Porcupine family

The porcupine family of temperaments tempers out the porcupine comma, 250/243, also called the maximal diesis.

Porcupine

Main article: Porcupine

The generator of porcupine is a minor whole tone, the 10/9 interval, and three of these add up to a perfect fourth (4/3), with two more giving the minor sixth (8/5). In fact, (10/9)³ = (4/3)⋅(250/243), and (10/9)⁵ = (8/5)⋅(250/243)². 3\22 is a very recommendable generator, and mos scales of 7, 8 and 15 notes make for some nice scale possibilities.

Subgroup: 2.3.5

Comma list: 250/243

Mapping: [⟨1 2 3], ⟨0 -3 -5]]

mapping generators: ~2, ~10/9

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 164.166

error map: ⟨0.000 +5.547 -7.143]

• POTE: ~2 = 1200.000, ~10/9 = 163.950

error map: ⟨0.000 +6.194 -6.065]

Tuning ranges:

• 5-odd-limit diamond monotone: ~10/9 = [150.000, 171.429] (1\8 to 1\7)
• 5-odd-limit diamond tradeoff: ~10/9 = [157.821, 166.015]

Optimal ET sequence: 7, 15, 22, 95c

Badness (Smith): 0.030778

Overview to extensions

7-limit extensions

The second comma of the normal comma list defines which 7-limit family member we are looking at. That means

• 64/63, the archytas comma, for septimal porcupine,
• 36/35, the septimal quarter tone, for hystrix,
• 50/49, the jubilisma, for hedgehog, and
• 49/48, the slendro diesis, for nautilus.

Temperaments discussed elsewhere include jamesbond.

Subgroup extensions

Notice 250/243 = (55/54)⋅(100/99), the temperament thus extends naturally to the 2.3.5.11 subgroup, sometimes known as porkypine, given right below.

2.3.5.11 subgroup (porkypine)

Subgroup: 2.3.5.11

Comma list: 55/54, 100/99

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

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

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 163.887
• POTE: ~2 = 1200.000, ~11/10 = 164.078

Optimal ET sequence: 7, 15, 22, 73ce, 95ce

Badness (Smith): 0.0097

Undecimation

Subgroup: 2.3.5.11.13

Comma list: 55/54, 100/99, 512/507

Sval mapping: [⟨1 5 8 8 2], ⟨0 -6 -10 -8 3]]

sval mapping generators: ~2, ~65/44

Optimal tunings:

• CTE: ~2 = 1200.000, ~88/65 = 518.086
• POTE: ~2 = 1200.000, ~88/65 = 518.209

Optimal ET sequence: 7, 23bc, 30, 37, 44

Badness (Smith): 0.0305

Septimal porcupine

Main article: Porcupine

Septimal porcupine uses six of its minor tone generator steps to get to 7/4. For this to work you need a small minor tone such as 22edo provides, and once again 3\22 is a good tuning choice, though we might pick in preference 8\59, 11\81, or 19\140 for our generator.

Subgroup: 2.3.5.7

Comma list: 64/63, 250/243

Mapping: [⟨1 2 3 2], ⟨0 -3 -5 6]]

Wedgie: ⟨⟨ 3 5 -6 1 -18 -28 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 163.203

error map: ⟨0.000 +8.435 -2.330 +10.394]

• POTE: ~2 = 1200.000, ~10/9 = 162.880

error map: ⟨0.000 +9.405 -0.714 +8.455]

Minimax tuning:

• 7-odd-limit: ~10/9 = [3/5 0 -1/5⟩

eigenmonzo (unchanged-interval) basis: 2.5

• 9-odd-limit: ~10/9 = [1/6 -1/6 0 1/12⟩

eigenmonzo (unchanged-interval) basis: 2.9/7

Tuning ranges:

• 7- and 9-odd-limit diamond monotone: ~10/9 = [160.000, 163.636] (2\15 to 3\22)
• 7-odd-limit diamond tradeoff: ~10/9 = [157.821, 166.015]
• 9-odd-limit diamond tradeoff: ~10/9 = [157.821, 182.404]

Optimal ET sequence: 7, 15, 22, 37, 59, 81bd

Badness (Smith): 0.041057

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 100/99

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 163.105
• POTE: ~2 = 1200.000, ~11/10 = 162.747

Minimax tuning:

• 11-odd-limit: ~11/10 = [1/6 -1/6 0 1/12⟩

eigenmonzo (unchanged-interval) basis: 2.9/7

Tuning ranges:

