Hemimage temperaments: Difference between revisions

Revision as of 08:44, 19 March 2022

This is a collection of temperaments tempering out the hemimage comma, [5 -7 -1 3⟩ = 10976/10935. These include commatic, chromat, degrees, subfourth, bisupermajor and cotoneum, considered below, as well as the following discussed elsewhere:

Quasisuper, {64/63, 2430/2401} → Archytas clan
Liese, {81/80, 686/675} → Meantone family
Unicorn, {126/125, 10976/10935} → Unicorn family
Magic, {225/224, 245/243} → Magic family
Guiron, {1029/1024, 10976/10935} → Gamelismic clan
Echidna, {1728/1715, 2048/2025} → Diaschismic family
Hemififths, {2401/2400, 5120/5103} → Breedsmic temperaments
Dodecacot, {3125/3087, 10976/10935} → Tetracot family
Parakleismic, {3136/3125, 4375/4374} → Ragismic microtemperaments
Pluto, {4000/3969, 10976/10935} → Mirkwai clan
Hendecatonic, {6144/6125, 10976/10935} → Porwell temperaments
Marfifths, {10976/10935, 15625/15552} → Kleismic family
Yarman I, {10976/10935, 244140625/243045684} → Turkish maqam music temperaments

Chromat

The chromat temperament has a period of 1/3 octave and tempers out the hemimage (10976/10935) and the triwellisma (235298/234375). It is also described as an amity extension with third-octave period.

Subgroup: 2.3.5.7

Comma list: 10976/10935, 235298/234375

Mapping: [⟨3 4 5 6], ⟨0 5 13 16]]

Wedgie: ⟨⟨ 15 39 48 27 34 2 ]]

Mapping generators: ~63/50, ~28/27

POTE generator: ~28/27 = 60.528

Template:Val list

Badness: 0.057499

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 4375/4356, 10976/10935

Mapping: [⟨3 4 5 6 6], ⟨0 5 13 16 29]]

POTE generator: ~28/27 = 60.430

Optimal GPV sequence: Template:Val list

Badness: 0.050379

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 625/624, 10976/10935

Mapping: [⟨3 4 5 6 6 4], ⟨0 5 13 16 29 47]]

POTE generator: ~28/27 = 60.428

Optimal GPV sequence: Template:Val list

Badness: 0.046006

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 364/363, 375/374, 441/440, 595/594, 3773/3757

Mapping: [⟨3 4 5 6 6 4 10], ⟨0 5 13 16 29 47 15]]

POTE generator: ~28/27 = 60.438

Optimal GPV sequence: Template:Val list

Badness: 0.031678

Catachrome

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 441/440, 1001/1000, 10976/10935

Mapping: [⟨3 4 5 6 6 12], ⟨0 5 13 16 29 -6]]

POTE generator: ~28/27 = 60.378

Optimal GPV sequence: Template:Val list

Badness: 0.043844

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 325/324, 375/374, 441/440, 4928/4913

Mapping: [⟨3 4 5 6 6 12 10], ⟨0 5 13 16 29 -6 15]]

POTE generator: ~28/27 = 60.377

Optimal GPV sequence: Template:Val list

Badness: 0.030218

Chromic

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 729/728, 1875/1859

Mapping: [⟨3 4 5 6 6 9], ⟨0 5 13 16 29 14]]

POTE generator: ~27/26 = 60.456

Optimal GPV sequence: Template:Val list

Badness: 0.049857

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 196/195, 352/351, 375/374, 595/594

Mapping: [⟨3 4 5 6 6 9 10], ⟨0 5 13 16 29 14 15]]

POTE generator: ~27/26 = 60.459

Optimal GPV sequence: Template:Val list

Badness: 0.031043

Bisupermajor

See also: Very high accuracy temperaments § Kwazy

Subgroup: 2.3.5.7

Comma list: 10976/10935, 65625/65536

Mapping: [⟨2 1 6 1], ⟨0 8 -5 17]]

Wedgie: ⟨⟨ 16 -10 34 -53 9 107 ]]

POTE generator: ~192/175 = 162.806

Template:Val list

Badness: 0.065492

11-limit

Subgroup: 2.3.5.7.11

Comma list: 385/384, 3388/3375, 9801/9800

Mapping: [⟨2 1 6 1 8], ⟨0 8 -5 17 -4]]

POTE generators: ~11/10 = 162.773

Optimal GPV sequence: Template:Val list

Badness: 0.032080

Commatic

The commatic temperament has a period of half octave and a generator of 20.4 cents. It is so named because the generator is a small interval ("commatic") which represents 81/80, 99/98, and 100/99 all tempered together.

