Starling temperaments
This page discusses some of the rank two temperaments tempering out 126/125, the starling comma or septimal semicomma. Since (6/5)3 = 126/125 × 12/7, these temperaments tend to have a relatively small complexity for 6/5. They also possess the starling tetrad, the 6/5-6/5-6/5-7/6 versions of the diminished seventh chord. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.
Temperaments discussed else where are pater, flat, opossum, diminished, keemun, augene, septimal meantone, mavila, gilead, muggles, diaschismic, wollemia, grackle and worschmidt.
Myna
In addition to 126/125, myna tempers out 1728/1715, the orwell comma, and 2401/2400, the breedsma. It can also be described as the 27&31 temperament, or in terms of its wedgie ⟨⟨ 10 9 7 -9 -17 -9 ]]. It has 6/5 as a generator, and 58edo can be used as a tuning, with 89edo being a better one, and fans of round amounts in cents may like 120edo. It is also possible to tune myna with pure fifths by taking 61/10 as the generator. Myna extends naturally but with much increased complexity to the 11 and 13 limits.
5-limit (mynic)
Subgroup: 2.3.5
Comma list: 10077696/9765625
Mapping: [⟨1 9 9], ⟨0 -10 -9]]
POTE generator: ~6/5 = 310.140
Badness: 0.2500
7-limit
Subgroup: 2.3.5.7
Comma list: 126/125, 1728/1715
Mapping: [⟨1 9 9 8], ⟨0 -10 -9 -7]]
Mapping generators: ~2, ~5/3
POTE generator: ~6/5 = 310.146
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [9/10 9/10 0 0⟩, [17/10 7/10 0 0⟩]
- Eigenmonzos: 2, 3
Badness: 0.0270
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 243/242
Mapping: [⟨1 9 9 8 22], ⟨0 -10 -9 -7 -25]]
POTE generator: ~6/5 = 310.144
Badness: 0.0168
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 126/125, 144/143, 176/175, 196/195
Mapping: [⟨1 9 9 8 22 0], ⟨0 -10 -9 -7 -25 5]]
POTE generator: ~6/5 = 310.276
Badness: 0.0171
Minah
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 91/90, 126/125, 176/175
Mapping: [⟨1 9 9 8 22 20], ⟨0 -10 -9 -7 -25 -22]]
POTE generator: ~6/5 = 310.381
Badness: 0.0276
Maneh
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 126/125, 540/539
Mapping: [⟨1 9 9 8 22 23], ⟨0 -10 -9 -7 -25 -26]]
POTE generator: ~6/5 = 309.804
Badness: 0.0299
Myno
Subgroup: 2.3.5.7.11
Comma list: 99/98, 126/125, 385/384
Mapping: [⟨1 9 9 8 -1], ⟨0 -10 -9 -7 6]]
POTE generator: ~6/5 = 309.737
Badness: 0.0334
Coleto
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 1728/1715
Mapping: [⟨1 9 9 8 2], ⟨0 -10 -9 -7 2]]
POTE generator: ~6/5 = 310.853
Badness: 0.0487
Sensi
Sensi tempers out 686/675, 245/243 and 4375/4374 in addition to 126/125, and can be described as the 19&27 temperament. It has as a generator half the size of a slightly wide major sixth, which gives an interval sharp of 9/7 and flat of 13/10, both of which can be used to identify it, as 2.3.5.7.13 sensi (sensation) tempers out 91/90. 22/17, in the middle, is even closer to the generator. 46edo is an excellent sensi tuning, and MOS of size 11, 19 and 27 are available. The name "sensi" is a play on the words "semi-" and "sixth."
