Sensipent family
Temperaments of the sensipent family temper out the sensipent comma, 78732/78125, also known as medium semicomma. The head of this family is sensipent i.e. the 5-limit version of sensi, generated by the naiadic interval of tempered 162/125. Two generators make 5/3, seven make harmonic 6 and nine make harmonic 10. Its ploidacot is beta-heptacot (pergen (P8, ccP5/7)) and its color name is Sepguti.
The second comma of the comma list determines which 7-limit family member we are looking at. Sensi adds 126/125. Sensei adds 225/224. Warrior adds 5120/5103. These are all strong extensions that use the same period and generator as sensipent.
Bison adds 6144/6125 with a semioctave period. Subpental adds 3136/3125 or 19683/19600 with a generator of ~56/45; two generator steps make the original. Trisensory adds 1728/1715 with a 1/3-octave period. Heinz adds 1029/1024 with a generator of ~48/35; three make the original. Catafourth adds 2401/2400 with a generator of ~250/189; four make the original. Finally, browser adds 16875/16807 with a generator of ~49/45; five make the original.
Temperaments discussed elsewhere include:
- Catafourth → Breedsmic temperaments (+2401/2400)
- Browser → Mirkwai clan (+16875/16807)
Considered below are sensi, sensei, warrior, bison, subpental, trisensory and heinz.
Sensipent
Subgroup: 2.3.5
Comma list: 78732/78125
Mapping: [⟨1 -1 -1], ⟨0 7 9]]
- mapping generators: ~2, ~162/125
Optimal tuning (POTE): ~2 = 1200.000, ~162/125 = 443.058
Optimal ET sequence: 8, 19, 46, 65, 539, 604c, 669c, 734c, 799c, 864c, 929c
- Smith: 0.035220
- Dirichlet: 0.826
2.3.5.31 subgroup
Fascinatingly, essentially the only simple and accurate extension that preserves the occurrence of sensipent's tempered 5-limit structure in such large edos as 539 is the one with prime 31 by interpreting the generator accurately as 31/24~40/31, tempering out S31 = 961/960, so that the 31-limit quarter-tones 32/31 and 31/30 are equated, as sensipent splits 16/15 into two equal parts. For a less sparse subgroup present in smaller edo tunings like 111edo at the cost of slight accuracy, see the extension to the 2.3.5.11.17.31 subgroup #Sensible.
Subgroup: 2.3.5.31
Comma list: 961/960, 2511/2500
Mapping: [⟨1 -1 -1 2], ⟨0 7 9 8]]
- mapping generators: ~2, ~31/24
Optimal ET sequence: 8, 11c, 19, 46, 65, 344, 409, 474, 539, 604c
Optimal tuning (CTE): ~2 = 1200.000, ~31/24 = 443.050
Badness (Dirichlet): 0.243
Sendai
Sendai is an accurate extension of (2.3.5.31) sensipent with primes 23 and 29 found by VIxen. It is named after the body of acquis designed to prevent disaster risk and improve civil protection through international cooperation and after the city in Japan of the same name where it was signed (and where an international music competition is held).
Subgroup: 2.3.5.23.29.31
Comma list: 465/464, 576/575, 621/620, 900/899
Mapping: [⟨1 -1 -1 6 -4 2], ⟨0 7 9 -4 24 8]]
Optimal ET sequence: 19, 46j, 65, 149, 363j
Optimal tuning (CTE): ~2 = 1200.000, ~31/24 = 442.989
Badness (Dirichlet): 0.283
Sensible
Sensible is an extension of sensipent with prime 11 of dubious canonicity but significantly higher accuracy than sensi. It interprets the generator as 165/128~128/99 by tempering out 8019/8000 so that 11/8 is reached as (10/9)3. This extension is very strong as supported by the optimal ET sequence going very far and as supported by another observation that it also tempers out the semiporwellisma, which is equal to S31 × S322 (thus forming the S-expression-based comma list). The vanish of the semiporwellisma, a lopsided comma, implies that this temperament equates (33/32)2 with 16/15 as well as that a natural extension to prime 31 exists through {S31, S32}, which we will see is very accurate, but this itself suggests that an extension with prime 17 is reasonably accurate through tempering out S33 so that a slightly sharp ~22/17 is equated with the generator.
