Dicot family
The 5-limit parent comma for the dicot family is 25/24, the classic chromatic semitone. Its monzo is [-3 -1 2⟩, and flipping that yields ⟨⟨2 1 -3]] for the wedgie. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are 7edo, 24edo using the val ⟨24 38 55] (24c) and 31edo using the val ⟨31 49 71] (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an exotemperament.
Dicot
Subgroup: 2.3.5
Comma list: 25/24
Mapping: [⟨1 1 2], ⟨0 2 1]]
POTE generator: ~5/4 = 348.594
- 5-odd-limit diamond monotone: ~5/4 = [300.000, 400.000] (1\4 to 1\3)
- 5-odd-limit diamond tradeoff: ~5/4 = [315.641, 386.314]
- 5-odd-limit diamond monotone and tradeoff: ~5/4 = [315.641, 386.314]
Optimal ET sequence: 3, 4, 7, 17, 24c, 31c
Badness: 0.013028
Seven limit children
The second comma of the normal comma list defines which 7-limit family member we are looking at. Septimal dicot, with wedgie ⟨⟨2 1 3 -3 -1 4]] adds 36/35, sharp with wedgie ⟨⟨2 1 6 -3 4 11]] adds 28/27, and dichotic with wedgie ⟨⟨2 1 -4 -3 -12 -12]] ads 64/63, all retaining the same period and generator. Decimal with wedgie ⟨⟨4 2 2 -6 -8 -1]] adds 49/48, sidi with wedgie ⟨⟨4 2 9 -3 6 15]] adds 245/243, and jamesbond with wedgie ⟨⟨0 0 7 0 11 16]] adds 81/80. Here decimal divides the period to 1/2 octave, and sidi uses 9/7 as a generator, with two of them making up the combined 5/3 and 8/5 neutral sixth. Jamesbond has a period of 1/7 octave, and uses an approximate 15/14 as generator.
Septimal dicot
Subgroup: 2.3.5.7
Comma list: 15/14, 25/24
Mapping: [⟨1 1 2 2], ⟨0 2 1 3]]
Wedgie: ⟨⟨2 1 3 -3 -1 4]]
POTE generator: ~5/4 = 336.381
Optimal ET sequence: 3d, 4, 7, 18bc, 25bccd
Badness: 0.019935
11-limit
Subgroup: 2.3.5.7.11
Comma list: 15/14, 22/21, 25/24
Mapping: [⟨1 1 2 2 2], ⟨0 2 1 3 5]]
POTE generator: ~5/4 = 342.125
Optimal ET sequence: 3de, 4e, 7
Badness: 0.019854
Eudicot
Subgroup: 2.3.5.7.11
Comma list: 15/14, 25/24, 33/32
Mapping: [⟨1 1 2 2 4], ⟨0 2 1 3 -2]]
POTE generator: ~5/4 = 336.051
Optimal ET sequence: 3d, 4, 7, 18bc, 25bccd
Badness: 0.027114
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 15/14, 25/24, 33/32, 40/39
Mapping: [⟨1 1 2 2 4 4], ⟨0 2 1 3 -2 -1]]
POTE generator: ~5/4 = 338.846
Optimal ET sequence: 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef
Badness: 0.023828
Flat
Subgroup: 2.3.5.7
Comma list: 21/20, 25/24
Mapping: [⟨1 1 2 3], ⟨0 2 1 -1]]
Wedgie: ⟨⟨2 1 -1 -3 -7 -5]]
POTE generator: ~5/4 = 331.916
Optimal ET sequence: 3, 4, 7d, 11cd, 18bcddd
Badness: 0.025381
11-limit
Subgroup: 2.3.5.7.11
Comma list: 21/20, 25/24, 33/32
Mapping: [⟨1 1 2 3 4], ⟨0 2 1 -1 -2]]
POTE generator: ~5/4 = 337.532
Optimal ET sequence: 3, 4, 7d
Badness: 0.024988
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 14/13, 21/20, 25/24, 33/32
Mapping: [⟨1 1 2 3 4 4], ⟨0 2 1 -1 -2 -1]]
POTE generator: ~5/4 = 341.023
Optimal ET sequence: 3, 4, 7d
Badness: 0.023420
Sharp
Subgroup: 2.3.5.7
Comma list: 25/24, 28/27
Mapping: [⟨1 1 2 1], ⟨0 2 1 6]]
POTE generator: ~5/4 = 357.938
Wedgie: ⟨⟨2 1 6 -3 4 11]]
Optimal ET sequence: 3d, 7d, 10, 37cd, 47bccd, 57bccdd
Badness: 0.028942
11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 28/27, 35/33
Mapping: [⟨1 1 2 1 2], ⟨0 2 1 6 5]]
POTE generator: ~5/4 = 356.106
Optimal ET sequence: 3de, 7d, 10, 17d, 27cde
Badness: 0.022366
Decimal
Subgroup: 2.3.5.7
Comma list: 25/24, 49/48