Subgroup: 2.3.5.7

Comma list: 10976/10935, 50421/50000

Mapping: [⟨2 3 4 5], ⟨0 5 19 18]]

Wedgie: ⟨⟨ 10 38 36 37 29 -23 ]]

POTE generator: ~81/80 = 20.377

Template:Val list

Badness: 0.084317

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3388/3375, 8019/8000

Mapping: [⟨2 3 4 5 6], ⟨0 5 19 18 27]]

POTE generator: ~81/80 = 20.390

Optimal GPV sequence: Template:Val list

Badness: 0.030461

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 729/728, 1001/1000

Mapping: [⟨2 3 4 5 6 7], ⟨0 5 19 18 27 12]]

POTE generator: ~66/65 = 20.427

Optimal GPV sequence: Template:Val list

Badness: 0.026336

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 196/195, 289/288, 352/351, 561/560

Mapping: [⟨2 3 4 5 6 7 8], ⟨0 5 19 18 27 12 5]]

POTE generator: ~66/65 = 20.378

Optimal GPV sequence: Template:Val list

Badness: 0.022396

Cotoneum

Main article: Cotoneum

The cotoneum temperament (41&217, named after the Latin for "quince") tempers out the quince comma, 823543/819200 and the garischisma, 33554432/33480783. This temperament is supported by 41, 176, 217, and 258 EDOs, and can be extended to the 11-, 13-, 17-, and 19-limit by adding 441/440, 364/363, 595/594, and 343/342 to the comma list in this order.

Subgroup: 2.3.5.7

Comma list: 10976/10935, 823543/819200

Mapping: [⟨1 2 -18 -3], ⟨0 -1 49 14]]

Wedgie: ⟨⟨ 1 -49 -14 -80 -25 105 ]]

POTE generator: ~3/2 = 702.317

Template:Val list

Badness: 0.105632

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 10976/10935, 16384/16335

Mapping: [⟨1 2 -18 -3 13], ⟨0 -1 49 14 -23]]

POTE generator: ~3/2 = 702.303

Optimal GPV sequence: Template:Val list

Badness: 0.050966

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 3584/3575, 10976/10935

Mapping: [⟨1 2 -18 -3 13 29], ⟨0 -1 49 14 -23 -61]]

POTE generator: ~3/2 = 702.306

Optimal GPV sequence: Template:Val list

Badness: 0.036951

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 364/363, 441/440, 595/594, 3584/3575, 8281/8262

Mapping: [⟨1 2 -18 -3 13 29 41], ⟨0 -1 49 14 -23 -61 -89]]

POTE generator: ~3/2 = 702.307

Optimal GPV sequence: Template:Val list

Badness: 0.029495

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 343/342, 364/363, 441/440, 595/594, 1216/1215, 1729/1728

Mapping: [⟨1 2 -18 -3 13 29 41 -14], ⟨0 -1 49 14 -23 -61 -89 44]]

POTE generator: ~3/2 = 702.308

Optimal GPV sequence: Template:Val list

Badness: 0.021811

Degrees

Degrees temperament has a period of 1/20 octave and tempers out the hemimage (10976/10935) and the dimcomp (390625/388962). In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70.

