Sensamagic clan: Difference between revisions
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The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. | The '''sensamagic clan''' tempers out the sensamagic comma, [[245/243]], a triprime [[comma]] with no factors of 2, {{val| 0 -5 1 2 }} to be exact. | ||
= Lambda = | == Lambda == | ||
Subgroup: 3.5.7 | Subgroup: 3.5.7 | ||
| Line 16: | Line 16: | ||
[[Val]]s: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | [[Val]]s: [[4edt|b4]], [[9edt|b9]], [[13edt|b13]], [[56edt|b56]], [[69edt|b69]], [[82edt|b82]], [[95edt|b95]] | ||
== Extensions == | === Extensions === | ||
For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], [[Amity family #Bamity|bamity]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere. | For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as [[Father family #Father|father]], [[Dicot family #Sidi|sidi]], [[Meantone family #Godzilla|godzilla]], [[Porcupine family #Hedgehog|hedgehog]], [[Archytas clan #Superpyth|superpyth]], [[Augmented family #Hemiaug|hemiaug]], [[Magic family #magic|magic]], [[Gamelismic clan#Rodan|rodan]], [[Tetracot family #Octacot|octacot]], [[Diaschismic family #Shrutar|shrutar]], [[Amity family #Bamity|bamity]], and [[Kleismic family #Clyde|clyde]] discussed elsewhere. | ||
Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], sensamagic, for which [[283edo]] is the [[optimal patent val]]. | Tempering out 245/243 alone in the full 7-limit leads to a [[Planar temperament|rank-3 temperament]], sensamagic, for which [[283edo]] is the [[optimal patent val]]. | ||
= Sensi = | == Sensi == | ||
{{main| Sensi }} | {{main| Sensi }} | ||
{{see also| Sensipent family #Sensi }} | {{see also| Sensipent family #Sensi }} | ||
| Line 27: | Line 27: | ||
Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], 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." | Sensi tempers out [[126/125]], [[686/675]] and [[4375/4374]] in addition to [[245/243]], 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." | ||
== Septimal sensi == | === Septimal sensi === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 54: | Line 54: | ||
[[Badness]]: 0.025622 | [[Badness]]: 0.025622 | ||
=== Sensation === | ==== Sensation ==== | ||
Subgroup: 2.3.5.7.13 | Subgroup: 2.3.5.7.13 | ||
| Line 69: | Line 69: | ||
Vals: {{Val list| 19, 27, 46, 111de, 157de }} | Vals: {{Val list| 19, 27, 46, 111de, 157de }} | ||
== Sensor == | === Sensor === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 82: | Line 82: | ||
Badness: 0.037942 | Badness: 0.037942 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 95: | Line 95: | ||
Badness: 0.025575 | Badness: 0.025575 | ||
== Sensis == | === Sensis === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 108: | Line 108: | ||
Badness: 0.028680 | Badness: 0.028680 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 121: | Line 121: | ||
Badness: 0.020017 | Badness: 0.020017 | ||
== Sensus == | === Sensus === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 134: | Line 134: | ||
Badness: 0.029486 | Badness: 0.029486 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 147: | Line 147: | ||
Badness: 0.020789 | Badness: 0.020789 | ||
== Sensa == | === Sensa === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 160: | Line 160: | ||
Badness: 0.036835 | Badness: 0.036835 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 173: | Line 173: | ||
Badness: 0.023258 | Badness: 0.023258 | ||
== Hemisensi == | === Hemisensi === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 186: | Line 186: | ||
Badness: 0.048714 | Badness: 0.048714 | ||
= Bohpier = | == Bohpier == | ||
Bohpier is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | Bohpier is named after its [[Relationship between Bohlen-Pierce and octave-ful temperaments|interesting relationship with the non-octave Bohlen-Pierce equal temperament]]. | ||
| Line 201: | Line 201: | ||
[[Badness]]: 0.860534 | [[Badness]]: 0.860534 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 216: | Line 216: | ||
[[Badness]]: 0.068237 | [[Badness]]: 0.068237 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 229: | Line 229: | ||
Badness: 0.033949 | Badness: 0.033949 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 242: | Line 242: | ||
Badness: 0.024864 | Badness: 0.024864 | ||
