Lehmerismic temperaments

These are rank-3 temperaments tempering out 3025/3024, but we can begin by looking at the rank-4 temperament.

Temperaments discussed elsewhere are:

• oxpecker, {121/120, 126/125} → Starling family #Oxpecker
• manwe, {176/175, 1331/1323} → Valinorsmic temperaments #Manwe
• spectacle, {225/224, 243/242} → Marvel family #Spectacle
• portent, {385/384, 441/440} → Gamelismic family #Portent
• indra, {540/539, 1375/1372} → Mirkwai family #Indra
• tolerant, {896/891, 2200/2187} → Tolermic family #Tolerant
• freya, {2401/2400, 3025/3024} → Breed family #Freya
• triglav, {3025/3024, 3136/3125} → Hemimean family #Triglav
• thor, {3025/3024, 4375/4374} → Ragismic family #Thor
• kapo, {3025/3024, 5120/5103} → Hemifamity family #Kapo

Lehmerismic

Subgroup: 2.3.5.7.11

Comma list: 3025/3024

Mapping: [⟨1 0 0 0 2], ⟨0 1 0 1 2], ⟨0 0 1 0 -1], ⟨0 0 0 2 1]]

Mapping generators: ~2, ~3, ~5, ~55/36

Tyr

See also: Landscape family

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 102487/102400

Mapping: [⟨3 0 0 4 8], ⟨0 2 0 -4 1], ⟨0 0 1 2 0]]

Mapping generators: ~63/50, ~400/231, ~5

Badness: 0.259 × 10^-3

Skadi

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 703125/702464

Mapping: [⟨1 0 5 8 1], ⟨0 1 1 3 2], ⟨0 0 -6 -14 -1]]

Mapping generators: ~2, ~3, ~18/11

Badness: 0.349 × 10^-3

Ganesha

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 5632/5625

Mapping: [⟨1 0 0 -22 -9], ⟨0 1 0 1 2], ⟨0 0 1 10 4]]

Mapping generators: ~2, ~3, ~5

Badness: 0.390 × 10^-3

Hanuman

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993

Mapping: [⟨1 2 0 -8 1], ⟨0 -3 0 11 1], ⟨0 0 1 4 1]]

Mapping generators: ~2, ~11/10, ~5

Badness: 0.500 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1575/1573, 2080/2079

Mapping: [⟨1 2 0 -8 1 -6], ⟨0 -3 0 11 1 3], ⟨0 0 1 4 1 4]]

Mapping generators: ~2, ~11/10, ~5

Vals: Template:Val list

Badness: 0.653 × 10^-3

Lux

7-limit

Subgroup: 2.3.5.7

Comma list: 26843545600/26795786661

Mapping: [⟨1 0 0 6], ⟨0 1 4 -1], ⟨0 0 -5 -2]]

Wedgie: ⟨⟨⟨ 5 2 13 30 ]]]

POTE generators: ~3/2 = 702.1152, ~40960/35721 = 235.5941

Badness: 1.709 × 10^-3

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 131072/130977

Mapping: [⟨1 0 0 6 5], ⟨0 1 4 -1 -3], ⟨0 0 -5 -2 4]]

Wedgie: ⟨⟨⟨ 5 2 -4 13 -1 10 30 25 34 71 ]]]

POTE generators: ~3/2 = 702.1117, ~55/48 = 235.5784

Badness: 0.5083 × 10^-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095

Mapping: [⟨1 0 0 6 5 6], ⟨0 1 4 -1 -3 -5], ⟨0 0 -5 -2 4 7]]

POTE generators: ~3/2 = 702.0674, ~55/48 = 235.5870

Vals: Template:Val list

Badness: 0.3602 × 10^-3