The aforementioned extension with prime 17 through tempering out S33 is equivalent to the one by tempering out S16 = 256/255 = (22/17)/(165/128).
Sensible uses the accurate mapping of prime 31 in sensipent, so that the sensible generator serves many roles in subgroup harmony, but it is not ~9/7 or ~13/10 which would incur more damage. Its S-expression-based comma list is {(S16, S9/S10,) S23, S24, S31, S32, S33} implying also tempering out 496/495 = S31 × S32 and 528/527 = S32 × S33 as well as 16337/16335 = S31/S33 = (34/30)/(33/31)2 = (17/15)/(33/31)2. A notable patent val tuning not appearing in the optimal ET sequence is 157edo.
Subgroup: 2.3.5.11
Comma list: 8019/8000, 16384/16335
Mapping: [⟨1 -1 -1 9], ⟨0 7 9 -15]]
- mapping generators: ~2, ~128/99
Optimal ET sequence: 19, 46, 65, 176, 241, 306
Optimal tuning (CTE): ~2 = 1200.000, ~128/99 = 443.115
Badness (Dirichlet): 0.728
2.3.5.11.17 subgroup
Subgroup: 2.3.5.11.17
Comma list: 256/255, 1089/1088, 1377/1375
Mapping: [⟨1 -1 -1 9 10], ⟨0 7 9 -15 -16]]
- mapping generators: ~2, ~22/17
Optimal ET sequence: 19, 46, 65, 111, 176g
Optimal tuning (CTE): ~2 = 1200.000, ~22/17 = 443.188
Badness (Dirichlet): 0.639
2.3.5.11.17.23 subgroup
Subgroup: 2.3.5.11.17.23
Comma list: 256/255, 576/575, 1089/1088, 1377/1375
Mapping: [⟨1 -1 -1 9 10 6], ⟨0 7 9 -15 -16 -4]]
Optimal ET sequence: 19, 46, 65, 111, 176g
Optimal tuning (CTE): ~2 = 1200.000, ~22/17 = 443.185
Badness (Dirichlet): 0.555
2.3.5.11.17.23.31 subgroup
Subgroup: 2.3.5.11.17.23.31
Comma list: 256/255, 576/575, 961/960, 1089/1088, 1377/1375
Mapping: [⟨1 -1 -1 9 10 6 2], ⟨0 7 9 -15 -16 -4 8]]
Optimal ET sequence: 19, 46, 65, 111, 176g
Badness (Dirichlet): 0.490
Sensi
Sensi tempers out 245/243, 686/675 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 scales of size 8, 11, 19 and 27 are available.
Septimal sensi
Subgroup: 2.3.5.7
Comma list: 126/125, 245/243
Mapping: [⟨1-1 -1 -2], ⟨0 7 9 13]]
- mapping generators: ~2, ~9/7
Wedgie: ⟨⟨ 7 9 13 -2 1 5 ]]
- 7-odd-limit: ~9/7 = [2/13 0 0 1/13⟩
- 9-odd-limit: ~9/7 = [1/5 2/5 -1/5 0⟩
- 7-odd-limit diamond monotone: ~9/7 = [442.105, 450.000] (7\19 to 3\8)
- 9-odd-limit diamond monotone: ~9/7 = [442.105, 444.444] (7\19 to 10\27)
- 7-odd-limit diamond tradeoff: ~9/7 = [442.179, 445.628]
- 9-odd-limit diamond tradeoff: ~9/7 = [435.084, 445.628]
Algebraic generator: The real root of x5 + x4 - 4x2 + x - 1, at 443.3783 cents.
