Subgroup temperaments: Difference between revisions

Revision as of 19:04, 3 June 2021

A subgroup temperament is a regular temperament defined on a just intonation subgroup that is not a full p-limit group.

Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on Chromatic pairs.

No-elevens subgroup

Sensi (aka Sensation)

For full 13-limit extensions, see Sensipent family or Sensi extensions.

Subgroup: 2.3.5.7.13

Comma list: 91/90, 126/125, 169/168

Gencom: [2 9/7; 91/90 126/125 169/168]

Gencom mapping: [⟨1 6 8 11 0 10], ⟨0 -7 -9 -13 0 -10]]

Sval mapping: [⟨1 6 8 11 10], ⟨0 -7 -9 -13 -10]]

POL2 generator: ~9/7 = 443.322

Template:Val list

RMS error: 1.321 cents

Tertiaseptal

For full 13- and 17-limit extensions, see Breedsmic temperaments #Tertiaseptal.

Subgroup: 2.3.5.7.13

Comma list: 625/624, 2401/2400, 4096/4095

Gencom: [2 117/112; 625/624 2401/2400 4096/4095]

Gencom mapping: [⟨1 3 2 3 0 1], ⟨0 -22 5 -3 0 42]]

Sval mapping: [⟨1 3 2 3 1], ⟨0 -22 5 -3 42]]

POL2 generator: ~117/112 = 77.173

Template:Val list

RMS error: 0.1383 cents

2.3.5.7.13.17

Subgroup: 2.3.5.7.13.17

Comma list: 625/624, 833/832, 1225/1224, 4096/4095

Gencom: [2 68/65; 625/624 833/832 1225/1224 4096/4095]

Gencom mapping: [⟨1 3 2 3 0 1 1], ⟨0 -22 5 -3 0 42 48]]

Sval mapping: [⟨1 3 2 3 1 1], ⟨0 -22 5 -3 42 48]]

POL2 generator: ~68/65 = 77.177

Template:Val list

RMS error: 0.1367 cents

No-sevens subgroup

Porkypine

Related temperament: Porcupine

Subgroup: 2.3.5.11

Comma list: 55/54, 100/99

Gencom: [2 10/9; 55/54, 100/99]

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

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

POL2 generator: ~11/10 = 164.078

Template:Val list

RMS error: 2.287 cents

Mohaha

Related temperament: mohajira, migration

Subgroup: 2.3.5.11

Comma list: 81/80, 121/120

Gencom: [2 11/9; 81/80 121/120]

Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 8 0 5]]

Sval mapping: [⟨1 1 0 2], ⟨0 2 8 5]]

POL2 generator: ~11/9 = 348.094

Template:Val list

RMS error: 1.392 cents

Music

Mohaha10ping2 by Billy Stiltner

Larry

Subgroup: 2.3.5.11

Comma list: 243/242, 4000/3993

Related temperaments: gravity, harry

Gencom: [2 40/27; 243/242 4000/3993]

Gencom mapping: [⟨1 5 12 0 12], ⟨0 -6 -17 0 -15]]

Sval mapping: [⟨1 5 12 12], ⟨0 -6 -17 -15]]

POL2 generator: ~40/27 = 683.166

Template:Val list

RMS error: 0.3025 cents

Tetracot

For full 11- and 13-limit extensions, see Tetracot family.

Subgroup: 2.3.5.11

Comma list: 100/99, 243/242

Gencom: [2 10/9; 100/99 243/242]

Gencom mapping: [⟨1 1 1 0 2], ⟨0 4 9 0 10]]

Sval mapping: [⟨1 1 1 2], ⟨0 4 9 10]]

POL2 generator: ~10/9 = 175.985

Template:Val list

RMS error: 1.182 cents

2.3.5.11.13

Subgroup: 2.3.5.11.13

Comma list: 100/99, 144/143, 243/242

Gencom: [2 10/9; 100/99 243/242]

Gencom mapping: [⟨1 1 1 0 2 4], ⟨0 4 9 0 10 -2]]

Sval mapping: [⟨1 1 1 2 4], ⟨0 4 9 10 -2]]

POL2 generator: ~10/9 = 176.196

Template:Val list

RMS error: 1.140 cents

Emka

For full 11- and 13-limit extensions, see Hemimean clan #Emka or Horwell temperaments #Emkay.