== Music == | === Music === | ||
by [[Chris Vaisvil]]: | by [[Chris Vaisvil]]: | ||
* [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3] | * [http://micro.soonlabel.com/bophier/bophier-1.mp3 bophier-1.mp3] | ||
* [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | * [http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 bophier-12equal-six-octaves.mp3] | ||
= Escaped = | == Escaped == | ||
{{see also| Escapade family #Escaped }} | {{see also| Escapade family #Escaped }} | ||
| Line 266: | Line 266: | ||
[[Badness]]: 0.088746 | [[Badness]]: 0.088746 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 279: | Line 279: | ||
Badness: 0.035844 | Badness: 0.035844 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 292: | Line 292: | ||
Badness: 0.031366 | Badness: 0.031366 | ||
= Salsa = | == Salsa == | ||
{{see also| Schismatic family }} | {{see also| Schismatic family }} | ||
| Line 309: | Line 309: | ||
[[Badness]]: 0.080152 | [[Badness]]: 0.080152 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 322: | Line 322: | ||
Badness: 0.039444 | Badness: 0.039444 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 335: | Line 335: | ||
Badness: 0.030793 | Badness: 0.030793 | ||
= Pycnic = | == Pycnic == | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | ||
| Line 352: | Line 352: | ||
[[Badness]]: 0.073735 | [[Badness]]: 0.073735 | ||
= Cohemiripple = | == Cohemiripple == | ||
{{see also| Ripple family }} | {{see also| Ripple family }} | ||
| Line 369: | Line 369: | ||
[[Badness]]: 0.190208 | [[Badness]]: 0.190208 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 382: | Line 382: | ||
Badness: 0.082716 | Badness: 0.082716 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 395: | Line 395: | ||
Badness: 0.049933 | Badness: 0.049933 | ||
= Superthird = | == Superthird == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 410: | Line 410: | ||
[[Badness]]: 0.139379 | [[Badness]]: 0.139379 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 423: | Line 423: | ||
Badness: 0.070917 | Badness: 0.070917 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 436: | Line 436: | ||
Badness: 0.052835 | Badness: 0.052835 | ||
= Magus = | == Magus == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 449: | Line 449: | ||
[[Badness]]: 0.360162 | [[Badness]]: 0.360162 | ||
== 7-limit == | === 7-limit === | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 464: | Line 464: | ||
[[Badness]]: 0.1084 | [[Badness]]: 0.1084 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 477: | Line 477: | ||
Badness: 0.045108 | Badness: 0.045108 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 490: | Line 490: | ||
Badness: 0.043024 | Badness: 0.043024 | ||
= Leapweek = | == Leapweek == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 503: | Line 503: | ||
[[Badness]]: 0.140577 | [[Badness]]: 0.140577 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 516: | Line 516: | ||
Badness: 0.050679 | Badness: 0.050679 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 529: | Line 529: | ||
Badness: 0.032727 | Badness: 0.032727 | ||
= Semiwolf = | == Semiwolf == | ||
[[Subgroup]]: 3/2.7/4.5/2 | [[Subgroup]]: 3/2.7/4.5/2 | ||
| Line 540: | Line 540: | ||
[[Vals]]: {{val list|8edf, 11edf, 13edf}} | [[Vals]]: {{val list|8edf, 11edf, 13edf}} | ||
== Semilupine == | === Semilupine === | ||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | [[Subgroup]]: 3/2.7/4.5/2.11/4 | ||
| Line 551: | Line 551: | ||
[[Vals]]: {{val list|8edf, 13edf}} | [[Vals]]: {{val list|8edf, 13edf}} | ||
== Hemilycan == | === Hemilycan === | ||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | [[Subgroup]]: 3/2.7/4.5/2.11/4 | ||
Revision as of 03:48, 2 June 2021
The sensamagic clan tempers out the sensamagic comma, 245/243, a triprime comma with no factors of 2, ⟨0 -5 1 2] to be exact.
Lambda
Subgroup: 3.5.7
Comma list: 245/243
Sval mapping: [⟨1 1 2], ⟨0 -2 1]]
Sval mapping generators: ~3, ~9/7
Gencom mapping: [⟨0 1 1 2], ⟨0 0 -2 1]]
POTE generator: ~9/7 = 440.4881
Vals: b4, b9, b13, b56, b69, b82, b95
Extensions
For full 7-limit extensions, we have sensi, bohpier, escaped, salsa, pycnic, cohemiripple, superthird, magus and leapweek discussed below, as well as father, sidi, godzilla, hedgehog, superpyth, hemiaug, magic, rodan, octacot, shrutar, bamity, and clyde discussed elsewhere.
