No-sevens subgroup temperaments
This is a collection of subgroup temperaments which omit the prime harmonic of 7.
Porkypine
Related temperament: Porcupine
Subgroup: 2.3.5.11
Comma list: 55/54, 100/99
Gencom: [2 10/9; 55/54, 100/99]
Gencom mapping: [⟨1 2 3 0 4], ⟨0 -3 -5 0 -4]]
Sval mapping: [⟨1 2 3 4], ⟨0 -3 -5 -4]]
POL2 generator: ~11/10 = 164.078
RMS error: 2.287 cents
Mohaha
Related temperament: mohajira, migration
Subgroup: 2.3.5.11
Comma list: 81/80, 121/120
Gencom: [2 11/9; 81/80 121/120]
Gencom mapping: [⟨1 1 0 0 2], ⟨0 2 8 0 5]]
Sval mapping: [⟨1 1 0 2], ⟨0 2 8 5]]
POL2 generator: ~11/9 = 348.094
RMS error: 1.392 cents
- Music
Mohaha10ping2 by Billy Stiltner
Tetracot
- For full 11- and 13-limit extensions, see Tetracot family.
Subgroup: 2.3.5.11
Comma list: 100/99, 243/242
Gencom: [2 10/9; 100/99 243/242]
Gencom mapping: [⟨1 1 1 0 2], ⟨0 4 9 0 10]]
Sval mapping: [⟨1 1 1 2], ⟨0 4 9 10]]
POL2 generator: ~10/9 = 175.985
RMS error: 1.182 cents
2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 100/99, 144/143, 243/242
Gencom: [2 10/9; 100/99 243/242]
Gencom mapping: [⟨1 1 1 0 2 4], ⟨0 4 9 0 10 -2]]
Sval mapping: [⟨1 1 1 2 4], ⟨0 4 9 10 -2]]
POL2 generator: ~10/9 = 176.196
RMS error: 1.140 cents
Larry
Subgroup: 2.3.5.11
Comma list: 243/242, 4000/3993
Related temperaments: gravity, harry
Gencom: [2 40/27; 243/242 4000/3993]
Gencom mapping: [⟨1 5 12 0 12], ⟨0 -6 -17 0 -15]]
Sval mapping: [⟨1 5 12 12], ⟨0 -6 -17 -15]]
POL2 generator: ~40/27 = 683.166
RMS error: 0.3025 cents
Twentcufo
- For full 11- and 13-limit extensions, see Hemimean clan #Undetrita.
Subgroup: 2.3.5.11
Comma list: 8019/8000, 14641/14580
Gencom: [2 400/363; 8019/8000 14641/14580]
Gencom mapping: [⟨1 0 -2 0 0], ⟨0 11 30 0 24]]
Sval mapping: [⟨1 0 -2 0], ⟨0 11 30 24]]
POL2 generator: ~400/363 = 172.8796
RMS error: 0.2393 cents
Emka
- For full 11- and 13-limit extensions, see Hemimean clan #Emka or Horwell temperaments #Emkay.
Subgroup: 2.3.5.11
Comma list: 4000/3993, 9453125/9437184
Gencom: [2 11/8; 4000/3993 9453125/9437184]
Gencom mapping: [⟨1 14 6 0 3], ⟨0 -27 -8 0 1]]
Sval mapping: [⟨1 14 6 3], ⟨0 -27 -8 1]]
POL2 generator: ~11/8 = 551.7778
RMS error: 0.1188 cents
2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 625/624, 2200/2197, 4000/3993
Gencom: [2 11/8; 625/624 2200/2197 4000/3993]
Gencom mapping: [⟨1 14 6 0 3 6], ⟨0 -27 -8 0 1 -5]]
Sval mapping: [⟨1 14 6 3 6], ⟨0 -27 -8 1 -5]]
POL2 generator: ~11/8 = 551.7753
RMS error: 0.1250 cents
Majvam
- For full 13- and 17-limit extensions, see Parkleiness temperaments #Majvamic or Cataharry temperaments #Majvamoid.
Subgroup: 2.3.5.13
Comma list: 676/675, 127401984/126953125
Gencom: [2 125/96; 676/675 127401984/126953125]
Gencom mapping: [⟨1 10 5 0 0 19], ⟨0 -22 -7 0 0 -40]]
Sval mapping: [⟨1 10 5 19], ⟨0 -22 -7 -40]]
POL2 generator: ~125/96 = 458.988
RMS error: 0.1171 cents
2.3.5.13.17
Subgroup: 2.3.5.13.17
Comma list: 676/675, 2601/2600, 24576/24565
Gencom: [2 125/96; 676/675 2601/2600 24576/24565]
Gencom mapping: [⟨1 10 5 0 0 19 6], ⟨0 -22 -7 0 0 -40 -5]]
Sval mapping: [⟨1 10 5 19 6], ⟨0 -22 -7 -40 -5]]
POL2 generator: ~125/96 = 458.991
RMS error: 0.1129 cents
Photia
Related temperament: Schismic
Subgroup: 2.3.5.17
Comma list: 256/255, 1458/1445
Gencom: [2 4/3; 256/255 1458/1445]
Gencom mapping: [⟨1 2 -1 0 0 0 7], ⟨0 -1 8 0 0 0 -7]]
Sval mapping: [⟨1 2 -1 7], ⟨0 -1 8 -7]]
POL2 generator: ~3/2 = 701.491
RMS error: 0.4842 cents
2.3.5.17.19
Subgroup: 2.3.5.17.19
Comma list: 171/170, 256/255, 324/323
Gencom: [2 4/3; 171/170 256/255 324/323]
Gencom mapping: [⟨1 2 -1 0 0 0 7 3], ⟨0 -1 8 0 0 0 -7 3]]
Sval mapping: [⟨1 2 -1 7 3], ⟨0 -1 8 -7 3]]
POL2 generator: ~3/2 = 701.470
RMS error: 0.5374 cents
Nestoria
Related temperament: Schismic
Subgroup: 2.3.5.19
Comma list: 361/360, 513/512
Gencom: [2 4/3; 361/360 513/512]
Gencom mapping: [⟨1 2 -1 0 0 0 0 3], ⟨0 -1 8 0 0 0 0 3]]
Sval mapping: [⟨1 2 -1 3], ⟨0 -1 8 3]]
POL2 generator: ~3/2 = 701.746
RMS error: 0.1763 cents