim

13-limit

Doublewide

11-limit

Fleetwood

13-limit

Cavalier

13-limit

Elvis

11-limit

13-limit

Crepuscular

11-limit

13-limit

Comic

11-limit

13-limit

Bipyth

11-limit

Sedecic

11-limit

Duodecim

Vigintiduo

Vigin

Navigation menu

@@ Line 2: / Line 2: @@
 == Jubilic ==
-The head of this clan, jubilic, is generated by an approximate [[5/4]]. That and a semioctave gives [[7/4]].
+The head of this clan, jubilic, is generated by [[~]][[5/4]]. That and a semioctave gives ~[[7/4]].
 [[Subgroup]]: 2.5.7
@@ Line 14: / Line 14: @@
 [[Gencom]] [[mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 0 1 1 }}]
-[[Optimal tuning]] ([[POTE]]) ~5/4 = 380.840
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~5/4 = 380.840
 {{Val list|legend=1| 2, 4, 6, 16, 22, 60d, 82d, 104dd }}
@@ Line 37: / Line 37: @@
 {{Main| Lemba }}
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 525/512
@@ Line 45: / Line 45: @@
 Mapping generators: ~7/5, ~8/7
-[[POTE generator]]: ~8/7 = 232.089
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~8/7 = 232.089
 {{Val list|legend=1| 10, 16, 26, 62c }}
@@ Line 58: / Line 58: @@
 Mapping: [{{val| 2 2 5 6 5 }}, {{val| 0 3 -1 -1 5 }}]
-POTE generator: ~8/7 = 230.974
+Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.974
 Optimal GPV sequence: {{Val list| 10, 16, 26 }}
@@ Line 71: / Line 71: @@
 Mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
-POTE generator: ~8/7 = 230.966
+Optimal tuning (POTE): ~7/5 = 1\2, ~8/7 = 230.966
 Optimal GPV sequence: {{Val list| 10, 16, 26 }}
@@ Line 79: / Line 79: @@
 == Diminished ==
 <div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
-{{see also|Dimipent family #Diminished}}
+{{See also| Dimipent family #Diminished }}
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 36/35, 50/49
@@ Line 89: / Line 89: @@
 Mapping generators: ~6/5, ~3
-[[POTE generator]]: ~3/2 = 699.523
+[[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~3/2 = 699.523
 {{Val list|legend=1| 4, 8d, 12 }}
@@ Line 104: / Line 104: @@
 Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]
-Mapping generators: ~6/5, ~3
+Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109
-POTE generator: ~3/2 = 709.109
 Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
@@ Line 121: / Line 119: @@
 Mapping: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]
-Mapping generators: ~6/5, ~3
+Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773
-POTE generator: ~3/2 = 713.773
 Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}
@@ Line 138: / Line 134: @@
 Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]
-Mapping generators: ~6/5, ~3
+Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881
-POTE generator: ~3/2 = 689.881
 Optimal GPV sequence: {{Val list| 12, 28, 40de }}
@@ Line 157: / Line 151: @@
 Mapping generators: ~6/5, ~11/7
-POTE generator: ~12/11 = 101.679
+Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 101.679
 Optimal GPV sequence: {{Val list| 8bce, 12 }}
@@ Line 170: / Line 164: @@
 Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}]
-POTE generator: ~12/11 = 102.299
+Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299
 Optimal GPV sequence: {{Val list| 8bcef, 12f }}
@@ Line 177: / Line 171: @@
 == Doublewide ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 875/864
@@ Line 183: / Line 177: @@
 [[Mapping]]: [{{val| 2 1 3 4 }}, {{val| 0 4 3 3 }}]
-[[POTE generator]]: ~6/5 = 325.719