Subgroup: 2.3.5.7

Comma list: 10976/10935, 390625/388962

Mapping: [⟨20 0 -17 -39], ⟨0 1 2 3]]

Wedgie: ⟨⟨ 20 40 60 17 39 27 ]]

POTE generator: ~3/2 = 703.015

Template:Val list

Badness: 0.106471

11-limit

Subgroup: 2.3.5.7.11

Comma list: 1331/1323, 1375/1372, 2200/2187

Mapping: [⟨20 0 -17 -39 -26], ⟨0 1 2 3 3]]

POTE generator: ~3/2 = 703.231

Optimal GPV sequence: Template:Val list

Badness: 0.046770

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 1001/1000, 1331/1323

Mapping: [⟨20 0 -17 -39 -26 74], ⟨0 1 2 3 3 0]]

POTE generator: ~3/2 = 703.080

Optimal GPV sequence: Template:Val list

Badness: 0.032718

Squarschmidt

A generator for the squarschimidt temperament is the fourth root of 5/2, (5/2)^1/4, tuned around 396.6 cents. The squarschimidt temperament can be described as 118&239 temperament, tempering out the hemimage comma and quasiorwellisma, 29360128/29296875 in the 7-limit. In the 11-limit, 118&239 tempers out 3025/3024, 5632/5625, and 12005/11979, and the generator represents ~44/35.

Subgroup: 2.3.5

Comma: [61 4 -29⟩

Mapping: [⟨1 -8 1], ⟨0 29 4]]

POTE generator: ~98304/78125 = 396.621

Template:Val list

Badness: 0.218314

7-limit

Subgroup: 2.3.5.7

Comma list: 10976/10935, 29360128/29296875

Mapping: [⟨1 -8 1 -20], ⟨0 29 4 69]]

Wedgie: ⟨⟨ 29 4 69 -61 28 149 ]]

POTE generator: ~1125/896 = 396.643

Template:Val list

Badness: 0.132821

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625, 10976/10935

Mapping: [⟨1 -8 1 -20 -21], ⟨0 29 4 69 74]]

POTE generator: ~44/35 = 396.644

Optimal GPV sequence: Template:Val list

Badness: 0.038186

Subfourth

Subgroup: 2.3.5.7

Comma list: 10976/10935, 65536/64827

Mapping: [⟨1 0 17 4], ⟨0 4 -37 -3]]

Wedgie: ⟨⟨ 4 -37 -3 -68 -16 97 ]]

POTE generator: ~21/16 = 475.991

Template:Val list

Badness: 0.140722

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891, 12005/11979

Mapping: [⟨1 0 17 4 11], ⟨0 4 -37 -3 -19]]

POTE generator: ~21/16 = 475.995

Optimal GPV sequence: Template:Val list

Badness: 0.045323

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 364/363, 540/539, 676/675

Mapping: [⟨1 0 17 4 11 16], ⟨0 4 -37 -3 -19 -31]]