• 11-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
• 11-odd-limit diamond tradeoff: ~11/10 = [150.637, 182.404]

Optimal ET sequence: 7, 15, 22, 37, 59

Badness (Smith): 0.021562

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 55/54, 64/63, 66/65

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 163.442
• POTE: ~2 = 1200.000, ~11/10 = 162.708

Minimax tuning:

• 13- and 15-odd-limit: ~10/9 = [1 0 0 0 -1/4⟩

eigenmonzo (unchanged-interval) basis: 2.11

Tuning ranges:

• 13-odd-limit diamond monotone: ~11/10 = [160.000, 163.636] (2\15 to 3\22)
• 15-odd-limit diamond monotone: ~11/10 = 163.636 (3\22)
• 13- and 15-odd-limit diamond tradeoff: ~11/10 = [138.573, 182.404]

Optimal ET sequence: 7, 15, 22f, 37f

Badness (Smith): 0.021276

Porcupinefish

See also: The Biosphere

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 91/90, 100/99

Mapping: [⟨1 2 3 2 4 6], ⟨0 -3 -5 6 -4 -17]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 162.636
• POTE: ~2 = 1200.000, ~11/10 = 162.277

Minimax tuning:

• 13- and 15-odd-limit: ~10/9 = [2/13 0 0 0 1/13 -1/13⟩

eigenmonzo (unchanged-interval) basis: 2.13/11

Tuning ranges:

• 13-odd-limit diamond monotone: ~10/9 = [160.000, 162.162] (2\15 to 5\37)
• 15-odd-limit diamond monotone: ~10/9 = 162.162 (5\37)
• 13- and 15-odd-limit diamond tradeoff: ~10/9 = [150.637, 182.404]

Optimal ET sequence: 15, 22, 37

Badness (Smith): 0.025314

Pourcup

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 100/99, 196/195

Mapping: [⟨1 2 3 2 4 1], ⟨0 -3 -5 6 -4 20]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 163.378
• POTE: ~2 = 1200.000, ~11/10 = 162.482

Minimax tuning:

• 13- and 15-odd-limit: ~11/10 = [1/14 0 0 -1/14 0 1/14⟩

eigenmonzo (unchanged-interval) basis: 2.13/7

Optimal ET sequence: 15f, 22f, 37, 59f

Badness (Smith): 0.035130

Porkpie

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 65/63, 100/99

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 163.678
• POTE: ~2 = 1200.000, ~11/10 = 163.688

Minimax tuning:

• 13- and 15-odd-limit: ~11/10 = [1/6 -1/6 0 1/12⟩

eigenmonzo (unchanged-interval) basis: 2.9/7

Optimal ET sequence: 7, 15f, 22

Badness (Smith): 0.026043

Opossum

Opossum can be described as 7d & 8d. Tempering out 28/27, the perfect fifth of three generator steps is conflated with not 32/21 as in porcupine but 14/9. Three such fifths or nine generator steps octave reduced give a flat 7/4. 2\15 is a good generator.

Subgroup: 2.3.5.7

Comma list: 28/27, 126/125

Mapping: [⟨1 2 3 4], ⟨0 -3 -5 -9]]

Wedgie: ⟨⟨ 3 5 9 1 6 7 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 161.306

error map: ⟨0.000 +14.126 +7.155 -20.583]

• POTE: ~2 = 1200.000, ~10/9 = 159.691

error map: ⟨0.000 +18.971 +15.229 -6.048]

Minimax tuning:

• 7- and 9-odd-limit eigenmonzo (unchanged-interval) basis: 2.7

Optimal ET sequence: 7d, 8d, 15

Badness (Smith): 0.040650

11-limit

Subgroup: 2.3.5.7.11

Comma list: 28/27, 55/54, 77/75

Mapping: [⟨1 2 3 4 4], ⟨0 -3 -5 -9 -4]]

Wedgie: ⟨⟨ 3 5 9 4 1 6 -4 7 -8 -20 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 161.365
• POTE: ~2 = 1200.000, ~11/10 = 159.807

Minimax tuning:

• 11-odd-limit eigenmonzo (unchanged-interval) basis: 2.7

Optimal ET sequence: 7d, 8d, 15

Badness (Smith): 0.022325

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 28/27, 40/39, 55/54, 66/65

Mapping: [⟨1 2 3 4 4 4], ⟨0 -3 -5 -9 -4 -2]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 161.631
• POTE: ~2 = 1200.000, ~11/10 = 158.805

Minimax tuning:

• 13- and 15-odd-limit eigenmonzo (unchanged-interval) basis: 2.7

Optimal ET sequence: 7d, 8d, 15, 38bceff

Badness (Smith): 0.019389

Porky

Porky can be described as 7d & 22, suggesting a less sharp perfect fifth. 7\51 is a good generator.