7-limit
Subgroup: 2.3.5.7
Comma list: 126/125, 245/243
Mapping: [⟨1 6 8 11], ⟨0 -7 -9 -13]]
Mapping generators: ~2, ~14/9
Wedgie: ⟨⟨ 7 9 13 -2 1 5 ]]
POTE generator: ~9/7 = 443.383
- [[1 0 0 0⟩, [1/13 0 0 7/13⟩, [5/13 0 0 9/13⟩, [0 0 0 1⟩]
- Eigenmonzos: 2, 7
- [[1 0 0 0⟩, [2/5 14/5 -7/5 0⟩, [4/5 18/5 -9/5 0⟩, [3/5 26/5 -13/5 0⟩]
- Eigenmonzos: 2, 9/5
Algebraic generator: The real root of x5 + x4 - 4x2 + x - 1, at 443.3783 cents.
Badness: 0.0256
Sensation
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Sval mapping: [⟨1 6 8 11 10], ⟨0 -7 -9 -13 -10]]
Gencom mapping: [⟨1 6 8 11 0 10], ⟨0 -7 -9 -13 0 -10]]
Gencom: [2 9/7; 91/90 126/125 169/168]
POTE generator: ~9/7 = 443.322
Sensor
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Mapping: [⟨1 6 8 11 -6], ⟨0 -7 -9 -13 15]]
POTE generator: ~9/7 = 443.294
Badness: 0.0379
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 385/384
Mapping: [⟨1 6 8 11 -6 10], ⟨0 -7 -9 -13 15 -10]]
POTE generator: ~9/7 = 443.321
Badness: 0.0256
Sensis
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: [⟨1 6 8 11 6], ⟨0 -7 -9 -13 -4]]
POTE generator: ~9/7 = 443.962
Badness: 0.0287
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: [⟨1 6 8 11 6 10], ⟨0 -7 -9 -13 -4 -10]]
POTE generator: ~9/7 = 443.945
Badness: 0.0200
Sensus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Mapping: [⟨1 6 8 11 23], ⟨0 -7 -9 -13 -31]]
POTE generator: ~9/7 = 443.626
Badness: 0.0295
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 352/351
Mapping: [⟨1 6 8 11 23 10], ⟨0 -7 -9 -13 -31 -10]]
POTE generator: ~9/7 = 443.559
Badness: 0.0208
Sensa
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Mapping: [⟨1 6 8 11 11], ⟨0 -7 -9 -13 -12]]
POTE generator: ~9/7 = 443.518
Badness: 0.0368
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 77/75, 143/140
Mapping: [⟨1 6 8 11 11 10], ⟨0 -7 -9 -13 -12 -11]]
POTE generator: ~9/7 = 443.506
Badness: 0.0233
Hemisensi
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Mapping: [⟨1 13 17 24 32], ⟨0 -14 -18 -26 -35]]
POTE generator: ~25/22 = 221.605
Badness: 0.0487
Valentine
Valentine tempers out 1029/1024 and 6144/6125 as well as 126/125, so it also fits under the heading of the gamelismic clan. It has a generator of 21/20, which can be stripped of its 2 and taken as 3×7/5. In this respect it resembles miracle, with a generator of 3×5/7, and casablanca, with a generator of 5×7/3. These three generators are the simplest in terms of the relationship of tetrads in the lattice of 7-limit tetrads. Valentine can also be described as the 31&46 temperament, and 77edo, 108edo or 185edo make for excellent tunings, which also happen to be excellent tunings for starling temperament, the 126/125 planar temperament. Hence 7-limit valentine can be used whenever starling is wanted, with the extra tempering out of 1029/1024 having no discernible effect on tuning accuracy. Another tuning for valentine uses (3/2)1/9 as a generator, giving pure 3/2 fifths. Valentine extends naturally to the 11-limit as ⟨⟨ 9 5 -3 7 … ]], tempering out 121/120 and 441/440; 46edo has a valentine generator 3\46 which is only 0.0117 cents sharp of the minimax generator, (11/7)1/10.
Valentine is very closely related to Carlos Alpha, the rank one nonoctave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in Beauty in the Beast suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank one temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. MOS of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.