Subgroup: 2.3.5.11

Comma list: 4000/3993, 9453125/9437184

Gencom: [2 11/8; 4000/3993 9453125/9437184]

Gencom mapping: [⟨1 14 6 0 3], ⟨0 -27 -8 0 1]]

Sval mapping: [⟨1 14 6 3], ⟨0 -27 -8 1]]

POL2 generator: ~11/8 = 551.7778

Template:Val list

RMS error: 0.1188 cents

2.3.5.11.13

Subgroup: 2.3.5.11.13

Comma list: 625/624, 2200/2197, 4000/3993

Gencom: [2 11/8; 625/624, 2200/2197, 4000/3993]

Gencom mapping: [⟨1 14 6 0 3 6], ⟨0 -27 -8 0 1 -5]]

Sval mapping: [⟨1 14 6 3 6], ⟨0 -27 -8 1 -5]]

POL2 generator: ~11/8 = 551.7753

Template:Val list

RMS error: 0.1250 cents

No-fives subgroup

Semaphore

Subgroup: 2.3.7

Comma: 49/48

Gencom: [2 8/7; 49/48]

Gencom mapping: [⟨1 2 0 3], ⟨0 -2 0 -1]]

Sval mapping: [⟨1 2 3], ⟨0 -2 -1]]

POL2 generator: ~7/6 = 250.385

Template:Val list

RMS error: 2.523 cents

Archy

Archy (properly pronounced "arky", after the Greek theorist Archytas) can be thought of as "no-fives dominant" or "no-fives superpyth". The name comes from the fact that it tempers out 64/63, the Archytas comma.

Subgroup: 2.3.7

Comma: 64/63

Gencom: [2 3/2; 64/63]

Gencom mapping: [⟨1 1 0 4], ⟨0 1 0 -2]]

Sval mapping: [⟨1 2 2], ⟨0 -1 2]]

POL2 generator: ~3/2 = 709.321

Template:Val list

RMS error: 1.856 cents

Supra

Subgroup: 2.3.7.11

Comma list: 64/63, 99/98

Gencom: [2 3/2; 64/63 99/98]

Gencom mapping: [⟨1 1 0 4 7], ⟨0 1 0 -2 -6]]

Sval mapping: [⟨1 0 6 13], ⟨0 1 -2 -6]]

POL2 generator: ~3/2 = 707.192

Template:Val list

RMS error: 1.977 cents

Supraphon

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 99/98

Gencom: [2 3/2; 64/63 78/77 99/98]

Gencom mapping: [⟨1 1 0 4 7 9], ⟨0 1 0 -2 -6 -9]]

Sval mapping: [⟨1 0 6 13 18], ⟨0 1 -2 -6 -9]]

POL2 generator: ~3/2 = 706.137

Template:Val list

RMS error: 2.095 cents

Suhajira

Subgroup: 2.3.7.11

Comma list: 64/63, 243/242

Gencom: [2 11/9; 64/63 243/242]

Gencom mapping: [⟨1 1 0 4 2], ⟨0 2 0 -4 5]]

Sval mapping: [⟨1 1 4 2], ⟨0 2 -4 5]]

POL2 generator: ~11/9 = 353.958

Template:Val list

RMS error: 1.968 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 144/143

Gencom: [2 11/9; 64/63 78/77 144/143]

Gencom mapping: [⟨1 1 0 4 2 4], ⟨0 2 0 -4 5 -1]]

Sval mapping: [⟨1 1 4 2 4], ⟨0 2 -4 5 -1]]

POL2 generator: ~11/9 = 353.775

Template:Val list

RMS error: 1.953 cents

Slendric

Subgroup: 2.3.7

Comma: 1029/1024

Gencom: [2 8/7; 1029/1024]

Gencom mapping: [⟨1 1 0 3], ⟨0 3 0 -1]]

Sval mapping: [⟨1 1 3], ⟨0 3 -1]]

POL2 generator: ~8/7 = 233.688

Template:Val list

RMS error: 0.3202 cents

Baladic

Subgroup: 2.3.7.13

Comma list: 169/168, 1029/1024

Gencom: [91/64 8/7; 169/168 1029/1024]

Sval mapping: [⟨2 2 6 7], ⟨0 3 -1 1]]

POL2 generator: ~8/7 = 233.6044

Template:Val list

RMS error: 0.5452 cents

2.3.7.13.17

Subgroup: 2.3.7.13.17

Comma list: 169/168, 273/272, 289/288

Gencom: [17/12 8/7; 169/168 273/272 289/288]