Tempering out 245/243 alone in the full 7-limit leads to a rank-3 temperament, sensamagic, for which 283edo is the optimal patent val.
Sensi
Sensi tempers out 126/125, 686/675 and 4375/4374 in addition to 245/243, 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."
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 ]]
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: 0.025622
Sensation
Subgroup: 2.3.5.7.13
Comma list: 91/90, 126/125, 169/168
Sval mapping: [⟨1 -1 -1 -2 0], ⟨0 7 9 13 10]]
Gencom mapping: [⟨1 -1 -1 -2 0 0], ⟨0 7 9 13 0 10]]
Gencom: [2 9/7; 91/90 126/125 169/168]
POTE generator: ~9/7 = 443.322
Vals: Template:Val list
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]]
POTE generator: ~9/7 = 443.294
Vals: Template:Val list
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]]
POTE generator: ~9/7 = 443.321
Vals: Template:Val list
Badness: 0.025575
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]]
POTE generator: ~9/7 = 443.962
Vals: Template:Val list
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]]
POTE generator: ~9/7 = 443.945
Vals: Template:Val list
Badness: 0.020017
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]]
POTE generator: ~9/7 = 443.626
Vals: Template:Val list
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]]
POTE generator: ~9/7 = 443.559
Vals: Template:Val list
Badness: 0.020789
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]]
POTE generator: ~9/7 = 443.518
Vals: Template:Val list
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]]
POTE generator: ~9/7 = 443.506
Vals: Template:Val list
Badness: 0.023258
Hemisensi
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]]
POTE generator: ~25/22 = 221.605
Vals: Template:Val list
Badness: 0.048714
Bohpier
Bohpier is named after its interesting relationship with the non-octave Bohlen-Pierce equal temperament.
Subgroup: 2.3.5
Comma list: 1220703125/1162261467
Mapping: [⟨1 0 0], ⟨0 13 19]]
POTE generator: ~27/25 = 146.476
Badness: 0.860534
7-limit
Subgroup: 2.3.5.7
Comma list: 245/243, 3125/3087
Mapping: [⟨1 0 0 0], ⟨0 13 19 23]]
Wedgie: ⟨⟨ 13 19 23 0 0 0 ]]
POTE generator: ~27/25 = 146.474
Badness: 0.068237
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 1344/1331
POTE generator: ~12/11 = 146.545
Mapping: [⟨1 0 0 0 2], ⟨0 13 19 23 12]]
Vals: Template:Val list
Badness: 0.033949
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 275/273
POTE generator: ~12/11 = 146.603
Mapping: [⟨1 0 0 0 2 2], ⟨0 13 19 23 12 14]]
Vals: Template:Val list
Badness: 0.024864
Music
by Chris Vaisvil:
Escaped
This temperament is also known as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. Not to be confused with 19e&27 temperament (sensi extension).
Subgroup: 2.3.5.7
Comma list: 245/243, 65625/65536
Mapping: [⟨1 2 2 4], ⟨0 -9 7 -26]]
Wedgie: ⟨⟨ 9 -7 26 -32 16 80 ]]
POTE generator: ~28/27 = 55.122
Badness: 0.088746
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 4000/3993
Mapping: [⟨1 2 2 4 3], ⟨0 -9 7 -26 10]]
POTE generator: ~28/27 = 55.126
Vals: Template:Val list
Badness: 0.035844
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 245/243, 352/351, 385/384, 625/624
Mapping: [⟨1 2 2 4 3 2], ⟨0 -9 7 -26 10 37]]
POTE generator: ~28/27 = 55.138
Vals: Template:Val list
Badness: 0.031366
Salsa
Subgroup: 2.3.5.7
Comma list: 245/243, 32805/32768
Mapping: [⟨1 1 7 -1], ⟨0 2 -16 13]]
Wedgie: ⟨⟨ 2 -16 13 -30 15 75 ]]
POTE generator: ~128/105 = 351.049
Badness: 0.080152
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 245/242, 385/384
Mapping: [⟨1 1 7 -1 2], ⟨0 2 -16 13 5]]
POTE generator: ~11/9 = 351.014
Vals: Template:Val list
Badness: 0.039444
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 243/242, 245/242
Mapping: [⟨1 1 7 -1 2 4], ⟨0 2 -16 13 5 -1]]
POTE generator: ~11/9 = 351.025
Vals: Template:Val list
Badness: 0.030793
Pycnic
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.
