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
• Waage, {225/224, 250047/250000} → Compton family
• Tritikleismic, {1029/1024, 15625/15552} → Kleismic family
• Trisensory, {1728/1715, 78732/78125} → Sensipent family
• Ennealimmal, {2401/2400, 4375/4374} → Ragismic microtemperaments
• Misty, {3136/3125, 5120/5103} → Misty family
• Nessafof, {6144/6125, 250047/250000} → Porwell temperaments
• Chromat, {10976/10935, 235298/234375} → Hemimage temperaments
• Term, {32805/32768, 250047/250000} → Schismatic family
• Caleb, {33075/32768, 250047/250000} → Mirwomo temperaments
• Mutt, {65625/65536, 250047/250000} → Horwell temperaments
• Stearnscape, {118098/117649, 250047/250000} → Stearnsmic clan
• Tritricot, {250047/250000, 11785390260224/11767897353375} → Tricot family

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

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

Optimal GPV sequence: Template:Val list

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

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

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

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

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

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

Optimal GPV sequence: Template:Val list

Badness: 0.014915