5-limit
Subgroup: 2.3.5
Comma list: 1990656/1953125
Mapping: [⟨1 1 2], ⟨0 9 5]]
POTE generator: ~25/24 = 78.039
Badness: 0.1228
7-limit
Subgroup: 2.3.5.7
Comma list: 126/125, 1029/1024
Mapping: [⟨1 1 2 3], ⟨0 9 5 -3]]
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.864
- [[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [17/6 5/12 0 -5/12⟩, [5/2 -1/4 0 1/4⟩]
- Eigenmonzos: 2, 7/6
- [[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [47/21 10/21 0 -5/21⟩, [20/7 -2/7 0 1/7⟩]
- Eigenmonzos: 2, 9/7
Algebraic generator: smaller root of x2 - 89x + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.
Badness: 0.0311
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 176/175
Mapping: [⟨1 1 2 3 3], ⟨0 9 5 -3 7]]
Mapping generators: ~2, ~21/20
POTE generator: ~21/20 = 77.881
Minimax tuning:
- 11-odd-limit
- [[1 0 0 0 0⟩, [1 0 0 -9/10 9/10⟩, [2 0 0 -1/2 1/2⟩, [3 0 0 3/10 -3/10⟩, [3 0 0 -7/10 7/10⟩]
- Eigenmonzos: 2, 11/7
Algebraic generator: positive root of 4x3 + 15x2 - 21, or else Gontrand2, the smallest positive root of 4x7 - 8x6 + 5.
Badness: 0.0167
Dwynwen
Commas: 91/90, 121/120, 126/125, 176/175
POTE generator: ~21/20 = 78.219
Map: [<1 1 2 3 3 2|, <0 9 5 -3 7 26|]
Badness: 0.0235
Lupercalia
Commas: 66/65, 105/104, 121/120, 126/125
POTE generator: ~21/20 = 77.709
Map: [<1 1 2 3 3 3|, <0 9 5 -3 7 11|]
Badness: 0.0213
Valentino
Commas: 121/120, 126/125, 176/175, 196/195
POTE generator: ~21/20 = 77.958
Map: [<1 1 2 3 3 5|, <0 9 5 -3 7 -20|]
EDOs: 15f, 31, 46, 77, 431ccdeeeef
Badness: 0.0207
Semivalentine
Commas: 121/120, 126/125, 169/168, 176/175
POTE generator: ~21/20 = 77.839
Map: [<2 2 4 6 6 7|, <0 9 5 -3 7 3|]
Badness: 0.0327
Alicorn
Commas: 126/125, 10976/10935
POTE generator: ~28/27 = 62.278
Map: [<1 2 3 4|, <0 -8 -13 -23|]
Wedgie: <<8 13 23 2 14 17||
Badness: 0.0409
11-limit
Commas: 126/125, 540/539, 896/891
POTE generator: ~28/27 = 62.101
Map: [<1 2 3 4 3|, <0 -8 -13 -23 9|]
Badness: 0.0392
13-limit
Commas: 126/125, 144/143, 196/195, 676/675
POTE generator: ~28/27 = 62.119
Map: [<1 2 3 4 3 5|, <0 -8 -13 -23 9 -25|]
Badness: 0.0237
Camahueto
Commas: 126/125, 10976/10935, 385/384
POTE generator: ~28/27 = 62.431
Map: [<1 2 3 4 2|, <0 -8 -13 -23 28|]
Badness: 0.0659
13-limit
Commas: 126/125, 196/195, 385/384, 676/675
POTE generator: ~28/27 = 62.434
Map: [<1 2 3 4 2 5|, <0 -8 -13 -23 28 -25|]
Badness: 0.0362
Coblack
In addition to 126/125, the coblack temperament tempers out the cloudy comma, 16807/16384, which is the amount by which five septimal supermajor seconds (8/7) fall short of an octave.