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~6/5 = 325.719
 {{Val list|legend=1| 4, 14bd, 18, 22, 48, 70c }}
@@ Line 196: / Line 190: @@
 Mapping: [{{val| 2 1 3 4 8 }}, {{val| 0 4 3 3 -2 }}]
-POTE generator: ~6/5 = 325.545
+Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 325.545
 Optimal GPV sequence: {{Val list| 4, 14bd, 18, 22, 48, 70c, 118cd }}
@@ Line 209: / Line 203: @@
 Mapping: [{{val| 2 1 3 4 2 }}, {{val| 0 4 3 3 9 }}]
-POTE generator: ~6/5 = 327.038
+Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.038
 Optimal GPV sequence: {{Val list| 4e, 18e, 22 }}
@@ Line 222: / Line 216: @@
 Mapping: [{{val| 2 1 3 4 2 3 }}, {{val| 0 4 3 3 9 8 }}]
-POTE generator: ~6/5 = 327.841
+Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 327.841
 Optimal GPV sequence: {{Val list| 4ef, 18e, 22, 84bddf }}
@@ Line 235: / Line 229: @@
 Mapping: [{{val| 2 1 3 4 1 }}, {{val| 0 4 3 3 11 }}]
-POTE generator: ~6/5 = 323.427
+Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.427
 Optimal GPV sequence: {{Val list| 22e, 26 }}
@@ Line 248: / Line 242: @@
 Mapping: [{{val| 2 1 3 4 1 2 }}, {{val| 0 4 3 3 11 10 }}]
-POTE generator: ~6/5 = 323.396
+Optimal tuning (POTE): ~7/5 = 1\2, ~6/5 = 323.396
 Optimal GPV sequence: {{Val list| 22ef, 26 }}
@@ Line 257: / Line 251: @@
 : ''For the 5-limit version of this temperament, see [[High badness temperaments #Elvis]].''
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 8505/8192
@@ Line 265: / Line 259: @@
 {{Multival|legend=1| 4 -10 -10 -25 -27 5 }}
-[[POTE generator]]: ~45/32 = 553.721
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~45/32 = 553.721
 {{Val list|legend=1| 2, 24c, 26 }}
@@ Line 278: / Line 272: @@
 Mapping: [{{val| 2 1 10 11 8 }}, {{val| 0 2 -5 -5 -1 }}]
-POTE generator: ~11/8 = 553.882
+Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.882
 Optimal GPV sequence: {{Val list| 2, 24c, 26 }}
@@ Line 291: / Line 285: @@
 Mapping: [{{val| 2 1 10 11 8 16 }}, {{val| 0 2 -5 -5 -1 -8 }}]
-POTE generator: ~11/8 = 553.892
+Optimal tuning (POTE): ~7/5 = 1\2, ~11/8 = 553.892
 Optimal GPV sequence: {{Val list| 2f, 24cf, 26 }}
@@ Line 298: / Line 292: @@
 == Crepuscular ==
-{{see also| Fifive family #Crepuscular }}
+{{See also| Fifive family #Crepuscular }}
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 4375/4374
-[[Mapping]]: [{{val|2 2 3 4}}, {{val|0 5 7 7}}]
+[[Mapping]]: [{{val| 2 2 3 4 }}, {{val| 0 5 7 7 }}]
 {{Multival|legend=1|10 14 14 -1 -6 -7}}
-[[POTE generator]]: ~27/25 = 140.349
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349
 {{Val list|legend=1| 8d, 26, 34d, 60d }}
@@ Line 319: / Line 313: @@
 Comma list: 50/49, 99/98, 864/847
-Mapping: [{{val|2 2 3 4 6}}, {{val|0 5 7 7 4}}]
+Mapping: [{{val| 2 2 3 4 6 }}, {{val| 0 5 7 7 4 }}]
-POTE generator: ~12/11 = 140.587
+Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.587
 Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
@@ Line 332: / Line 326: @@
 Comma list: 50/49, 78/77, 99/98, 144/143
-Mapping: [{{val|2 2 3 4 6 6}}, {{val|0 5 7 7 4 6}}]
+Mapping: [{{val| 2 2 3 4 6 6 }}, {{val| 0 5 7 7 4 6 }}]
-POTE generator: ~12/11 = 140.554
+Optimal tuning (POTE): ~7/5 = 1\2, ~12/11 = 140.554
 Optimal GPV sequence: {{Val list| 8d, 26, 34d, 60d }}
@@ Line 343: / Line 337: @@
 : ''For the 5-limit version of this temperament, see [[High badness temperaments #Comic]].''
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 2240/2187
@@ Line 351: / Line 345: @@
