Landscape microtemperaments
Landscape microtemperaments are rank-2 temperaments tempering out the landscape comma ([-4 6 -6 3⟩ = 250047/250000).
Landscape rank-2 temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are:
- Augene, {64/63, 126/125} → Augmented family #Augene
- Waage, {225/224, 250047/250000} → Compton family #Compton
- Tritikleismic, {1029/1024, 15625/15552} → Kleismic family #Tritikleismic
- Ennealimmal, {2401/2400, 4375/4374} → Ragismic microtemperaments #Ennealimmal
- Misty, {3136/3125, 5120/5103} → Hemimean clan #Misty
- Nessafof, {6144/6125, 250047/250000} → Porwell temperaments #Nessafof
- Chromat, {10976/10935, 235298/234375} → Hemimage temperaments #Chromat
- Term, {32805/32768, 250047/250000} → Schismatic family #Term
- Caleb, {33075/32768, 250047/250000} → Mirwomo temperaments #Caleb
- Mutt, {65625/65536, 250047/250000} → Horwell temperaments #Mutt
- Stearnscape, {118098/117649, 250047/250000} → Stearnsmic clan #Stearnscape
- Tritricot, {250047/250000, 11785390260224/11767897353375} → Tricot family #Tritricot
Sextile
Subgroup: 2.3.5.7
Comma list: 250047/250000, 33554432/33480783
Mapping: [⟨6 0 71 150], ⟨0 1 -6 -14]]
Wedgie: ⟨⟨6 -36 -84 -71 -150 -94]]
POTE generator: ~3/2 = 702.212
Vals: 12, 234d, 246d, 258, 270, 1362c, 1632c, 1902c, 2172c
Badness: 0.070097
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 151263/151250
Mapping: [⟨6 0 71 150 230], ⟨0 1 -6 -14 -22]]
POTE generator: ~3/2 = 702.202
Vals: 12, 246dee, 258e, 270, 822, 1092
Badness: 0.029677
Septichrome
Subgroup: 2.3.5.7
Comma list: 250047/250000, 2460375/2458624
Mapping: [⟨3 3 1 0], ⟨0 5 17 24]]
Wedgie: ⟨⟨15 51 72 46 72 24]]
POTE generator: ~243/224 = 140.367
Vals: 60, 111, 171, 795, 966, 1137, 1308, 5403b, 6711b, 8019bc
Badness: 0.016814
Pnict
Subgroup: 2.3.5.7
Comma list: 250047/250000, 2100875/2097152
Mapping: [⟨3 10 11 6], ⟨0 -13 -10 6]]
Wedgie: ⟨⟨39 30 -18 -43 -138 -126]]
POTE generator: ~192/175 = 161.399
Vals: 15, 141, 156, 171, 2409cd, 2580cd, …, 4461bccddd, 4632bccddd
Badness: 0.045660
Domain
- See also: Minortonic family
Subgroup: 2.3.5.7
Comma list: 250047/250000, 645700815/645657712
Mapping: [⟨3 -3 -9 -8], ⟨0 17 35 36]]
Wedgie: ⟨⟨51 105 108 48 28 -44]]
POTE generator: ~10/9 = 182.467
Vals: 171, 1164, 1335, 1506, 1677, 1848, 2019, 2190, 11943, 13962, 15981, 18000, 20019, 22038
Badness: 0.013979
Avicenna
Subgroup: 2.3.5.7
Comma list: 250047/250000, 29360128/29296875
Mapping: [⟨3 2 8 16], ⟨0 8 -3 -22]]
Wedgie: ⟨⟨24 -9 -66 -70 -172 -128]]
POTE generator: ~1024/945 = 137.768
Vals: 87, 183, 270, 723, 993, 1263, 2796cd, 4059bccd
Badness: 0.062187
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 102487/102400
Mapping: [⟨3 2 8 16 9], ⟨0 8 -3 -22 4]]
POTE generator: ~693/640 = 137.771
Vals: 87, 183, 270, 1263, 1533, 1803c, 2073c
Badness: 0.023085
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 4096/4095
Mapping: [⟨3 2 8 16 9 8], ⟨0 8 -3 -22 4 9]]
POTE generator: ~13/12 = 137.777
Badness: 0.015557
Terture
- See also: Vulture family
Subgroup: 2.3.5.7
Comma list: 250047/250000, 359661568/358722675
Mapping: [⟨3 4 3 2], ⟨0 4 21 34]]
POTE generator: ~392/375 = 75.555
Badness: 0.087156
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 19712/19683, 102487/102400
Mapping: [⟨3 4 3 2 10], ⟨0 4 21 34 2]]
POTE generator: ~392/375 = 75.550
Vals: 111, 159, 270, 1239, 1509, 1779, 2049, 2319
Badness: 0.029326
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024, 10985/10976
Mapping: [⟨3 4 3 2 10 6], ⟨0 4 21 34 2 27]]
POTE generator: ~117/112 = 75.553
Badness: 0.018647
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 936/935, 1001/1000, 4928/4913
Mapping: [⟨3 4 3 2 10 6 10], ⟨0 4 21 34 2 27 12]]
POTE generator: ~117/112 = 75.560
Badness: 0.018705
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 676/675, 715/714, 936/935, 1001/1000, 1216/1215, 1617/1615
Mapping: [⟨3 4 3 2 10 6 10 5], ⟨0 4 21 34 2 27 12 41]]
POTE generator: ~95/91 = 75.560
Badness: 0.013902
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 460/459, 529/528, 676/675, 715/714, 936/935, 1001/1000, 1216/1215
Mapping: [⟨3 4 3 2 10 6 10 5 13], ⟨0 4 21 34 2 27 12 41 3]]
POTE generator: ~24/23 = 75.548
Badness: 0.014915