Sval mapping: [⟨2 2 6 7 7], ⟨0 3 -1 1 3]]

POL2 generator: ~8/7 = 233.6155

Template:Val list

RMS error: 0.5073 cents

Lee

Subgroup: 2.3.7

Comma: 177147/175616

Gencom: [2 81/56; 177147/175616]

Gencom mapping: [⟨1 0 0 -3], ⟨0 3 0 11]]

Sval mapping: [⟨1 0 -3], ⟨0 3 11]]

POL2 generator: ~81/56 = 633.525

Template:Val list

RMS error: 0.3519 cents

Skwares

Related temperament: squares

Subgroup: 2.3.7

Comma: 19683/19208

Gencom: [2 9/7; 19683/19208]

Gencom mapping: [⟨1 3 6], ⟨0 -4 -9]]

Sval mapping: [⟨1 3 6], ⟨0 -4 -9]]

POL2 generator: ~9/7 = 425.365

Template:Val list

RMS error: 1.149 cents

2.3.7.11

Subgroup: 2.3.7.11

Comma list: 99/98, 243/242

Gencom: [2 9/7; 99/98 243/242]

Gencom mapping: [⟨1 3 0 6 7], ⟨0 -4 0 -9 -10]]

Sval mapping: [⟨1 3 6 7], ⟨0 -4 -9 -10]]

POL2 generator: ~9/7 = 425.244

Template:Val list

RMS error: 1.099 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 78/77, 99/98, 243/242

Gencom: [2 9/7; 78/77, 99/98, 243/242]

Gencom mapping: [⟨1 3 0 6 7 9], ⟨0 -4 0 -9 -10 -15]]

Sval mapping: [⟨1 3 6 7 9], ⟨0 -4 -9 -10 -15]]

POL2 generator: ~9/7 = 424.457

Template:Val list

RMS error: 1.769 cents

Skwairs

Subgroup: 2.3.7.11.13

Comma list: 99/98, 144/143, 243/242

Gencom: [2 9/7; 99/98, 144/143, 243/242]

Gencom mapping: [⟨1 3 0 6 7 3], ⟨0 -4 0 -9 -10 2]]

Sval mapping: [⟨1 3 6 7 3], ⟨0 -4 -9 -10 2]]

POL2 generator: ~9/7 = 424.702

Template:Val list

RMS error: 1.290 cents

Bleu

Subgroup: 2.3.7

Comma: 17496/16807

Gencom: [2 54/49; 17496/16807]

Gencom mapping: [⟨1 1 0 2], ⟨0 5 0 7]]

Sval mapping: [⟨1 1 2], ⟨0 5 7]]

POL2 generator: ~54/49 = 139.848

Template:Val list

RMS error: 1.917 cents

2.3.7.11

Subgroup: 2.3.7.11

Comma list: 99/98, 864/847

Gencom: [2 12/11; 99/98 864/847]

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

Sval mapping: [⟨1 1 2 3], ⟨0 5 7 4]]

POL2 generator: ~12/11 = 140.005

Template:Val list

RMS error: 1.829 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

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

Gencom: [2 12/11; 78/77 99/98 144/143]

Gencom mapping: [⟨1 1 0 2 3 3], ⟨0 5 0 7 4 6]]

Sval mapping: [⟨1 1 2 3 3], ⟨0 5 7 4 6]]

POL2 generator: ~12/11 = 139.990

Template:Val list

RMS error: 1.752 cents

Hemif

Related temperament: hemififths, namo

Subgroup: 2.3.7

Comma: 1605632/1594323

Gencom: [2 2187/1792; 1605632/1594323]

Gencom mapping: [⟨1 1 0 -1], ⟨0 2 0 13]]

Sval mapping: [⟨1 1 -1], ⟨0 2 13]]

POL2 generator: ~2187/1792 = 351.485

Template:Val list

RMS error: 0.2344 cents

2.3.7.11

Subgroup: 2.3.7.11

Comma list: 243/242, 896/891

Gencom: [2 11/9; 243/242 896/891]

Gencom mapping: [⟨1 1 0 -1 2], ⟨0 2 0 13 5]]

Sval mapping: [⟨1 1 -1 2], ⟨0 2 13 5]]

POL2 generator: ~11/9 = 351.535

Template:Val list

RMS error: 0.6108 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 144/143, 243/242, 364/363

Gencom: [2 11/9; 144/143 243/242 364/363]