Optimal ET sequence: 19, 27, 46
Badness: 0.025622
2.3.5.7.13 subgroup (sensation)
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Mapping: [⟨1 -1 -1 -2 0], ⟨0 7 9 13 10]]
- mapping generators: ~2, ~9/7
Optimal tuning (CTE): ~2 = 1200.000, ~9/7 = 443.4016
Optimal ET sequence: 19, 27, 46, 111df
Sensor
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/243, 385/384
Mapping: [⟨1 -1 -1 -2 9], ⟨0 7 9 13 -15]]
- mapping generators: ~2, ~9/7
Wedgie: ⟨⟨ 7 9 13 -15 -2 1 -48 5 -66 -87 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.2987
- POTE: ~2 = 1200.000, ~9/7 = 443.294
Optimal ET sequence: 19, 27, 46, 111d
Badness: 0.037942
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 385/384
Mapping: [⟨1 -1 -1 -2 9 0], ⟨0 7 9 13 -15 10]]
Wedgie: ⟨⟨ 7 9 13 -15 10 -2 1 -48 -10 5 -66 -10 -87 -20 90 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.3658
- POTE: ~2 = 1200.000, ~9/7 = 443.321
Optimal ET sequence: 19, 27, 46, 111df
Badness: 0.025575
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 154/153, 169/168, 256/255
Mapping: [⟨1 -1 -1 -2 9 0 10], ⟨0 7 9 13 -15 10 -16]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.3775
- POTE: ~2 = 1200.000, ~9/7 = 443.365
Optimal ET sequence: 19, 27, 46
Badness: 0.022908
Sensus
Subgroup: 2.3.5.7.11
Comma list: 126/125, 176/175, 245/243
Mapping: [⟨1 -1 -1 -2 -8], ⟨0 7 9 13 31]]
- mapping generators: ~2, ~9/7
Wedgie: ⟨⟨ 7 9 13 31 -2 1 25 5 41 42 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.4783
- POTE: ~2 = 1200.000, ~9/7 = 443.626
Optimal ET sequence: 19e, 27e, 46, 119c
Badness: 0.029486
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 352/351
Mapping: [⟨1 -1 -1 -2 -8 0], ⟨0 7 9 13 31 10]]
Wedgie: ⟨⟨ 7 9 13 31 10 -2 1 25 -10 5 41 -10 42 -20 -80 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.5075
- POTE: ~2 = 1200.000, ~9/7 = 443.559
Optimal ET sequence: 19e, 27e, 46
Badness: 0.020789
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 126/125, 136/135, 154/153, 169/168
Mapping: [⟨1 -1 -1 -2 -8 0 -7], ⟨0 7 9 13 31 10 30]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.5050
- POTE: ~2 = 1200.000, ~9/7 = 443.551
Optimal ET sequence: 19eg, 27eg, 46
Badness: 0.016238
Sensis
Subgroup: 2.3.5.7.11
Comma list: 56/55, 100/99, 245/243
Mapping: [⟨1 -1 -1 -2 2], ⟨0 7 9 13 4]]
- mapping generators: ~2, ~9/7
Wedgie: ⟨⟨ 7 9 13 4 -2 1 -18 5 -22 -34 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.1886
- POTE: ~2 = 1200.000, ~9/7 = 443.962
Optimal ET sequence: 8d, 19, 27e
Badness: 0.028680
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 78/77, 91/90, 100/99
Mapping: [⟨1 -1 -1 -2 2 0], ⟨0 7 9 13 4 10]]
Wedgie: ⟨⟨ 7 9 13 4 10 -2 1 -18 -10 5 -22 -10 -34 -20 20 ]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.2863
- POTE: ~2 = 1200.000, ~9/7 = 443.945
Optimal ET sequence: 8d, 19, 27e
Badness: 0.020017
Sensa
Subgroup: 2.3.5.7.11
Comma list: 55/54, 77/75, 99/98
Mapping: [⟨1 -1 -1 -2 -1], ⟨0 7 9 13 12]]
- mapping generators: ~2, ~9/7
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.7814
- POTE: ~2 = 1200.000, ~9/7 = 443.518
Optimal ET sequence: 8d, 19e, 27
Badness: 0.036835
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 55/54, 66/65, 77/75, 143/140
Mapping: [⟨1 -1 -1 -2 -1 0], ⟨0 7 9 13 12 11]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~9/7 = 443.7877
- POTE: ~2 = 1200.000, ~9/7 = 443.506
Optimal ET sequence: 8d, 19e, 27
Badness: 0.023258
Bisensi
Bisensi has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)).