POTE generator: ~21/16 = 475.996

Optimal GPV sequence: Template:Val list

Badness: 0.023800

Hemimage temperaments: Difference between revisions

Revision as of 08:44, 19 March 2022

Contents

Chromat

11-limit

13-limit

17-limit

Catachrome

17-limit

Chromic

17-limit

Bisupermajor

11-limit

Commatic

11-limit

13-limit

17-limit

Cotoneum

11-limit

13-limit

17-limit

19-limit

Degrees

11-limit

13-limit

Squarschmidt

7-limit

11-limit

Subfourth

11-limit

13-limit

Navigation menu

@@ Line 13: / Line 13: @@
 * ''[[Marfifths]]'', {10976/10935, 15625/15552} → [[Kleismic family #Marfifths|Kleismic family]]
 * ''[[Yarman I]]'', {10976/10935, 244140625/243045684} → [[Turkish maqam music temperaments #Yarman I|Turkish maqam music temperaments]]
-== Commatic ==
-The commatic temperament has a period of half octave and a generator of 20.4 cents. It is so named because the generator is a small interval ("commatic") which represents 81/80, 99/98, and 100/99 all tempered together.
-Subgroup: 2.3.5.7
-[[Comma list]]: 10976/10935, 50421/50000
-[[Mapping]]: [{{val| 2 3 4 5 }}, {{val| 0 5 19 18 }}]
-{{Multival|legend=1| 10 38 36 37 29 -23 }}
-[[POTE generator]]: ~81/80 = 20.377
-{{Val list|legend=1| 58, 118, 294, 412d, 530d }}
-[[Badness]]: 0.084317
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 441/440, 3388/3375, 8019/8000
-Mapping: [{{val| 2 3 4 5 6 }}, {{val| 0 5 19 18 27 }}]
-POTE generator: ~81/80 = 20.390
-Optimal GPV sequence: {{Val list| 58, 118, 294, 412d }}
-Badness: 0.030461
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 196/195, 352/351, 729/728, 1001/1000
-Mapping: [{{val| 2 3 4 5 6 7 }}, {{val| 0 5 19 18 27 12 }}]
-POTE generator: ~66/65 = 20.427
-Optimal GPV sequence: {{Val list| 58, 118, 176f }}
-Badness: 0.026336
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 170/169, 196/195, 289/288, 352/351, 561/560
-Mapping: [{{val| 2 3 4 5 6 7 8 }}, {{val| 0 5 19 18 27 12 5 }}]
-POTE generator: ~66/65 = 20.378
-Optimal GPV sequence: {{Val list| 58, 118, 294ffg, 412dffgg }}
-Badness: 0.022396
 == Chromat ==
@@ Line 80: / Line 24: @@
 {{Multival|legend=1| 15 39 48 27 34 2 }}
+Mapping generators: ~63/50, ~28/27
 [[POTE generator]]: ~28/27 = 60.528
@@ Line 124: / Line 70: @@
 Optimal GPV sequence: {{Val list| 99ef, 159, 258, 417dg }}
-Badness: 0.046006
+Badness: 0.031678
-==== Catachromat ====
+==== Catachrome ====
 Subgroup: 2.3.5.7.11.13
@@ Line 152: / Line 98: @@
 Badness: 0.030218
-== Degrees ==
+==== Chromic ====
-Degrees temperament has a period of 1/20 octave and tempers out the hemimage (10976/10935) and the dimcomp (390625/388962). In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70.
+Subgroup: 2.3.5.7.11.13
-Subgroup: 2.3.5.7
+Comma list: 196/195, 352/351, 729/728, 1875/1859
-[[Comma list]]: 10976/10935, 390625/388962
+Mapping: [{{val| 3 4 5 6 6 9 }}, {{val| 0 5 13 16 29 14 }}]
-[[Mapping]]: [{{val| 20 0 -17 -39 }}, {{val| 0 1 2 3 }}]
+POTE generator: ~27/26 = 60.456
-{{Multival|legend=1| 20 40 60 17 39 27 }}
+Optimal GPV sequence: {{Val list| 60e, 99ef, 159f, 258ff }}
-[[POTE generator]]: ~3/2 = 703.015
+Badness: 0.049857
-{{Val list|legend=1| 60, 80, 140, 640b, 780b, 920b }}
+===== 17-limit =====
+Subgroup: 2.3.5.7.11.13.17
-[[Badness]]: 0.106471
+Comma list: 170/169, 196/195, 352/351, 375/374, 595/594
-=== 11-limit ===