Gencom mapping: [⟨1 1 0 -1 2 4], ⟨0 2 0 13 5 -1]]

Sval mapping: [⟨1 1 -1 2 4], ⟨0 2 13 5 -1]]

POL2 generator: ~11/9 = 351.691

Template:Val list

RMS error: 0.7167 cents

Ennea

Subgroup: 2.3.7.11

Comma list: 41503/41472, 43923/43904

Gencom: [2 99/98; 41503/41472, 43923/43904]

Gencom mapping: [⟨1 14/9 0 25/9 31/9], ⟨0 2 0 2 1]]

Sval mapping: [⟨9 0 11 24], ⟨0 2 2 1]]

POL2 generator: ~99/98 = 17.6258

Template:Val list

RMS error: 0.0383 cents

Leapfrog

See also: Gentle region

Subgroup: 2.3.7

Comma list: 14680064/14348907

Gencom: [2 3/2; 14680064/14348907]

Gencom mapping: [⟨1 1 0 -6], ⟨0 1 0 15]]

Sval mapping: [⟨1 0 -21], ⟨0 1 15]]

POL2 generator: ~3/2 = 704.721 cents

Template:Val list

RMS error: 0.6202 cents

2.3.7.11

Subgroup: 2.3.7.11

Comma list: 896/891, 1331/1323

Gencom: [2 3/2; 896/891 1331/1323]

Gencom mapping: [⟨1 1 0 -6 -3], ⟨0 1 0 15 11]]

Sval mapping: [⟨1 0 -21 -14], ⟨0 1 15 11]]

POL2 generator: ~3/2 = 704.753 cents

Template:Val list

RMS error: 0.6047 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 169/168, 352/351, 364/363

Gencom: [2 3/2; 169/169 352/351 364/363]

Gencom mapping: [⟨1 1 0 -6 -3 -1], ⟨0 1 0 15 11 8]]

Sval mapping: [⟨1 0 -21 -14 -9], ⟨0 1 15 11 8]]

POL2 generator: ~3/2 = 704.745 cents

Template:Val list

RMS error: 0.7541 cents

Music

Suite for Harpsichord in A Locrian, tuning: Eb-G# in 46edo by IlL (in progress):
- I. Prelude
- II. Allemande
- III. Courante
- IV. Sarabande (score, 17edo version)
- V. Menuet and Trio
- VI. Gavotte I and II
- VII. Gigue

Parapyth (Rank 3)

Subgroup: 2.3.7.11

Comma list: 896/891

Gencom: [2 3/2 28/27; 896/891]

Gencom mapping: [⟨1 1 0 1 4], ⟨0 1 0 3 -1], ⟨0 0 0 1 1]]

Sval mapping: [⟨1 0 0 7], ⟨0 1 0 -4], ⟨0 0 1 1]]

POL2 tuning: ~3 = 1903.834, ~7 = 3369.872

Template:Val list

RMS error: 0.4149 cents

2.3.7.11.13

Subgroup: 2.3.7.11.13

Comma list: 352/351, 364/363

The gencom below gives Margo Schulter's favored basis

Gencom: [2 3/2 28/27; 352/351 364/363]

Gencom mapping: [⟨1 1 0 1 4 6], ⟨0 1 0 3 -1 -4], ⟨0 0 0 1 1 1]]

Sval mapping: [⟨1 0 0 7 12], ⟨0 1 0 -4 -7], ⟨0 0 1 1 1]]

POL2 tuning: ~3 = 1903.856, ~7 = 3369.907

Template:Val list

RMS error: 0.3789 cents

Neutral

Neutral can be thought of as the 2.3.11 version of either mohajira or maqamic, as well as suhajira and ringo. Among other things, it is the temperament optimizing the neutral tetrad.

Subgroup: 2.3.11

Comma: 243/242

Gencom: [2 11/9; 243/242]

Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 0 0 5]]

Sval mapping: [⟨1 1 2], ⟨0 2 5]]

POL2 generator: ~11/9 = 350.525

Template:Val list

RMS error: 0.3021 cents

Seven note albitonic scale

Ten note chromatic scale

Seventeen note mega chromatic scale

Namo

Subgroup: 2.3.11.13

Comma list: 144/143, 243/242

Gencom: [2 11/9; 144/143 243/242]

Gencom mapping: [⟨1 1 0 0 2 4], ⟨0 2 0 0 5 -1]]