Subgroup: 2.3.5.7

Comma list: 225/224, 250/243

Mapping: [⟨1 2 3 5], ⟨0 -3 -5 -16]]

Wedgie: ⟨⟨ 3 5 16 1 17 23 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 164.391

error map: ⟨0.000 +4.871 -8.270 +0.913]

• POTE: ~2 = 1200.000, ~10/9 = 164.412

error map: ⟨0.000 +4.809 -8.375 +0.580]

Minimax tuning:

• 7- and 9-odd-limit: ~10/9 = [2/11 0 1/11 -1/11⟩

eigenmonzo (unchanged-interval) basis: 2.7/5

Optimal ET sequence: 7d, 15d, 22, 29, 51, 73c

Badness (Smith): 0.054389

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 225/224

Mapping: [⟨1 2 3 5 4], ⟨0 -3 -5 -16 -4]]

Wedgie: ⟨⟨ 3 5 16 4 1 17 -4 23 -8 -44 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 164.321
• POTE: ~2 = 1200.000, ~11/10 = 164.552

Minimax tuning:

• 11-odd-limit: ~11/10 = [2/11 0 1/11 -1/11⟩

eigenmonzo (unchanged-interval) basis: 2.7/5

Optimal ET sequence: 7d, 15d, 22, 51

Badness (Smith): 0.027268

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 91/90, 100/99

Mapping: [⟨1 2 3 5 4 3], ⟨0 -3 -5 -16 -4 5]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 164.478
• POTE: ~2 = 1200.000, ~11/10 = 164.953

Optimal ET sequence: 7d, 22, 29, 51f, 80cdeff

Badness (Smith): 0.026543

Music

• Improvisation in 29edo (2024) by Budjarn Lambeth – in Palace scale, 29edo tuning

Coendou

Coendou can be described as 7 & 29, suggesting an even less sharp or near-just perfect fifth. 9\65 is a good generator.

Subgroup: 2.3.5.7

Comma list: 250/243, 525/512

Mapping: [⟨1 2 3 1], ⟨0 -3 -5 13]]

Wedgie: ⟨⟨ 3 5 -13 1 -29 -44 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 166.094

error map: ⟨0.000 -0.236 -16.783 -9.607]

• POTE: ~2 = 1200.000, ~10/9 = 166.041

error map: ⟨0.000 -0.077 -16.516 -10.299]

Minimax tuning:

• 7- and 9-odd-limit: ~10/9 = [2/3 -1/3⟩

eigenmonzo (unchanged-interval) basis: 2.3

Optimal ET sequence: 7, 22d, 29, 65c, 94cd

Badness (Smith): 0.118344

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 525/512

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 165.925
• POTE: ~2 = 1200.000, ~11/10 = 165.981

Minimax tuning:

• 11-odd-limit: ~11/10 = [2/3 -1/3⟩

eigenmonzo (unchanged-interval) basis: 2.3

Optimal ET sequence: 7, 22d, 29, 65ce

Badness (Smith): 0.049669

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/64, 100/99, 105/104

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 166.046
• POTE: ~2 = 1200.000, ~11/10 = 165.974

Minimax tuning:

• 13- and 15-odd-limit: ~11/10 = [2/3 -1/3⟩

eigenmonzo (unchanged-interval) basis: 2.3

Optimal ET sequence: 7, 22d, 29, 65cef

Badness (Smith): 0.030233

Hystrix

Hystrix provides a less complex avenue to the 7-limit, with the generator taking on the role of approximating 8/7. Unfortunately in temperaments as in life you get what you pay for, and hystrix is very high in error due to the large disparity between typical porcupine generators and a justly-tuned 8/7, and is usually considered an exotemperament. A generator of 2\15 or 9\68 can be used for hystrix.