+Mapping: [{{val| 3 4 5 6 6 9 10 }}, {{val| 0 5 13 16 29 14 15 }}]
-Subgroup: 2.3.5.7.11
-Comma list: 1331/1323, 1375/1372, 2200/2187
+POTE generator: ~27/26 = 60.459
-Mapping: [{{val| 20 0 -17 -39 -26 }}, {{val| 0 1 2 3 3 }}]
+Optimal GPV sequence: {{Val list| 60e, 99ef, 159f, 258ff }}
-POTE generator: ~3/2 = 703.231
+Badness: 0.031043
-Optimal GPV sequence: {{Val list| 60e, 80, 140, 360, 500be, 860bde }}
+== Bisupermajor ==
+{{see also| Very high accuracy temperaments #Kwazy }}
-Badness: 0.046770
+Subgroup: 2.3.5.7
-=== 13-limit ===
+[[Comma list]]: 10976/10935, 65625/65536
-Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 352/351, 1001/1000, 1331/1323
+[[Mapping]]: [{{val| 2 1 6 1 }}, {{val| 0 8 -5 17 }}]
-Mapping: [{{val| 20 0 -17 -39 -26 74 }}, {{val| 0 1 2 3 3 0 }}]
+{{Multival|legend=1| 16 -10 34 -53 9 107 }}
-POTE generator: ~3/2 = 703.080
+[[POTE generator]]: ~192/175 = 162.806
-Optimal GPV sequence: {{Val list| 60e, 80, 140, 500be, 640be, 780be }}
+{{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398, 656d }}
-Badness: 0.032718
+[[Badness]]: 0.065492
-== Subfourth ==
+=== 11-limit ===
-Subgroup: 2.3.5.7
+Subgroup: 2.3.5.7.11
-[[Comma list]]: 10976/10935, 65536/64827
+Comma list: 385/384, 3388/3375, 9801/9800
-[[Mapping]]: [{{val| 1 0 17 4 }}, {{val| 0 4 -37 -3 }}]
+Mapping: [{{val| 2 1 6 1 8 }}, {{val| 0 8 -5 17 -4 }}]
-{{Multival|legend=1| 4 -37 -3 -68 -16 97 }}
+POTE generators: ~11/10 = 162.773
-[[POTE generator]]: ~21/16 = 475.991
+Optimal GPV sequence: {{Val list| 22, 74d, 96d, 118, 258e, 376de }}
-{{Val list|legend=1| 58, 121, 179, 300bd, 479bcd }}
+Badness: 0.032080
-[[Badness]]: 0.140722
+== Commatic ==
+The commatic temperament has a period of half octave and a generator of 20.4 cents. It is so named because the generator is a small interval ("commatic") which represents 81/80, 99/98, and 100/99 all tempered together.
-=== 11-limit ===
+Subgroup: 2.3.5.7
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 896/891, 12005/11979
+[[Comma list]]: 10976/10935, 50421/50000
-Mapping: [{{val| 1 0 17 4 11 }}, {{val| 0 4 -37 -3 -19 }}]
+[[Mapping]]: [{{val| 2 3 4 5 }}, {{val| 0 5 19 18 }}]
-POTE generator: ~21/16 = 475.995
+{{Multival|legend=1| 10 38 36 37 29 -23 }}
-Optimal GPV sequence: {{Val list| 58, 121, 179e, 300bde }}
+[[POTE generator]]: ~81/80 = 20.377
-Badness: 0.045323
+{{Val list|legend=1| 58, 118, 294, 412d, 530d }}
-=== 13-limit ===
+[[Badness]]: 0.084317
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 364/363, 540/539, 676/675
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Mapping: [{{val| 1 0 17 4 11 16 }}, {{val| 0 4 -37 -3 -19 -31 }}]
+Comma list: 441/440, 3388/3375, 8019/8000
-POTE generator: ~21/16 = 475.996
+Mapping: [{{val| 2 3 4 5 6 }}, {{val| 0 5 19 18 27 }}]
-Optimal GPV sequence: {{Val list| 58, 121, 179ef, 300bdef }}
+POTE generator: ~81/80 = 20.390
-Badness: 0.023800
+Optimal GPV sequence: {{Val list| 58, 118, 294, 412d }}
-== Bisupermajor ==
+Badness: 0.030461
-{{see also| Very high accuracy temperaments #Kwazy }}
-Subgroup: 2.3.5.7
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-[[Comma list]]: 10976/10935, 65625/65536
+Comma list: 196/195, 352/351, 729/728, 1001/1000
-[[Mapping]]: [{{val| 2 1 6 1 }}, {{val| 0 8 -5 17 }}]
+Mapping: [{{val| 2 3 4 5 6 7 }}, {{val| 0 5 19 18 27 12 }}]
-{{Multival|legend=1| 16 -10 34 -53 9 107 }}
+POTE generator: ~66/65 = 20.427