Sval mapping: [⟨1 1 2 4], ⟨0 2 5 -1]]

POL2 generator: ~11/9 = 351.488

Template:Val list

RMS error: 0.7038 cents

No-threes subgroup

Didacus

Related temperaments: roulette, hemithirds

Subgroup: 2.5.7

Comma: 3136/3125

Gencom: [2 28/25; 3136/3125]

Gencom map: [⟨1 0 2 2], ⟨0 0 2 5]]

Sval mapping: [⟨1 2 2], ⟨0 2 5]]

POL2 generator: ~28/25 = 93.772

Template:Val list

RMS error: 0.2138 cents

Llywelyn

Subgroup: 2.5.7

Comma: 4194304/4117715

Gencom: [2 8/7; 4194304/4117715]

Gencom mapping: [⟨1 0 1 3], ⟨0 0 7 -1]]

Sval mapping: [⟨1 1 3], ⟨0 7 -1]]

POL2 generator: ~8/7 = 226.910

Template:Val list

RMS error: 0.5391 cents

Rainy

Three generators make an 8/7; five generators make a 5/4. This is the no-threes version of tertiaseptal.

Subgroup: 2.5.7

Comma: 2100875/2097152

Gencom: [2 256/245; 2100875/2097152]

Gencom mapping: [⟨1 0 2 3], ⟨0 0 5 -3]]

Sval mapping: [⟨1 2 3], ⟨0 5 -3]]

POL2 generator: ~256/245 = 77.205

Template:Val list

RMS error: 0.058596 cents

2.9.7.11 subgroup

Machine

Subgroup: 2.9.7.11

Commas: 64/63, 99/98

Gencom: [2 8/7; 64/63 99/98]

Gencom mapping: [⟨1 3/2 0 3 4], ⟨0 1/2 0 -1 -3]]

Sval mapping: [⟨1 0 6 13], ⟨0 1 -1 -3]]

POL2 generator: ~8/7 = 214.384

Template:Val list

RMS error: 1.977 cents

Apparatus

Subgroup: 2.9.7.11

Comma list: 41503/41472, 322102/321489

Gencom: [2 77/72; 41503/41472 322102/321489]

Gencom mapping: [⟨1 5/2 0 3 5], ⟨0 -19/2 0 -2 -16]]

Sval mapping: [⟨1 5 3 5], ⟨0 -19 -2 -16]]

POL2 generator: ~77/72 = 115.570

Template:Val list

RMS error: 0.0673 cents

Mechanism

Subgroup: 2.9.7.11

Comma list: 896/891, 26411/26244

Gencom: [2 9/7; 896/891 26411/26244]

Gencom mapping: [⟨1 5/2 0 5 2], ⟨0 -5/2 0 -6 4]]

Sval mapping: [⟨1 5 5 2], ⟨0 -5 -6 4]]

POL2 generator: ~9/7 = 438.465

Template:Val list

RMS error: 0.4262 cents

2.9.15.7 subgroup

Stacks (aka 2magic)

Subgroup: 2.9.15.7

Comma list: 225/224, 245/243

Gencom: [2 9/7; 225/224 245/243]

Gencom mapping: [⟨1 5/2 5/2 5], ⟨0 -5/2 -1/2 -6]]

Sval mapping: [⟨1 0 2 -1], ⟨0 5 3 6]]

POL2 generator: ~9/7 = 439.296

Template:Val list

RMS error: 1.074 cents

2.9.15.7.11

Subgroup: 2.9.15.7.11

Comma list: 100/99, 225/224, 245/243

Gencom: [2 9/7; 100/99 225/224 245/243]

Gencom mapping: [⟨1 5/2 5/2 5 2], ⟨0 -5/2 -1/2 -6 4]]

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

POL2 generator: ~9/7 = 438.607

Vals: Template:Val list

RMS error: 1.226 cents

2.9.15.7.11.13

Subgroup: 2.9.15.7.11.13

Comma list: 100/99, 105/104, 144/143, 196/195

Gencom: [2 9/7; 100/99 105/104 144/143 196/195]

Gencom mapping: [⟨1 5/2 5/2 5 2 7], ⟨0 -5/2 -1/2 -6 4 -9]]

Sval map: [⟨1 0 2 -1 6 -2], ⟨0 5 3 6 -4 9]]

POL2 generator: ~9/7 = 438.977

Vals: Template:Val list

RMS error: 1.540 cents

2.9.21 subgroup

A-team

Subgroup: 2.9.21

Comma: 1029/1024

Gencom: [2 21/16; 1029/1024]