Mapping: [⟨2 0 3 4], ⟨0 2 1 1]]
Wedgie: ⟨⟨4 2 2 -6 -8 -1]]
POTE generator: ~7/6 = 251.557
Optimal ET sequence: 4, 10, 14c, 24c, 38ccd, 62cccdd
Badness: 0.028334
11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 49/48
Mapping: [⟨2 0 3 4 -1], ⟨0 2 1 1 5]]
POTE generator: ~7/6 = 253.493
Optimal ET sequence: 10, 14c, 24c, 38ccd, 52cccde
Badness: 0.026712
Decimated
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 49/48
Mapping: [⟨2 0 3 4 10], ⟨0 2 1 1 -2]]
POTE generator: ~7/6 = 255.066
Optimal ET sequence: 4, 10e, 14c
Badness: 0.031456
Decibel
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 49/48
Mapping: [⟨2 0 3 4 7], ⟨0 2 1 1 0]]
POTE generator: ~8/7 = 243.493
Optimal ET sequence: 4, 6, 10
Badness: 0.032385
Dichotic
Subgroup: 2.3.5.7
Comma list: 25/24, 64/63
Mapping: [⟨1 1 2 4], ⟨0 2 1 -4]]
Wedgie: ⟨⟨2 1 -4 -3 -12 -12]]
POTE generator: ~5/4 = 356.264
Optimal ET sequence: 3, 7, 10, 17, 27c, 37c, 64bccc
Badness: 0.037565
11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 64/63
Mapping: [⟨1 1 2 4 2], ⟨0 2 1 -4 5]]
POTE generator: ~5/4 = 354.262
Optimal ET sequence: 7, 10, 17, 27ce, 44cce
Badness: 0.030680
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 40/39, 45/44, 64/63
Mapping: [⟨1 1 2 4 2 4], ⟨0 2 1 -4 5 -1]]
POTE generator: ~5/4 = 354.365
Optimal ET sequence: 7, 10, 17, 27ce, 44cce
Badness: 0.021674
Dichotomic
Subgroup: 2.3.5.7.11
Comma list: 22/21, 25/24, 33/32
Mapping: [⟨1 1 2 4 4], ⟨0 2 1 -4 -2]]
POTE generator: ~5/4 = 354.073
Optimal ET sequence: 3, 7, 10e, 17e
Badness: 0.031719
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 22/21, 25/24, 33/32, 40/39
Mapping: [⟨1 1 2 4 4 4], ⟨0 2 1 -4 -2 -1]]
POTE generator: ~5/4 = 354.313
Optimal ET sequence: 3, 7, 10e, 17e
Badness: 0.022741
Dichosis
Subgroup: 2.3.5.7.11
Comma list: 25/24, 35/33, 64/63
Mapping: [⟨1 1 2 4 5], ⟨0 2 1 -4 -5]]
POTE generator: ~5/4 = 360.659
Optimal ET sequence: 3, 7e, 10
Badness: 0.041361
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 35/33, 40/39, 64/63
Mapping: [⟨1 1 2 4 5 4], ⟨0 2 1 -4 -5 -1]]
POTE generator: ~5/4 = 360.646
Optimal ET sequence: 3, 7e, 10
Badness: 0.027938
Jamesbond
Subgroup: 2.3.5.7
Comma list: 25/24, 81/80
Mapping: [⟨7 11 16 0], ⟨0 0 0 1]]
Wedgie: ⟨⟨0 0 7 0 11 16]]
POTE generator: ~8/7 = 258.139
Badness: 0.041714
11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 33/32, 45/44
Mapping: [⟨7 11 16 0 24], ⟨0 0 0 1 0]]
POTE generator: ~8/7 = 258.910
Badness: 0.023524
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 27/26, 33/32, 40/39
Mapping: [⟨7 11 16 0 24 26], ⟨0 0 0 1 0 0]]
POTE generator: ~8/7 = 250.764
Badness: 0.023003
Septimal
Subgroup: 2.3.5.7.11.13
Comma list: 25/24, 33/32, 45/44, 65/63
Mapping: [⟨7 11 16 0 24 6], ⟨0 0 0 1 0 1]]
POTE generator: ~8/7 = 247.445
Badness: 0.022569
Sidi
Subgroup: 2.3.5.7
Comma list: 25/24, 245/243
Mapping: [⟨1 3 3 6], ⟨0 -4 -2 -9]]
Wedgie: ⟨⟨4 2 9 -12 3 15]]
POTE generator: ~9/7 = 427.208
Optimal ET sequence: 3d, 14c, 45cc, 59bcccd
Badness: 0.056586
11-limit
Subgroup: 2.3.5.7.11
Comma list: 25/24, 45/44, 99/98
Mapping: [⟨1 3 3 6 7], ⟨0 -4 -2 -9 -10]]
POTE generator: ~9/7 = 427.273
Optimal ET sequence: 3de, 14c, 45cce, 59bcccdee
Badness: 0.032957
Quad
Subgroup: 2.3.5.7
Comma list: 9/8, 25/24
Mapping: [⟨4 6 9 0], ⟨0 0 0 1]]
Wedgie: ⟨⟨0 0 4 0 6 9]]
POTE generator: ~8/7 = 324.482
Badness: 0.045911