-[[POTE generator]]: ~192/175 = 162.806
+Optimal GPV sequence: {{Val list| 58, 118, 176f }}
-{{Val list|legend=1| 22, 74d, 96d, 118, 140, 258, 398, 656d }}
+Badness: 0.026336
-[[Badness]]: 0.065492
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
-=== 11-limit ===
+Comma list: 170/169, 196/195, 289/288, 352/351, 561/560
-Subgroup: 2.3.5.7.11
-Comma list: 385/384, 3388/3375, 9801/9800
+Mapping: [{{val| 2 3 4 5 6 7 8 }}, {{val| 0 5 19 18 27 12 5 }}]
-Mapping: [{{val| 2 1 6 1 8 }}, {{val| 0 8 -5 17 -4 }}]
+POTE generator: ~66/65 = 20.378
-POTE generators: ~11/10 = 162.773
+Optimal GPV sequence: {{Val list| 58, 118, 294ffg, 412dffgg }}
-Optimal GPV sequence: {{Val list| 22, 74d, 96d, 118, 258e, 376de }}
+Badness: 0.022396
-Badness: 0.032080
 == Cotoneum ==
@@ Line 336: / Line 280: @@
 Badness: 0.021811
+== Degrees ==
+Degrees temperament has a period of 1/20 octave and tempers out the hemimage (10976/10935) and the dimcomp (390625/388962). In this temperament, one period equals ~28/27, two equals ~15/14, three equals ~10/9, five equals ~25/21, six equals ~16/13, seven equals ~14/11, nine equals ~15/11, and ten equals ~99/70.
+Subgroup: 2.3.5.7
+[[Comma list]]: 10976/10935, 390625/388962
+[[Mapping]]: [{{val| 20 0 -17 -39 }}, {{val| 0 1 2 3 }}]
+{{Multival|legend=1| 20 40 60 17 39 27 }}
+[[POTE generator]]: ~3/2 = 703.015
+{{Val list|legend=1| 60, 80, 140, 640b, 780b, 920b }}
+[[Badness]]: 0.106471
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 1331/1323, 1375/1372, 2200/2187
+Mapping: [{{val| 20 0 -17 -39 -26 }}, {{val| 0 1 2 3 3 }}]
+POTE generator: ~3/2 = 703.231
+Optimal GPV sequence: {{Val list| 60e, 80, 140, 360, 500be, 860bde }}
+Badness: 0.046770
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 325/324, 352/351, 1001/1000, 1331/1323
+Mapping: [{{val| 20 0 -17 -39 -26 74 }}, {{val| 0 1 2 3 3 0 }}]
+POTE generator: ~3/2 = 703.080
+Optimal GPV sequence: {{Val list| 60e, 80, 140, 500be, 640be, 780be }}
+Badness: 0.032718
 == Squarschmidt ==
@@ Line 379: / Line 366: @@
 Badness: 0.038186
+== Subfourth ==
+Subgroup: 2.3.5.7
+[[Comma list]]: 10976/10935, 65536/64827
+[[Mapping]]: [{{val| 1 0 17 4 }}, {{val| 0 4 -37 -3 }}]
+{{Multival|legend=1| 4 -37 -3 -68 -16 97 }}
+[[POTE generator]]: ~21/16 = 475.991
+{{Val list|legend=1| 58, 121, 179, 300bd, 479bcd }}
+[[Badness]]: 0.140722
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 540/539, 896/891, 12005/11979
+Mapping: [{{val| 1 0 17 4 11 }}, {{val| 0 4 -37 -3 -19 }}]
+POTE generator: ~21/16 = 475.995
+Optimal GPV sequence: {{Val list| 58, 121, 179e, 300bde }}
+Badness: 0.045323
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 364/363, 540/539, 676/675
+Mapping: [{{val| 1 0 17 4 11 16 }}, {{val| 0 4 -37 -3 -19 -31 }}]
+POTE generator: ~21/16 = 475.996
+Optimal GPV sequence: {{Val list| 58, 121, 179ef, 300bdef }}
+Badness: 0.023800
 [[Category:Temperament collections]]
 [[Category:Hemimage]]
 [[Category:Rank 2]]

Hemimage temperaments: Difference between revisions

Revision as of 08:44, 19 March 2022

Chromat

11-limit

13-limit

17-limit

Catachrome

17-limit

Chromic

17-limit

Bisupermajor

11-limit

Commatic

11-limit

13-limit

17-limit

Cotoneum

11-limit

13-limit

17-limit

19-limit

Degrees

11-limit

13-limit

Squarschmidt

7-limit

11-limit

Subfourth

11-limit

13-limit

Navigation menu

Search