 {{Multival|legend=1| 4 14 14 13 11 -7 }}
-[[POTE generator]]: ~81/80 = 54.699
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~81/80 = 54.699
 {{Val list|legend=1| 20cd, 22 }}
@@ Line 364: / Line 358: @@
 Mapping: [{{val| 2 1 -3 -2 -4 }}, {{val| 0 2 7 7 10 }}]
-POTE generator: ~81/80 = 55.184
+Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 55.184
 Optimal GPV sequence: {{Val list| 20cde, 22 }}
@@ Line 377: / Line 371: @@
 Mapping: [{{val| 2 1 -3 -2 -4 3 }}, {{val| 0 2 7 7 10 4 }}]
-POTE generator: ~81/80 = 54.435
+Optimal tuning (POTE): ~7/5 = 1\2, ~81/80 = 54.435
 Optimal GPV sequence: {{Val list| 22 }}
@@ Line 384: / Line 378: @@
 == Bipyth ==
-{{see also| Archytas clan #Superpyth }}
+{{See also| Archytas clan #Superpyth }}
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 20480/19683
@@ Line 394: / Line 388: @@
 {{Multival|legend=1| 2 18 18 24 23 -9 }}
-[[POTE generator]]: ~3/2 = 709.437
+[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~3/2 = 709.437
 {{Val list|legend=1| 10cd, 12cd, 22 }}
@@ Line 407: / Line 401: @@
 Mapping: [{{val| 2 0 -24 -23 -9 }}, {{val| 0 1 9 9 5 }}]
-POTE generator: ~3/2 = 709.310
+Optimal tuning (POTE): ~7/5 = 1\2, ~3/2 = 709.310
 Optimal GPV sequence: {{Val list| 10cd, 12cde, 22 }}
@@ Line 414: / Line 408: @@
 == Sedecic ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 546875/524288
@@ Line 422: / Line 416: @@
 {{Multival|legend=1| 16 0 0 -37 -45 0 }}
-[[POTE generator]]: ~3/2 = 700.554
+[[Optimal tuning]] ([[POTE]]): ~128/125 = 1\16, ~3/2 = 700.554
 {{Val list|legend=1| 16, 32, 48 }}
@@ Line 435: / Line 429: @@
 Mapping: [{{val| 16 0 37 45 30 }}, {{val| 0 1 0 0 1 }}]
-POTE generator: ~3/2 = 700.331
+Optimal tuning (POTE): ~22/21 = 1\16, ~3/2 = 700.331
 Optimal GPV sequence: {{Val list| 16, 32, 48 }}
@@ Line 442: / Line 436: @@
 == Duodecim ==
-{{see also| Compton family #Duodecim }}
+{{See also| Compton family #Duodecim }}
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 36/35, 50/49, 64/63
@@ Line 450: / Line 444: @@
 [[Mapping]]: [{{val| 12 19 28 34 0 }}, {{val| 0 0 0 0 1 }}]
-[[POTE generator]]: ~11/8 = 565.023
+[[Optimal tuning]] ([[POTE]]): ~16/15 = 1\12, ~11/8 = 565.023
 {{Val list|legend=1| 12, 24d, 36d }}
@@ Line 457: / Line 451: @@
 == Vigintiduo ==
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
 [[Comma list]]: 50/49, 64/63, 245/243
@@ Line 463: / Line 457: @@
 [[Mapping]]: [{{val| 22 35 51 62 0 }}, {{val| 0 0 0 0 1 }}]
-[[POTE generator]]: ~11/8 = 557.563
+[[Optimal tuning]] ([[POTE]]): ~36/35 = 1\22, ~11/8 = 557.563
 {{Val list|legend=1| 22, 66de, 88bde, 110bd, 198bcdde }}
@@ Line 470: / Line 464: @@
 == Vigin ==
-Subgroup: 2.3.5.7.11.13
+[[Subgroup]]: 2.3.5.7.11.13
 [[Comma list]]: 50/49, 55/54, 64/63, 99/98
@@ Line 476: / Line 470: @@
 [[Mapping]]: [{{val| 22 35 51 62 76 0 }}, {{val| 0 0 0 0 0 1 }}]
-[[POTE generator]]: ~13/8 = 844.624
+[[Optimal tuning]] ([[POTE]]): ~33/32 = 1\22, ~13/8 = 844.624
 {{Val list|legend=1| 22, 44 }}

Jubilismic clan: Difference between revisions

Revision as of 09:11, 13 March 2023

Jubilic

Overview to extensions

Lemba

11-limit

13-limit

Diminished

11-limit

13-limit

Demolished

Cohedim

13-limit

Doublewide

11-limit

Fleetwood

13-limit

Cavalier

13-limit

Elvis

11-limit

13-limit

Crepuscular

11-limit

13-limit

Comic

11-limit

13-limit

Bipyth

11-limit

Sedecic

11-limit

Duodecim

Vigintiduo

Vigin

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