Commas: 126/125, 16807/16384
POTE generator: ~21/20 = 73.044
Map: [<5 1 7 14|, <0 3 2 0|]
Badness: 0.1073
11-limit
Commas: 126/125, 245/242, 385/384
POTE generator: ~21/20 = 73.264
Map: [<5 1 7 14 15|, <0 3 2 0 1|]
Casablanca
Aside from 126/125, casablanca tempers out the no-threes comma 823543/819200 and also 589824/588245, and may also be described by its wedgie, <<19 14 4 -22 -47 -30||, or as 31&73. 74\135 or 91\166 supply good tunings for the generator, and 20 and 31 note MOS are available.
It may not seem like casablanca has much to offer, but peering under the hood a bit harder suggests otherwise. For one thing, the 35/24 generator is particularly interesting; like 15/14 and 21/20, it represents an interval between one vertex of a hexany and the opposite vertex, which makes it particularly simple with regard to the cubic lattice of tetrads. For another, if we add 385/384 to the list of commas, 35/24 is identified with 16/11, and casablanca is revealed as an 11-limit temperament with a very low complexity for 11 and not too high a one for 7; we might compare 1, 4, 14, 19, the generator steps to 11, 7, 5 and 3 respectively, with 1, 4, 10, 18, the steps to 3, 5, 7 and 11 in 11-limit meantone.
Commas: 126/125, 589824/588245
POTE generator: ~35/24 = 657.818
Map: [<1 12 10 5|, <0 -19 -14 -4|]
EDOs: 11b, 20b, 31, 104c, 135c, 166c
Badness: 0.1012
11-limit
Commas: 126/125, 385/384, 2420/2401
POTE generator: ~16/11 = 657.923
Map: [<1 12 10 5 4|, |0 -19 -14 -4 -1>]
Badness: 0.0623
Marrakesh
Commas: 126/125, 176/175, 14641/14580
POTE generator: ~22/15 = 657.791
Map: [<1 12 10 5 21|, |0 -19 -14 -4 -32>]
Badness: 0.0405
13-limit
Commas: 126/125, 176/175, 196/195, 14641/14580
POTE generator: ~22/15 = 657.756
Map: [<1 12 10 5 21 -10|, |0 -19 -14 -4 -32 25>]
EDOs: 31, 73, 104c, 135c, 239ccf
Badness: 0.0408
Murakuc
Commas: 126/125, 144/143, 176/175, 1540/1521
POTE generator: ~22/15 = 657.700
Map: [<1 12 10 5 21 7|, |0 -19 -14 -4 -32 -6>]
Badness: 0.0414
Nusecond
Nusecond tempers out 2430/2401 and 16875/16807 in addition to 126/125, and may be described as 31&70, or in terms of its wedgie as <<11 13 17 -5 -4 3||. It has a neutral second generator of 49/45, two of which make up a 6/5 minor third since 2430/2401 is tempered out. 31edo can be used as a tuning, or 132edo with a val which is the sum of the patent vals for 31 and 101. Because 49/45 is flat of 12/11 by only 540/539, nusecond is more naturally thought of as an 11-limit temperament with a combined 12/11 and 11/10 as a generator, tempering out 99/98, 121/120 and 540/539. Because of all the neutral seconds, an exotic Middle Eastern sound comes naturally to nusecond. MOS of 15, 23, or 31 notes are enough to give fuller effect to the harmony, but the 8-note MOS might also be considered from the melodic point of view.