Subgroup: 2.3.5.7.11
Comma list: 121/120, 126/125, 245/243
Mapping:
- common form: [⟨2 -2 -2 -4 1], ⟨0 7 9 13 8]]
- mapping generators: ~99/70, ~9/7
- mingen form: [⟨2 5 7 9 9], ⟨0 -7 -9 -13 -8]]
- mapping generators: ~99/70, ~11/10
Optimal tunings:
- CTE: ~99/70 = 600.000, ~9/7 = 443.3688 (~11/10 = 156.6312)
- POTE: ~99/70 = 600.000, ~9/7 = 443.308 (~11/10 = 156.692)
Optimal ET sequence: 8d, …, 38d, 46
Badness: 0.041723
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 126/125, 169/168
Mapping:
- common form: [⟨2 -2 -2 -4 1 0], ⟨0 7 9 13 8 10]]
- mapping generators: ~99/70, ~9/7
- mingen form: [⟨2 5 7 9 9 10], ⟨0 -7 -9 -13 -8 -10]]
- mapping generators: ~99/70, ~11/10
Optimal tunings:
- CTE: ~55/39 = 600.000, ~9/7 = 443.4416, ~11/10 = 156.5584
- POTE: ~55/39 = 600.000, ~9/7 = 443.275, ~11/10 = 156.725
Optimal ET sequence: 8d, …, 38df, 46
Badness: 0.026339
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 91/90, 121/120, 126/125, 154/153, 169/168
Mapping:
- common form: [⟨2 -2 -2 -4 1 0 3], ⟨0 7 9 13 8 10 7]]
- mapping generators: ~99/70, ~9/7
- mingen form: [⟨2 5 7 9 9 10 10], ⟨0 -7 -9 -13 -8 -10 -7]]
- mapping generators: ~99/70, ~11/10
Optimal tunings:
- CTE: ~17/12 = 600.000, ~9/7 = 443.4466 (~11/10 = 156.5534)
Optimal ET sequence: 8d, …, 38df, 46
Badness: 0.0188
Hemisensi
Hemisensi splits the ~9/7 generator in two, each for ~25/22. Its ploidacot is beta-tetradecacot (pergen (P8, ccP5/14)).
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 245/242
Mapping: [⟨1 -1 -1 -2 -3], ⟨0 14 18 26 35]]
- mapping generators: ~2, ~25/22
Optimal tunings:
- CTE: ~2 = 1200.000, ~25/22 = 221.5981
- POTE: ~2 = 1200.000, ~25/22 = 221.605
Optimal ET sequence: 27e, 38d, 65
Badness: 0.048714
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 126/125, 169/168, 243/242
Mapping: [⟨1 -1 -1 -2 -3 0], ⟨0 14 18 26 35 20]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~25/22 = 221.6333
- POTE: ~2 = 1200.000, ~25/22 = 221.556
Optimal ET sequence: 27e, 38df, 65f
Badness: 0.033016
Sensei
Subgroup: 2.3.5.7
Comma list: 225/224, 78732/78125
Mapping: [⟨1 -1 -1 -9], ⟨0 7 9 32]]
- mapping generators: ~2, ~162/125
Wedgie: ⟨⟨ 7 9 32 -2 31 49 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~162/125 = 442.755
Optimal ET sequence: 19, 65d, 84, 103, 187, 290b
Badness: 0.059218
Warrior
Subgroup: 2.3.5.7
Comma list: 5120/5103, 78732/78125
Mapping: [⟨1 -1 -1 15], ⟨0 7 9 -33]]
- mapping generators: ~2, ~162/125