Gencom mapping: [⟨1 1 0 3], ⟨0 3/2 0 -1/2]]

Sval mapping: [⟨1 2 4], ⟨0 3 1]]

POL2 generator: ~21/16 = 467.375

Template:Val list

RMS error: 0.3202 cents

Miscellaneous subgroup temperaments

Historical

Subgroup: 2.3.7/5.11/5.13/5

Comma list: 364/363, 441/440, 1001/1000

Sval mapping: [⟨1 2 0 1 2], ⟨0 -6 7 2 -9]]

POL2 generator: ~21/20 = 83.016

Template:Val list

RMS error: 0.2562 cents

Hypnosis

Related temperament: hypnos, tricot

Subgroup: 2.3.7.11/5.13

Comma list: 169/168, 540/539, 729/728

Sval mapping: [⟨1 0 -3 8 0], ⟨0 3 11 -13 7]]

POL2 generator: ~13/9 = 633.518

Template:Val list

RMS error: 0.5379 cents

@@ Line 3: / Line 3: @@
 Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on [[Chromatic pairs]].
-= No-elevens subgroup =
+== No-elevens subgroup  ==
-== Sensi (aka Sensation) ==
+=== Sensi (aka Sensation)  ===
 <small>''For full 13-limit extensions, see [[Sensipent family]] or [[Sensi extensions]].''</small>
@@ Line 24: / Line 24: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.321 cents
-==[[Tertiaseptal]]==
+=== [[Tertiaseptal]] ===
 <small>''For full 13- and 17-limit extensions, see [[Breedsmic temperaments #Tertiaseptal]].''</small>
@@ Line 43: / Line 43: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.1383 cents
-=== 2.3.5.7.13.17 ===
+==== 2.3.5.7.13.17  ====
 Subgroup: 2.3.5.7.13.17
@@ Line 60: / Line 60: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.1367 cents
-= No-sevens subgroup =
+== No-sevens subgroup  ==
-== Porkypine ==
+=== Porkypine  ===
 Related temperament: [[Porcupine]]
@@ Line 81: / Line 81: @@
 [[Tp tuning #T2 tuning|RMS error]]: 2.287 cents
-== Mohaha ==
+=== Mohaha  ===
 Related temperament: [[mohajira]], [[Meantone family #Migration|migration]]
@@ Line 100: / Line 100: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.392 cents
-=== Music ===
+==== Music  ====
 [http://micro.soonlabel.com/gene_ward_smith/Others/Stiltner/mohaha10ping2.mp3 Mohaha10ping2] by [[Billy Stiltner]]
-== Larry ==
+=== Larry  ===
 Subgroup: 2.3.5.11
@@ Line 122: / Line 122: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3025 cents
-== Tetracot ==
+=== Tetracot  ===
 <small>''For full 11- and 13-limit extensions, see [[Tetracot family]].''</small>
@@ Line 141: / Line 141: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.182 cents
-=== 2.3.5.11.13 ===
+==== 2.3.5.11.13  ====
 Subgroup: 2.3.5.11.13
@@ Line 158: / Line 158: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.140 cents
-== Emka ==
+=== Emka  ===
 <small>''For full 11- and 13-limit extensions, see [[Hemimean clan #Emka]] or [[Horwell temperaments #Emkay]].''</small>
@@ Line 177: / Line 177: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.1188 cents
-=== 2.3.5.11.13 ===
+==== 2.3.5.11.13  ====
 Subgroup: 2.3.5.11.13
@@ Line 194: / Line 194: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.1250 cents
-= No-fives subgroup =
+== No-fives subgroup  ==
-==[[Semaphore and Godzilla|Semaphore]]==
+=== [[Semaphore and Godzilla|Semaphore]] ===
 Subgroup: 2.3.7
@@ Line 213: / Line 213: @@
 [[Tp tuning# T2 tuning|RMS error]]: 2.523 cents
-== Archy ==
+=== Archy  ===
 Archy (properly pronounced "arky", after the Greek theorist Archytas) can be thought of as "no-fives [[dominant]]" or "no-fives [[superpyth]]". The name comes from the fact that it tempers out 64/63, the Archytas comma.
@@ Line 232: / Line 232: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.856 cents
-=== Supra ===
+==== Supra  ====
 Subgroup: 2.3.7.11
@@ Line 249: / Line 249: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
-==== Supraphon ====
+===== Supraphon  =====