Subgroup: 2.3.5.7
Comma list: 245/243, 525/512
Mapping: [⟨1 3 -1 8], ⟨0 -3 7 -11]]
Wedgie: ⟨⟨ 3 -7 11 -18 9 45 ]]
POTE generator: ~45/32 = 567.720
Badness: 0.073735
Cohemiripple
Subgroup: 2.3.5.7
Comma list: 245/243, 1323/1250
Mapping: [⟨1 -3 -5 -5], ⟨0 10 16 17]]
Wedgie: ⟨⟨ 10 16 17 2 -1 -5 ]]
POTE generator: ~7/5 = 549.944
Badness: 0.190208
11-limit
Subgroup: 2.3.5.7.11
Comma list: 77/75, 243/242, 245/242
Mapping: [⟨1 -3 -5 -5 -8], ⟨0 10 16 17 25]]
POTE generator: ~7/5 = 549.945
Vals: Template:Val list
Badness: 0.082716
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 77/75, 147/143, 243/242
Mapping: [⟨1 -3 -5 -5 -8 -5], ⟨0 -10 -16 -17 -25 -19]]
POTE generator: ~7/5 = 549.958
Vals: Template:Val list
Badness: 0.049933
Superthird
Subgroup: 2.3.5.7
Comma list: 245/243, 78125/76832
Mapping: [⟨1 -5 -5 -10], ⟨0 18 20 35]]
Wedgie: ⟨⟨ 18 20 35 -10 5 25 ]]
POTE generator: ~9/7 = 439.076
Badness: 0.139379
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 245/243, 78125/76832
Mapping: [⟨1 -5 -5 -10 2], ⟨0 18 20 35 4]]
POTE generator: ~9/7 = 439.152
Vals: Template:Val list
Badness: 0.070917
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 100/99, 144/143, 196/195, 1375/1352
Mapping: [⟨1 -5 -5 -10 2 -8], ⟨0 18 20 35 4 32]]
POTE generator: ~9/7 = 439.119
Vals: Template:Val list
Badness: 0.052835
Magus
Subgroup: 2.3.5
Comma list: 50331648/48828125
Mapping: [⟨1 -2 2], ⟨0 11 1]]
POTE generator: ~5/4 = 391.225
Badness: 0.360162
7-limit
Subgroup: 2.3.5.7
Comma list: 245/243, 28672/28125
Mapping: [⟨1 -2 2 -6], ⟨0 11 1 27]]
Wedgie: ⟨⟨ 11 1 27 -24 12 60 ]]
POTE generator: ~5/4 = 391.465
Badness: 0.1084
11-limit
Subgroup: 2.3.5.7.11
Comma list: 176/175, 245/243, 1331/1323
Mapping: [⟨1 -2 2 -6 -6], ⟨0 11 1 27 29]]
POTE generator: ~5/4 = 391.503
Vals: Template:Val list
Badness: 0.045108
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 176/175, 245/243, 1331/1323
Mapping: [⟨1 -2 2 -6 -6 5], ⟨0 11 1 27 29 -4]]
POTE generator: ~5/4 = 391.366
Vals: Template:Val list
Badness: 0.043024
Leapweek
Subgroup: 2.3.5.7
Comma list: 245/243, 2097152/2066715
Mapping: [⟨1 1 17 -6], ⟨0 1 -25 15]]
POTE generator: ~3/2 = 704.536
Badness: 0.140577
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/243, 385/384, 1331/1323
Mapping: [⟨1 1 17 -6 -3], ⟨0 1 -25 15 11]]
POTE generator: ~3/2 = 704.554
Vals: Template:Val list
Badness: 0.050679
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 245/243, 352/351, 364/363
Mapping: [⟨1 1 17 -6 -3 -1], ⟨0 1 -25 15 11 8]]
POTE generator: ~3/2 = 704.571
Vals: Template:Val list
Badness: 0.032727
Semiwolf
Subgroup: 3/2.7/4.5/2
Mapping: [⟨1 1 3], ⟨0 1 -2]]
POL2 generator: ~7/6 = 262.1728
Semilupine
Subgroup: 3/2.7/4.5/2.11/4
Mapping: [⟨1 1 3 4], ⟨0 1 -2 -4]]
POL2 generator: ~7/6 = 264.3771
Hemilycan
Subgroup: 3/2.7/4.5/2.11/4
Mapping: [⟨1 1 3 1], ⟨0 1 -2 4]]
POL2 generator: ~7/6 = 261.5939