Landscape microtemperaments

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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:

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

Vals12, 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

Vals60, 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

Vals15, 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

Vals171, 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

Vals87, 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

Vals: 87, 183, 270

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

Vals111, 159, 270

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

Vals: 111, 159, 270

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

Vals: 111, 159, 270

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

Vals: 111, 159, 270

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

Vals: 111, 159, 270

Badness: 0.014915