 Subgroup: 2.3.7.11.13
@@ Line 266: / Line 266: @@
 [[Tp tuning #T2 tuning|RMS error]]: 2.095 cents
-=== Suhajira ===
+==== Suhajira  ====
 Subgroup: 2.3.7.11
@@ Line 283: / Line 283: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.968 cents
-==== 2.3.7.11.13 ====
+===== 2.3.7.11.13  =====
 Subgroup: 2.3.7.11.13
@@ Line 300: / Line 300: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.953 cents
-==[[Slendric]]==
+=== [[Slendric]] ===
 Subgroup: 2.3.7
@@ Line 317: / Line 317: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
-==[[Gamelismic clan #Baladic|Baladic]]==
+=== [[Gamelismic clan #Baladic|Baladic]] ===
 Subgroup: 2.3.7.13
@@ Line 332: / Line 332: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.5452 cents
-=== 2.3.7.13.17 ===
+==== 2.3.7.13.17  ====
 Subgroup: 2.3.7.13.17
@@ Line 347: / Line 347: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.5073 cents
-== Lee ==
+=== Lee  ===
 Subgroup: 2.3.7
@@ Line 364: / Line 364: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3519 cents
-== Skwares ==
+=== Skwares  ===
 Related temperament: [[Meantone family #Squares|squares]]
@@ Line 383: / Line 383: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.149 cents
-=== 2.3.7.11 ===
+==== 2.3.7.11  ====
 Subgroup: 2.3.7.11
@@ Line 400: / Line 400: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.099 cents
-=== 2.3.7.11.13 ===
+==== 2.3.7.11.13  ====
 Subgroup: 2.3.7.11.13
@@ Line 417: / Line 417: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.769 cents
-=== Skwairs ===
+==== Skwairs  ====
 Subgroup: 2.3.7.11.13
@@ Line 434: / Line 434: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.290 cents
-== Bleu ==
+=== Bleu  ===
 Subgroup: 2.3.7
@@ Line 451: / Line 451: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.917 cents
-=== 2.3.7.11 ===
+==== 2.3.7.11  ====
 Subgroup: 2.3.7.11
@@ Line 468: / Line 468: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.829 cents
-=== 2.3.7.11.13 ===
+==== 2.3.7.11.13  ====
 Subgroup: 2.3.7.11.13
@@ Line 485: / Line 485: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.752 cents
-== Hemif ==
+=== Hemif  ===
 Related temperament: [[Breedsmic temperaments #Hemififths|hemififths]], namo
@@ Line 504: / Line 504: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.2344 cents
-=== 2.3.7.11 ===
+==== 2.3.7.11  ====
 Subgroup: 2.3.7.11
@@ Line 521: / Line 521: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.6108 cents
-=== 2.3.7.11.13 ===
+==== 2.3.7.11.13  ====
 Subgroup: 2.3.7.11.13
@@ Line 538: / Line 538: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.7167 cents
-== Ennea ==
+=== Ennea  ===
 Subgroup: 2.3.7.11
@@ Line 555: / Line 555: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.0383 cents
-== Leapfrog ==
+=== Leapfrog  ===
 {{see also|Gentle region}}
@@ Line 574: / Line 574: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.6202 cents
-=== 2.3.7.11 ===
+==== 2.3.7.11  ====
 Subgroup: 2.3.7.11
@@ Line 591: / Line 591: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.6047 cents
-=== 2.3.7.11.13 ===
+==== 2.3.7.11.13  ====
 Subgroup: 2.3.7.11.13
@@ Line 608: / Line 608: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.7541 cents
-=== Music ===
+==== Music  ====
 *Suite for Harpsichord in A Locrian, tuning: Eb-G# in [[46edo]] by [[User:IlL|IlL]] (in progress):
 **I. Prelude
@@ Line 618: / Line 618: @@
 **[[:File:Locrian Suite Gigue.mp3|VII. Gigue]]
-== Parapyth (Rank 3) ==
+=== Parapyth (Rank 3)  ===
 Subgroup: 2.3.7.11
@@ Line 635: / Line 635: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.4149 cents
-=== 2.3.7.11.13 ===
