Jubilismic clan: Difference between revisions

Revision as of 07:05, 18 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. Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.

Lemba, astrology, and doublewide 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

Astrology

See also: Magic family

Subgroup: 2.3.5.7

Comma list: 50/49, 3125/3072

Mapping: [⟨2 0 4 5], ⟨0 5 1 1]]

Mapping geenerators: ~7/5, ~5/4

Wedgie: ⟨⟨ 10 2 2 -20 -25 -1 ]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.578

Template:Val list

Badness: 0.082673

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 121/120, 176/175

Mapping: [⟨2 0 4 5 5], ⟨0 5 1 1 3]]

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 380.530

Optimal GPV sequence: Template:Val list

Badness: 0.039151

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 65/64, 78/77, 121/120

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

Optimal tuning (POTE): ~7/5 = 1\2, ~5/4 = 379.787

Optimal GPV sequence: Template:Val list

Badness: 0.034376

Music

Astrology Percussion Quintet No 1^{[dead link]} play^{[dead link]} by Joel Taylor

Horoscope

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 66/65, 105/104, 121/120

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

POTE generator: ~5/4 = 379.837

Optimal GPV sequence: Template:Val list

Badness: 0.035284

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

@@ Line 19: / Line 19: @@
 === 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 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]]. Diminished splits the ~7/5 period into a further two. Pajara slices the ~7/4 into two. Injera slices the ~5/1 into four. Hedgehog slices the ~7/1 into five.
-Lemba, astrology, doublewide, and diminished are discussed below; others in the clan are
+Lemba, astrology, and doublewide are discussed below; others in the clan are
+* [[Diminished]] → [[Dimipent family #Diminished|Dimipent family]]
 * [[Pajara]] → [[Diaschismic family #Pajara|Diaschismic family]]
 * [[Decimal]] → [[Dicot family #Decimal|Dicot family]]
@@ Line 136: / Line 137: @@
 Badness: 0.035284
-== Diminished ==
-<div style="float: right">[[:de:Verminderte Temperaturen|Deutsch]]</div>
-{{See also| Dimipent family #Diminished }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 36/35, 50/49
-[[Mapping]]: [{{val| 4 0 3 5 }}, {{val| 0 1 1 1 }}]
-Mapping generators: ~6/5, ~3
-[[Optimal tuning]] ([[POTE]]): ~6/5 = 1\4, ~3/2 = 699.523
-{{Val list|legend=1| 4, 8d, 12 }}
-[[Badness]]: 0.022401
-Scales: [[diminished12]]
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 36/35, 50/49, 56/55
-Mapping: [{{val| 4 0 3 5 14 }}, {{val| 0 1 1 1 0 }}]
-Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 709.109
-Optimal GPV sequence: {{Val list| 4, 8d, 12, 32cddee, 44cddeee }}
-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: [{{val| 4 0 3 5 14 15 }}, {{val| 0 1 1 1 0 0 }}]
-Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 713.773
-Optimal GPV sequence: {{Val list| 4, 8d, 12f, 20cdef }}
-Badness: 0.019509
-Scales: [[diminished12]]
-=== Demolished ===
-Subgroup: 2.3.5.7.11
-Comma list: 36/35, 45/44, 50/49
-Mapping: [{{val| 4 0 3 5 -5 }}, {{val| 0 1 1 1 3 }}]
-Optimal tuning (POTE): ~6/5 = 1\4, ~3/2 = 689.881
-Optimal GPV sequence: {{Val list| 12, 28, 40de }}
-Badness: 0.026574
-=== 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.
-Subgroup: 2.3.5.7.11
-Comma list: 36/35, 50/49, 125/121
-Mapping: [{{val| 4 1 4 6 6 }}, {{val| 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: {{Val list| 8bce, 12 }}
-Badness: 0.054965
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 36/35, 50/49, 66/65, 125/121
-Mapping: [{{val| 4 1 4 6 6 7 }}, {{val| 0 2 2 2 3 3 }}]
-Optimal tuning (POTE): ~6/5 = 1\4, ~12/11 = 102.299
-Optimal GPV sequence: {{Val list| 8bcef, 12f }}
-Badness: 0.041707
 == Doublewide ==

Jubilismic clan: Difference between revisions

Revision as of 07:05, 18 March 2023

Contents

Jubilic

Overview to extensions

Lemba

11-limit

13-limit

Astrology

11-limit

13-limit

Horoscope

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

Jubilismic clan: Difference between revisions

Revision as of 07:05, 18 March 2023

Jubilic

Overview to extensions

Lemba

11-limit

13-limit

Astrology

11-limit

13-limit

Horoscope

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

Search