5-limit
Comma: 51018336/48828125
POTE generator: ~3125/2916 = 154.523
Map: [<1 3 4|, <0 -11 -13|]
EDOs: 8, 23, 31, 70, 101, 132c, 233c, 365bcc
Badness: 0.4665
7-limit
Commas: 126/125, 2430/2401
7-limit minimax
[|1 0 0 0>, |-5/13 0 11/13 0>, |0 0 1 0>, |-3/13 0 17/13 0>]
Eigenmonzos: 2, 5
9-limit minimax
[|1 0 0 0>, |0 1 0 0>, |5/11 13/11 0 0>, |4/11 17/11 0 0>]
Eigenmonzos: 2, 3
POTE generator: 154.579
Map: [<1 3 4 5|, <0 -11 -13 -17|]
Generators: 2, 49/45
EDOs: 8d, 23d, 31, 101, 132c, 163c
Badness: 0.0504
11-limit
Commas: 99/98, 121/120, 126/125
11-limit minimax
[|1 0 0 0 0>, |19/10 11/5 0 0 -11/10>, |27/10 13/5 0 0 -13/10>, |33/10 17/5 0 0 -17/10>, |19/5 12/5 0 0 -6/5>]
Eigenmonzos: 2, 11/9
POTE generator: ~11/10 = 154.645
Algebraic generator: positive root of 15x^2-10x-7, or (5+sqrt(130))/15, at 154.6652 cents. The recurrence converges very quickly.
Map: [<1 3 4 5 5|, <0 -11 -13 -17 -12|]
Generators: 2, 11/10
EDOs: 8d, 23de, 31, 101, 132ce, 163ce, 194cee
Badness: 0.0256
13-limit
Commas: 66/65, 99/98, 121/120, 126/125
POTE generator: ~11/10 = 154.478
Map: [<1 3 4 5 5 5|, <0 -11 -13 -17 -12 -10|]
EDOs: 8d, 23de, 31, 70f, 101ff
Badness: 0.0233
Thuja
Commas: 126/125, 65536/64827
POTE generator: ~175/128 = 558.605
Map: [<1 8 5 -2|, <0 -12 -5 9|]
Wedgie: <<12 5 -9 -20 -48 -35||
Badness: 0.0884
11-limit
Commas: 126/125, 176/175, 1344/1331
POTE generator: ~11/8 = 558.620
Map: [<1 8 5 -2 4|, <0 -12 -5 9 -1|]
Badness: 0.0331
13-limit
Commas: 126/125, 144/143, 176/175, 364/363
POTE generator: ~11/8 = 558.589
Map: [<1 8 5 -2 4 16|, <0 -12 -5 9 -1 -23|]
Badness: 0.0228
29-limit
POTE generator: ~11/8 = 558.520
Map: [<1 -4 0 7 3 -7 12 1 5 3|, <0 12 5 -9 1 23 -17 7 -1 4|]
(Raison d'etre of this entry being the simple and accurate approximation of factor twenty-nine, the 2.5.11.21.29 subgroup being of especially good accuracy and simplicity.)
Cypress
5-limit
Comma: 258280326/244140625
POTE generator: ~4374/3125 = 541.726
Map: [<1 7 10|, <0 -12 -17|]
EDOs: 11c, 20c, 31, 113c, 144c, 175c, 381bcc
Badness: 0.8166
7-limit
Commas: 126/125, 19683/19208
POTE generator: ~135/98 = 541.828
Map: [<1 7 10 15|, <0 -12 -17 -27|]
Wedgie: <<12 17 27 -1 9 15||
EDOs: 11cd, 20cd, 31, 206bcd, 237bcd, 268bcd, 299bcd, 330bbcd
Badness: 0.0998
11-limit
Commas: 99/98, 126/125, 243/242
POTE generator: ~15/11 = 541.772
Map: [<1 7 10 15 17|, <0 -12 -17 -27 -30|]
EDOs: 11cdee, 20cde, 31, 144cd, 175cd, 206bcde, 237bcde
Badness: 0.0427
13-limit
Commas: 66/65, 99/98. 126/125, 243/242
POTE generator: ~15/11 = 541.778