+==== 2.3.7.11.13  ====
 Subgroup: 2.3.7.11.13
@@ Line 654: / Line 654: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3789 cents
-== Neutral ==
+=== Neutral  ===
 Neutral can be thought of as the 2.3.11 version of either [[mohajira]] or [[maqamic]], as well as suhajira and ringo. Among other things, it is the temperament optimizing the [[neutral tetrad]].
@@ Line 679: / Line 679: @@
 [[neutraltet17|Seventeen note mega chromatic scale]]
-=== Namo ===
+==== Namo  ====
 Subgroup: 2.3.11.13
@@ Line 696: / Line 696: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.7038 cents
-= No-threes subgroup =
+== No-threes subgroup  ==
-== Didacus ==
+=== Didacus  ===
 Related temperaments: [[Chromatic pairs #Roulette|roulette]], [[Gamelismic clan #Hemithirds|hemithirds]]
@@ Line 717: / Line 717: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.2138 cents
-== Llywelyn ==
+=== Llywelyn  ===
 Subgroup: 2.5.7
@@ Line 734: / Line 734: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.5391 cents
-== Rainy ==
+=== Rainy  ===
 Three generators make an [[8/7]]; five generators make a [[5/4]]. This is the no-threes version of [[tertiaseptal]].
@@ Line 753: / Line 753: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.058596 cents
-= 2.9.7.11 subgroup =
+== 2.9.7.11 subgroup  ==
-== Machine ==
+=== Machine  ===
 Subgroup: 2.9.7.11
@@ Line 772: / Line 772: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.977 cents
-== Apparatus ==
+=== Apparatus  ===
 Subgroup: 2.9.7.11
@@ Line 789: / Line 789: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.0673 cents
-== Mechanism ==
+=== Mechanism  ===
 Subgroup: 2.9.7.11
@@ Line 806: / Line 806: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.4262 cents
-= 2.9.15.7 subgroup =
+== 2.9.15.7 subgroup  ==
-== Stacks (aka 2magic) ==
+=== Stacks (aka 2magic)  ===
 Subgroup: 2.9.15.7
@@ Line 825: / Line 825: @@
 [[Tp tuning #T2 tuning|RMS error]]: 1.074 cents
-=== 2.9.15.7.11 ===
+==== 2.9.15.7.11  ====
 Subgroup: 2.9.15.7.11
@@ Line 842: / Line 842: @@
 RMS error: 1.226 cents
-=== 2.9.15.7.11.13 ===
+==== 2.9.15.7.11.13  ====
 Subgroup: 2.9.15.7.11.13
@@ Line 859: / Line 859: @@
 RMS error: 1.540 cents
-= 2.9.21 subgroup =
+== 2.9.21 subgroup  ==
-== A-team ==
+=== A-team  ===
 Subgroup: 2.9.21
@@ Line 878: / Line 878: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.3202 cents
-= Miscellaneous subgroup temperaments =
+== Miscellaneous subgroup temperaments  ==
-== Historical ==
+=== Historical  ===
 Subgroup: 2.3.7/5.11/5.13/5
@@ Line 893: / Line 893: @@
 [[Tp tuning #T2 tuning|RMS error]]: 0.2562 cents
-== Hypnosis ==
+=== Hypnosis  ===
 Related temperament: [[Swetismic temperaments #Hypnos|hypnos]], [[Hemifamity temperaments #Tricot|tricot]]

Subgroup temperaments: Difference between revisions

Revision as of 19:04, 3 June 2021

No-elevens subgroup

Sensi (aka Sensation)

Tertiaseptal

2.3.5.7.13.17

No-sevens subgroup

Porkypine

Mohaha

Music

Larry

Tetracot

2.3.5.11.13

Emka

2.3.5.11.13

No-fives subgroup

Semaphore

Archy

Supra

Supraphon

Suhajira

2.3.7.11.13

Slendric

Baladic

2.3.7.13.17

Lee

Skwares

2.3.7.11

2.3.7.11.13

Skwairs

Bleu

2.3.7.11

2.3.7.11.13

Hemif

2.3.7.11

2.3.7.11.13

Ennea

Leapfrog

2.3.7.11

2.3.7.11.13

Music

Parapyth (Rank 3)

2.3.7.11.13

Neutral

Namo

No-threes subgroup

Didacus

Llywelyn

Rainy

2.9.7.11 subgroup

Machine

Apparatus

Mechanism

2.9.15.7 subgroup

Stacks (aka 2magic)

2.9.15.7.11

2.9.15.7.11.13

2.9.21 subgroup

A-team

Miscellaneous subgroup temperaments

Historical

Hypnosis

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