Landscape microtemperaments

Landscape microtemperaments are rank two temperaments tempering out the landscape comma ([-4 6 -6 3⟩ = 250047/250000).

Landscape rank-two temperaments include sextile, septichrome, pnict, and domain. Considered elsewhere are caleb, chromat, ennealimmal, misty, mutt, nessafof, and term.

Sextile

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

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: Template:Val list

Badness: 0.029677

Septichrome

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

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

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

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

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: Template:Val list

Badness: 0.023085

13-limit

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

Vals: Template:Val list

Badness: 0.015557

Terture

See also: Vulture family

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

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: Template:Val list

Badness: 0.029326

13-limit

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

Vals: Template:Val list

Badness: 0.018647

17-limit

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

Vals: Template:Val list

Badness: 0.018705

19-limit

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

Vals: Template:Val list

Badness: 0.013902

23-limit

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

Vals: Template:Val list

Badness: 0.014915