Map: [<1 7 10 15 17 15|, <0 -12 -17 -27 -30 -25|]
Badness: 0.0378
Bisemidim
Commas: 126/125, 118098/117649
POTE generator: ~35/27 = 455.445
Map: [<2 1 2 2|, <0 9 11 15|]
Wedgie: <<18 22 30 -7 -3 8||
EDOs: 50, 58, 108, 166c, 408ccc
Badness: 0.0978
11-limit
Commas: 126/125, 540/539, 1344/1331
POTE generator: ~35/27 = 455.373
Map: [<2 1 2 2 5|, <0 9 11 15 8|]
EDOs: 50, 58, 108, 166ce, 224cee
Badness: 0.0412
13-limit
Commas: 126/125, 144/143, 196/195, 364/363
POTE generator: ~35/27 = 455.347
Map: [<2 1 2 2 5 5|, <0 9 11 15 8 10|]
EDOs: 50, 58, 166cef, 224ceeff
Badness: 0.0239
Vines
Commas: 126/125, 84035/82944
POTE generator: ~6/5 = 312.602
Map: [<2 7 8 8|, <0 -8 -7 -5|]
EDOs: 42, 46, 96d, 142d, 238dd
Badness: 0.0780
11-limit
Commas: 126/125, 385/384, 2401/2376
POTE generator: ~6/5 = 312.601
Map: [<2 7 8 8 5|, <0 -8 -7 -5 4|]
EDOs: 42, 46, 96d, 142d, 238dd
Badness: 0.0445
13-limit
Commas: 126/125, 196/195, 364/363, 385/384
POTE generator: ~6/5 = 312.564
Map: [<2 7 8 8 5 5|, <0 -8 -7 -5 4 5|]
Badness: 0.0297
Kumonga
5-limit
Comma: 1289945088/1220703125
POTE generator: ~144/125 = 222.912
Map: [<1 4 4|, <0 -13 -9|]
Badness: 0.7296
7-limit
Commas: 126/125, 12288/12005
POTE generator: ~8/7 = 222.797
Map: [<1 4 4 3|, <0 -13 -9 -1|]
Wedgie: <<13 9 1 -16 -35 -23||
Badness: 0.0875
11-limit
Commas: 126/125, 176/175, 864/847
POTE generator: ~8/7 = 222.898
Map: [<1 4 4 3 7|, <0 -13 -9 -1 -19|]
Badness: 0.0433
13-limit
Commas: 78/77, 126/125, 144/143, 176/175
POTE generator: ~8/7 = 222.961
Map: [<1 4 4 3 7 5|, <0 -13 -9 -1 -19 -7|]
EDOs: 16, 27e, 43, 70e, 113cdee
Badness: 0.0289
Amigo
Commas: 126/125, 2097152/2083725
POTE generator: ~5/4 = 391.094
Map: [<1 9 3 -10|, <0 -11 -1 19|]
Badness: 0.1109
11-limit
Commas: 126/125, 176/175, 16384/16335
POTE generator: ~5/4 = 391.075
Map: [<1 9 3 -10 -8|, <0 -11 -1 19 17|]
Badness: 0.0434
13-limit
Commas: 126/125, 169/168, 176/175, 364/363
POTE generator: ~5/4 = 391.072
Map: [<1 9 3 -10 -8 1|, <0 -11 -1 19 17 4|]
EDOs: 43, 46, 89, 135cf, 224cf
Badness: 0.0307
Oolong
5-limit
Comma: [11 18 -17>
POTE generator: ~6/5 = 311.6942
Map: [<1 6 7|, <0 -17 -18|]
Badness: 0.9428
7-limit
Commas: 126/125, 117649/116640
POTE generator: ~6/5 = 311.6793
Map: [<1 6 7 8|, <0 -17 -18 -20|]
Badness: 0.0735
11-limit
Commas: 126/125, 176/175, 26411/26244
POTE generator: ~6/5 = 311.5873
Map: [<1 6 7 8 18|, <0 -17 -18 -20 -56|]
Badness: 0.0569
13-limit
Commas: 126/125, 176/175, 196/195, 13013/12960
POTE generator: ~6/5 = 311.5908
Map: [<1 6 7 8 18 5|, <0 -17 -18 -20 -56 -5|]
Badness: 0.0356