Subgroup: 2.3.5.7

Comma list: 36/35, 160/147

Mapping: [⟨1 2 3 3], ⟨0 -3 -5 -1]]

Wedgie: ⟨⟨ 3 5 1 1 -7 -12 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 165.185

error map: ⟨0.000 +2.491 -12.236 +65.990]

• POTE: ~2 = 1200.000, ~10/9 = 158.868

error map: ⟨0.000 +21.442 +19.348 +72.306]

Minimax tuning:

• 7- and 9-odd-limit: ~10/9 = [3/5 0 -1/5⟩

eigenmonzo (unchanged-interval) basis: 2.5

Optimal ET sequence: 7, 8d, 15d

Badness (Smith): 0.044944

11-limit

Subgroup: 2.3.5.7.11

Comma list: 22/21, 36/35, 80/77

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

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/10 = 164.768
• POTE: ~2 = 1200.000, ~11/10 = 158.750

Optimal ET sequence: 7, 8d, 15d

Badness (Smith): 0.026790

Oxygen

Oxygen is perhaps not meant to be used as a serious temperament of harmony. Its comma basis suggests potential utility to construct Fokker blocks.

Subgroup: 2.3.5.7

Comma list: 21/20, 175/162

Mapping: [⟨1 2 3 3], ⟨0 -3 -5 -2]]

Wedgie: ⟨⟨ 3 5 2 1 -5 -9 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/9 = 161.341

error map: ⟨0.000 +14.023 +6.982 -91.507]

• POTE: ~2 = 1200.000, ~10/9 = 169.112

error map: ⟨0.000 -9.291 -31.873 -107.050]

Optimal ET sequence: 1c, …, 6bcd, 7d

Badness (Smith): 0.059866

Hedgehog

See also: Sensamagic clan and Stearnsmic clan

Hedgehog has a period 1/2 octave and a generator which can be taken to be 9/7 instead of 10/9. It also tempers out 245/243, the sensamagic comma. It is a strong extension of BPS (as BPS has no 2 or sqrt(2)). 22edo provides the obvious (i.e the only patent val) tuning, but if you are looking for an alternative you could try the ⟨146 232 338 411] (146bccdd) val with generator 10\73, or you could try 164 cents if you are fond of round numbers. The 14-note mos gives scope for harmony while stopping well short of 22. A related temperament is echidna, which offers much more accuracy. They merge on 22edo.

Subgroup: 2.3.5.7

Comma list: 50/49, 245/243

Mapping: [⟨2 1 1 2], ⟨0 3 5 5]]

mapping generators: ~7/5, ~9/7

Wedgie: ⟨⟨ 6 10 10 2 -1 -5 ]]

Optimal tunings:

• CTE: ~7/5 = 600.000, ~9/7 = 435.258

error map: ⟨0.000 +3.819 -10.024 +7.464]

• POTE: ~7/5 = 600.000, ~9/7 = 435.648

error map: ⟨0.000 +4.989 -8.074 +9.414]

Optimal ET sequence: 8d, 14c, 22

Badness (Smith): 0.043983

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨2 1 1 2 4], ⟨0 3 5 5 4]]

Wedgie: ⟨⟨ 6 10 10 8 2 -1 -8 -5 -16 -12 ]]

Optimal tunings:

• CTE: ~7/5 = 600.000, ~9/7 = 435.528
• POTE: ~7/5 = 600.000, ~9/7 = 435.386

Optimal ET sequence: 8d, 14c, 22, 58ce

Badness (Smith): 0.023095

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 50/49, 55/54, 65/63, 99/98

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

Optimal tunings:

• CTE: ~7/5 = 600.000, ~9/7 = 436.309
• POTE: ~7/5 = 600.000, ~9/7 = 435.861

Optimal ET sequence: 8d, 14cf, 22

Badness (Smith): 0.021516

Urchin

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 50/49, 55/54, 66/65

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

Optimal tunings:

• CTE: ~7/5 = 600.000, ~9/7 = 435.186
• POTE: ~7/5 = 600.000, ~9/7 = 437.078

Optimal ET sequence: 14c, 22f

Badness (Smith): 0.025233

Hedgepig

Subgroup: 2.3.5.7.11

Comma list: 50/49, 245/243, 385/384

Mapping: [⟨2 1 1 2 12], ⟨0 3 5 5 -7]]

Wedgie: ⟨⟨ 6 10 10 -14 2 -1 -43 -5 -67 -74 ]]

Optimal tunings:

• CTE: ~7/5 = 600.000, ~9/7 = 435.329
• POTE: ~7/5 = 600.000, ~9/7 = 435.425

Optimal ET sequence: 22

Badness (Smith): 0.068406

Music

• Phobos Light by Chris Vaisvil – in hedgehog[14], 22edo tuning.