Wedgie: ⟨⟨ 7 9 -33 -2 -72 -102 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~162/125 = 443.289
Optimal ET sequence: 46, 111, 157, 268cd
Badness: 0.118239
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 1331/1323, 5120/5103
Mapping: [⟨1 -1 -1 15 9], ⟨0 7 9 -33 -15]]
- mapping generators: ~2, ~128/99
Optimal tuning (POTE): ~2 = 1200.000, ~128/99 = 443.274
Optimal ET sequence: 46, 65d, 111, 268cd, 379cdd
Badness: 0.046383
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 847/845, 1331/1323
Mapping: [⟨1 -1 -1 15 9 17], ⟨0 7 9 -33 -15 -36]]
- mapping generators: ~2, ~84/65
Optimal tuning (POTE): ~2 = 1200.000, ~84/65 = 443.270
Optimal ET sequence: 46, 65d, 111, 268cd, 379cddf
Badness: 0.028735
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 256/255, 351/350, 442/441, 715/714
Mapping: [⟨1 -1 -1 15 9 17 10], ⟨0 7 9 -33 -15 -36 -16]]
- mapping generators: ~2, ~22/17
Optimal tuning (POTE): ~2 = 1200.000, ~22/17 = 443.270
Optimal ET sequence: 46, 65d, 111, 268cdg, 379cddfg
Badness: 0.018105
Bison
Bison has a 1/2-octave period. Its ploidacot is diploid delta-heptacot (pergen (P8/2, ccP5/7)). Related page: Bison/Eliora's Approach.
Subgroup: 2.3.5.7
Comma list: 6144/6125, 78732/78125
- common form: [⟨2 -2 -2 13], ⟨0 7 9 -10]]
- mapping generators: ~567/400, ~162/125
- mingen form: [⟨2 5 7 3], ⟨0 -7 -9 10]]
- mapping generators: ~567/400, ~35/32
Wedgie: ⟨⟨ 14 18 -20 -4 -71 -97 ]]
Optimal tuning (POTE): ~567/400 = 600.000, ~162/125 = 443.075 (~35/32 = 156.925)
Optimal ET sequence: 8, 38, 46, 84, 130
Badness: 0.070375
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 6144/6125, 8019/8000
Mapping:
- common form: [⟨2 -2 -2 13 18], ⟨0 7 9 -10 -15]]
- mapping generators: ~567/400, ~162/125
- mingen form: [⟨2 5 7 3 3], ⟨0 -7 -9 10 15]]
- mapping generators: ~567/400, ~35/32
Optimal tuning (POTE): ~99/70 = 600.000, ~162/125 = 443.117 (~35/32 = 156.883)
Optimal ET sequence: 46, 84, 130, 306, 436ce
Badness: 0.037132
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 10985/10976
Mapping:
- common form: [⟨2 -2 -2 13 18 17], ⟨0 7 9 -10 -15 -13]]
- mapping generators: ~55/39, ~162/125
- mingen form: [⟨2 5 7 3 3 4], ⟨0 -7 -9 10 15 13]]
- mapping generators: ~55/39, ~35/32
Optimal tuning (POTE): ~55/39 = 600.000, ~162/125 = 443.096 (~35/32 = 156.904)
Optimal ET sequence: 46, 84, 130, 566ce, 596cef
Badness: 0.023504
Subpental
Subpental splits the generator ~14/9 in two. Its ploidacot is theta-tetradecacot (pergen (P8, c4P4/14)).
