Quintaleap family
The quintaleap family tempers out [37 -16 -5⟩, equating a stack of two Pythagorean commas with a stack of five schismas, making it a member of the schismic-Pythagorean equivalence continuum. It is also the temperament where 4/3 is identified by a stack of five 135/128's.
Quintaleap
Subgroup: 2.3.5
Comma list: [37 -16 -5⟩ = 137438953472/134521003125
Mapping: [⟨1 2 1], ⟨0 -5 16]]
POTE generator: ~135/128 = 99.267
Badness: 0.444506
2.3.5.17.19 subgroup
Subgroup: 2.3.5.17.19
Comma list: 256/255, 361/360, 4624/4617
Sval mapping: [⟨1 2 1 5 4], ⟨0 -5 16 -11 3]]
Gencom: [2 18/17; 256/255 361/360 4624/4617]
POTE generator: ~18/17 = 99.276
Vals: Template:Val list
Badness: 0.014623
Quintupole
The quintupole temperament tempers out the octagar comma and the mistisma (458752/455625) in the 7-limit; 896/891 (pentacircle), 1375/1372 (moctdel), and 4375/4356 (fantares, luluzoquadyo) in the 11-limit. The word "quintupole" means five poles, but also a play on the words "quintuple" and "polypyth". It is so named because the generator is 1/5 of the polypyth fourth (~4/3, about 495.8 cents). Proper pronunciation of the word "quintupole" is /'kwɪntʊpəʊl/ or /'kwɪntʊpoʊl/, like as "quin-to-pole". Not to be confused with quintapole temperament (12&85).
Subgroup: 2.3.5.7
Comma list: 4000/3969, 458752/455625
Mapping: [⟨1 2 1 0], ⟨0 -5 16 34]]
Wedgie: ⟨⟨ 5 -16 -34 -37 -68 -34 ]]
POTE generator: ~135/128 = 99.175
Optimal ET sequence: 12, 97, 109, 121
Badness: 0.111620
11-limit
Subgroup: 2.3.5.7.11
Comma list: 896/891, 1375/1372, 4375/4356
Mapping: [⟨1 2 1 0 -1], ⟨0 -5 16 34 54]]
POTE generator: ~35/33 = 99.156
Vals: Template:Val list
Badness: 0.056501
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 364/363, 625/624, 2704/2695
Mapping: [⟨1 2 1 0 -1 -2], ⟨0 -5 16 34 54 69]]
POTE generator: ~35/33 = 99.165
Vals: Template:Val list
Badness: 0.038431
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 256/255, 352/351, 364/363, 375/374, 442/441
Mapping: [⟨1 2 1 0 -1 -2 5], ⟨0 -5 16 34 54 69 -11]]
POTE generator: ~18/17 = 99.172
Vals: Template:Val list
Badness: 0.028721
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 190/189, 256/255, 352/351, 361/360, 364/363, 375/374
Mapping: [⟨1 2 1 0 -1 -2 5 4], ⟨0 -5 16 34 54 69 -11 3]]
POTE generator: ~18/17 = 99.164
Vals: Template:Val list
Badness: 0.023818
Quintapole
Aside from the marvel comma, the quintapole temperament (12&85) tempers out 7812500/7411887 (sepru-atritriyo). In the 11-limit, it tempers out the ptolemisma (100/99) as well as 85184/84035 (trilo-aquinru-agu). It is so named for the following reasons - it has the same commas as the apollo temperament, and its generator is a semitone five of which gives a flat fourth (~4/3, about 495 cents). Proper pronunciation of the word "quintapole" is /'kwɪntəpəʊl/ or /'kwɪntəpoʊl/, like as "quint-a-pole". Not to be confused with quintupole temperament (12&121).
Subgroup: 2.3.5.7
Comma list: 225/224, 7812500/7411887
Mapping: [⟨1 2 1 1], ⟨0 -5 16 22]]
POTE generator: ~21/20 = 98.994
Badness: 0.192498
11-limit
Subgroup: 2.3.5.7.11
Comma list: 100/99, 225/224, 85184/84035
Mapping: [⟨1 2 1 1 0], ⟨0 -5 16 22 42]]
POTE generator: ~21/20 = 98.954
Vals: Template:Val list
Badness: 0.104353
Quinticosiennic
The quinticosiennic temperament (12&145) tempers out the hemifamity comma (5120/5103) and 395136/390625 (trizo-aquadbigu) in the 7-limit; 441/440 (werckisma), 896/891 (pentacircle), and 78408/78125 (lolosepgu) in the 11-limit. The word "quinticosiennic" means 5 (quintuple) × 29 (είκοσι εννέα) = 145, and so named because 1/5 of 29EDO fourth, i.e. 12\145, is a possible generator.
Subgroup: 2.3.5.7
Comma list: 5120/5103, 395136/390625
Mapping: [⟨1 2 1 -1], ⟨0 -5 16 46]]
Wedgie: ⟨⟨ 5 -16 -46 -37 -87 -62 ]]
POTE generator: ~135/128 = 99.345
Badness: 0.158041
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 78408/78125
Mapping: [⟨1 2 1 -1 -2], ⟨0 -5 16 46 66]]
POTE generator: ~35/33 = 99.318
Vals: Template:Val list
Badness: 0.080674
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 78408/78125
Mapping: [⟨1 2 1 -1 -2 -3], ⟨0 -5 16 46 66 81]]
POTE generator: ~35/33 = 99.307
Vals: Template:Val list
Badness: 0.052464
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 3757/3750
Mapping: [⟨1 2 1 -1 -2 -3 5], ⟨0 -5 16 46 66 81 -11]]
POTE generator: ~18/17 = 99.308
Vals: Template:Val list
Badness: 0.037108
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 352/351, 361/360, 364/363, 476/475
Mapping: [⟨1 2 1 -1 -2 -3 5 4], ⟨0 -5 16 46 66 81 -11 3]]
POTE generator: ~18/17 = 99.303
Vals: Template:Val list
Badness: 0.028440