Nautilus

Subgroup: 2.3.5.7

Comma list: 49/48, 250/243

Mapping: [⟨1 2 3 3], ⟨0 -6 -10 -3]]

mapping generators: ~2, ~21/20

Wedgie: ⟨⟨ 6 10 3 2 -12 -21 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~21/20 = 81.914

error map: ⟨0.000 +6.559 -5.457 -14.569]

• POTE: ~2 = 1200.000, ~21/20 = 82.505

error map: ⟨0.000 +3.012 -11.368 -16.342]

Optimal ET sequence: 14c, 15, 29, 44d

Badness (Smith): 0.057420

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 245/242

Mapping: [⟨1 2 3 3 4], ⟨0 -6 -10 -3 -8]]

Wedgie: ⟨⟨ 6 10 3 8 2 -12 -8 -21 -16 12 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~21/20 = 81.802
• POTE: ~2 = 1200.000, ~21/20 = 82.504

Optimal ET sequence: 14c, 15, 29, 44d

Badness (Smith): 0.026023

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 91/90, 100/99

Mapping: [⟨1 2 3 3 4 5], ⟨0 -6 -10 -3 -8 -19]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~21/20 = 81.912
• POTE: ~2 = 1200.000, ~21/20 = 82.530

Optimal ET sequence: 14cf, 15, 29, 44d

Badness (Smith): 0.022285

Belauensis

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 49/48, 55/54, 66/65

Mapping: [⟨1 2 3 3 4 4], ⟨0 -6 -10 -3 -8 -4]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~21/20 = 82.034
• POTE: ~2 = 1200.000, ~21/20 = 81.759

Optimal ET sequence: 14c, 15, 29f, 44dff

Badness (Smith): 0.029816

Music

• Nautilus Reverie by Igliashon Calvin Jones-Coolidge

Ammonite

Subgroup: 2.3.5.7

Comma list: 250/243, 686/675

Mapping: [⟨1 5 8 10], ⟨0 -9 -15 -19]]

mapping generators: ~2, ~9/7

Wedgie: ⟨⟨ 9 15 19 3 5 2 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~9/7 = 454.550

error map: ⟨0.000 +7.095 -4.564 -5.276]

• POTE: ~2 = 1200.000, ~9/7 = 454.448

error map: ⟨0.000 +8.009 -3.040 -3.346]

Optimal ET sequence: 8d, 21cd, 29, 37, 66

Badness (Smith): 0.107686

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 686/675

Mapping: [⟨1 5 8 10 8], ⟨0 -9 -15 -19 -12]]

Wedgie: ⟨⟨ 9 15 19 12 3 5 -12 2 -24 -32 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~9/7 = 454.505
• POTE: ~2 = 1200.000, ~9/7 = 454.512

Optimal ET sequence: 8d, 21cde, 29, 37, 66

Badness (Smith): 0.045694

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 91/90, 100/99, 169/168

Mapping: [⟨1 5 8 10 8 9], ⟨0 -9 -15 -19 -12 -14]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~13/10 = 454.480
• POTE: ~2 = 1200.000, ~13/10 = 454.529

Optimal ET sequence: 8d, 21cdef, 29, 37, 66

Badness (Smith): 0.027168

Ceratitid

Subgroup: 2.3.5.7

Comma list: 250/243, 1728/1715

Mapping: [⟨1 2 3 3], ⟨0 -9 -15 -4]]

mapping generators: ~2, ~36/35

Wedgie: ⟨⟨ 9 15 4 3 -19 -33 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~36/35 = 54.804

error map: ⟨0.000 +4.809 -8.374 +11.958]

• POTE: ~2 = 1200.000, ~36/35 = 54.384

error map: ⟨0.000 +8.585 -2.081 +13.636]

Optimal ET sequence: 1c, 21c, 22

Badness (Smith): 0.115304

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99, 352/343

Mapping: [⟨1 2 3 3 4], ⟨0 -9 -15 -4 -12]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~36/35 = 54.702
• POTE: ~2 = 1200.000, ~36/35 = 54.376

Optimal ET sequence: 1ce, 21ce, 22

Badness (Smith): 0.051319

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 65/63, 100/99, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -9 -15 -4 -12 -7]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~36/35 = 54.575
• POTE: ~2 = 1200.000, ~36/35 = 54.665

Optimal ET sequence: 1ce, 21cef, 22

Badness (Smith): 0.044739