No-sevens subgroup temperaments
This is a collection of subgroup temperaments which omit the prime harmonic of 7. Many of these have been removed from this page and placed on their appropriate family pages in an effort to include extensions other than incremental-prime-limit; sections for them remain on this page due to extensive linkage.
2.3.5.11 temperaments
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
Optimal ET sequence: 7, 111, 118
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
Optimal ET sequence: 37, 50, 87, 137, 224
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
Optimal ET sequence: 37, 50, 87, 137, 224
RMS error: 0.1250 cents
Tremka
- For full 11- and 13-limit extensions, see Hemimean clan#Tremka.
Subgroup: 2.3.5.11
Comma list: 6912/6875, 526153617/524288000
Gencom: [2 363/320; 6912/6875 526153617/524288000]
Gencom mapping: [⟨1 -4 -2 0 4], ⟨0 31 24 0 -3]]
Sval mapping: [⟨1 -4 -2 4], ⟨0 31 24 -3]]
POL2 generator: ~363/320 = 216.182
Optimal ET sequence: 11b, 28bbcc, 39bc, 50, 111, 161, 272
RMS error: 0.3717 cents
2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 2200/2197, 3267/3250, 6656/6655
Gencom: [2 192/169; 2200/2197 3267/3250 6656/6655]
Gencom mapping: [⟨1 -4 -2 0 4 1], ⟨0 31 24 0 -3 15]]
Sval mapping: [⟨1 -4 -2 4 1], ⟨0 31 24 -3 15]]
POL2 generator: ~192/169 = 216.186
Optimal ET sequence: 11b, 28bbccf, 39bc, 50, 111, 272, 383cf
RMS error: 0.3705 cents
Yarman
- For full 11- and 13-limit extensions, see Quartonic family.
Subgroup: 2.3.5.11
Comma list: 4000/3993, 390625000/387420489
Gencom: [2 100/99; 4000/3993 390625000/387420489]
Gencom mapping: [⟨1 2 3 0 4], ⟨0 -33 -54 0 -43]]
Sval mapping: [⟨1 2 3 4], ⟨0 -33 -54 -43]]
POL2 generator: ~100/99 = 15.0773
Optimal ET sequence: 79, 80, 159, 239, 398
RMS error: 0.1682 cents
2.3.5.11.13
Subgroup: 2.3.5.11.13
Comma list: 325/324, 4000/3993, 85683/85184
Gencom: [2 100/99; 325/324 4000/3993 85683/85184]
Gencom mapping: [⟨1 2 3 0 4 4], ⟨0 -33 -54 0 -43 -24]]
Sval mapping: [⟨1 2 3 4 4], ⟨0 -33 -54 -43 -24]]
POL2 generator: ~100/99 = 15.0885
Optimal ET sequence: 79, 80, 159
RMS error: 0.2830 cents
Dicot
Mavila
Tetracot
Porkypine
Mohaha
Larry
Dequarter
Hypnotone
2.3.5.13 temperaments
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
Optimal ET sequence: 34, 149, 183, 217, 400
RMS error: 0.1171 cents
2.3.5.13.17
The comma list shown here is interestingly a possible minimal S-expression-based comma list for majvam: {S13/S15 = S26, S16/S17, S51} (though the order of the last two commas is swapped to make the commas appear in ascending prime limit).
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
Optimal ET sequence: 34, 149, 183, 217, 400
RMS error: 0.1129 cents
Tricot
Taylor
2.3.5.17 temperaments
Quintaleap
Quindromeda
Photia
Quintilischis
- For full 17- and 19-limit extensions, see Schismatic family #Quintilipyth or Schismatic family #Quintaschis.
2.3.5.19 temperaments
Rarity
- For the 5-limit version of this temperament, see High badness temperaments #Rarity.
Rarity generator is so close to 23/19, and some edos supporting it have good 19th and 23rd harmonics that it is natural to prescribe a 2.3.5.19.23 extension. Since the generator is also mapped to 368/225, this means that 4275/4232 is tempered out.
Subgroup: 2.3.5.19.23
Comma list: 1035/1024, 16875/16606, 192375/188416
Sval mapping: [⟨1 11 -10 -3 -2], ⟨0 -13 17 10 9]]
- Sval mapping generators: ~1\1 = 2, ~368/225 = 869.420
Optimal tuning (CTE): ~368/225 = 869.420
Optimal ET sequence: 11, 29, 69, 98c
Badness: 0.0656
Stützel
Devisemi
Nestoria
- See also: No-elevens subgroup temperaments #Garibaldia and #Pontia