Subgroup: 2.3.5.7
Comma list: 3136/3125, 19683/19600
Mapping: [⟨1 6 8 17], ⟨0 -14 -18 -45]]
- mapping generators: ~2, ~56/45
Wedgie: ⟨⟨ 14 18 45 -4 32 54 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~56/45 = 378.467
Optimal ET sequence: 19, 111, 130, 929c, 1059c, 1189bc, 1319bc
Badness: 0.054303
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 3136/3125, 8019/8000
Mapping: [⟨1 6 8 17 -6], ⟨0 -14 -18 -45 30]]
Optimal tuning (POTE): ~2 = 1200.000, ~56/45 = 378.440
Optimal ET sequence: 19, 111, 130, 241, 371ce, 501cde, 872cde
Badness: 0.045352
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 676/675, 3136/3125
Mapping: [⟨1 6 8 17 -6 16], ⟨0 -14 -18 -45 30 -39]]
Optimal tuning (POTE): ~2 = 1200.000, ~56/45 = 378.437
Optimal ET sequence: 19, 111, 130, 241, 371ce
Badness: 0.023940
Heinz
Heinz splits the generator ~18/7 in three. Its ploidacot is theta-21-cot (pergen (P8, c9P5/21)). A notable tuning of heinz not shown below for those who like 19edo's representation of the 5-limit is 57edo (57 = 103 - 46).
Subgroup: 2.3.5.7
Comma list: 1029/1024, 78732/78125
Mapping: [⟨1 -8 -10 6], ⟨0 21 27 -7]]
- mapping generators: ~2, ~48/35
Wedgie: ⟨⟨ 21 27 -7 -6 -70 -92 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~48/35 = 546.815
Optimal ET sequence: 46, 103, 149, 699bdd
Badness: 0.115385
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 78732/78125
Mapping: [⟨1 -8 -10 6 3], ⟨0 21 27 -7 1]]
- mapping generators: ~2, ~11/8
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.631
Optimal ET sequence: 46, 103, 149, 252e, 401bdee
Badness: 0.042412
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 -8 -10 6 3 11], ⟨0 21 27 -7 1 -16]]
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.629
Optimal ET sequence: 46, 103, 149, 252ef, 401bdeef
Badness: 0.025779
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440, 847/845
Mapping: [⟨1 -8 -10 6 3 11 5], ⟨0 21 27 -7 1 -16 -2]]
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.635
Optimal ET sequence: 46, 103, 149, 252ef, 401bdeef
Badness: 0.018479
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 171/170, 209/208, 351/350, 385/384, 441/440, 969/968
Mapping: [⟨1 -8 -10 6 3 11 5 12], ⟨0 21 27 -7 1 -16 -2 -17]]
Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 547.614
Optimal ET sequence: 46, 103h, 149h, 252efhh
Badness: 0.019005
Trisensory
Trisensory has 1/3-octave period. Its ploidacot is triploid digamma-heptacot (pergen (P8/3, M6/21)).
Subgroup: 2.3.5.7
Comma list: 1728/1715, 78732/78125
Mapping: [⟨3 4 6 8], ⟨0 7 9 4]]
- mapping generators: ~63/50, ~36/35
Wedgie: ⟨⟨ 21 27 12 -6 -40 -48 ]]
Optimal tuning (POTE): ~63/50 = 400.000, ~36/35 = 43.147
Optimal ET sequence: 27, 57, 84, 111, 195d, 306d
Badness: 0.089740
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539, 78732/78125
Mapping: [⟨3 4 6 8 8], ⟨0 7 9 4 22]]
Optimal tuning (POTE): ~63/50 = 400.000, ~36/35 = 43.292
Optimal ET sequence: 27e, 84e, 111
Badness: 0.058413
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539, 9295/9261
Mapping: [⟨3 4 6 8 8 11], ⟨0 7 9 4 22 1]]
- mapping generators: ~49/39, ~36/35
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.288
Optimal ET sequence: 27e, 84e, 111
Badness: 0.034829
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 176/175, 351/350, 442/441, 540/539, 715/714
Mapping: [⟨3 4 6 8 8 11 10], ⟨0 7 9 4 22 1 21]]
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.276
Optimal ET sequence: 27eg, 84e, 111
Badness: 0.024120
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 176/175, 286/285, 324/323, 351/350, 400/399, 476/475
Mapping: [⟨3 4 6 8 8 11 10 12], ⟨0 7 9 4 22 1 21 7]]
Optimal tuning (POTE): ~49/39 = 400.000, ~36/35 = 43.292
Optimal ET sequence: 27eg, 84e, 111
Badness: 0.018466