User:Eliora/Proposed concept names
Minutes
Defined as the 2460 & 4320 temperament, and named "minutes" for period-60, since there's 60 minutes in an hour. In the limits below 13, it's a contorted atomic temperament.
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 250047/250000, 371293/371250, 184549376/184528125
Mapping: 60 60 385 730 1085 573, 0 1 7 -16 -25 -10
Mapping generators: ~2704/2673, ~3/2
Optimal tuning (CTE): ~3/2 = 701.948
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 9801/9800, 12376/12375, 28561/28560, 250047/250000, 253755392/253746675
Mapping: 60 60 385 730 1085 573 877, 0 1 7 -16 -25 -10 -18
Mapping generators: ~3520/3213, ~3/2
Optimal tuning (CTE): ~3/2 = 701.948
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: to be filled in
Mapping: to be filled in
Mapping generators: ~3520/3213, ~3/2
Optimal tuning (CTE): ~3/2 = 701.948
Nuclear matter
Defined as the 22 & 69 temperament, and the comma in the 5-limit is [-41, 1, 17⟩. The name comes from the fact that nuclear matter density is 4.1 * 10^17 kg/m^3.
Subgroup: 2.3.5
Comma list: [-41, 1, 17⟩
Optimal tuning (CTE): ~5/4
Vals: 22, 69
Berkelium
A remarkable high-limit temperament, extended as high as the 29-limit owing to the fact that both 388edo and 2619edo are consistent that high. Named after the 97th element.
Subgroup: 2.3.5.7.11.13
Comma list: 4375/4374, 405769/405504, 1063348/1063125, ...
Mapping generators: ~144/143, ~3/2
Optimal tuning (CTE): ~3/2 = 701.945
EDOs: 388, 2619, ...
Point Zero Seven
A meantone version of sextilififths that's quite bad at JI. Named because the generator is 7\100, and since the name sounds like an alcohol percentage, it corresponds to the "drunken and imprecise feel" of the badness of JI of the scale.
Subgroup: 2.3.5.7
Comma list: 81/80, 121500/117649
Mapping: [1 2 4 4], [0 -6 -24 -17]
Optimal tuning (CTE): ~21/20 = 83.888
Vals: 14, 43, 100
Mabon
Named after the celebration of the autumn equinox, and defined as the 11 & 62 temperament in the 2.9.7, since the 11/62 solar calendar leap rule representes the autumn equinox. Three below 600c generators amount to 16/9.
Subgroup: 2.9.7
Comma list: 44957696/43046721
Sval mapping: [1 1 -3], [0 3 8]
Optimal tuning (CTE): ~729/448 = 870.792
Vals: 11, 29, 40, 51, 62, ...
11-limit
In the 11-limit, the 11th harmonic plus an octave is reached by stacking two 16/11.
Subgroup: 2.9.7.11
Comma list: 896/891, 1331/1296
Sval mapping: [1 1 -3 2], [0 3 8 2]
Optimal tuning (CTE): ~18/11
Leaves
Defined as the 323 & 2023 temperament, and also as the no-11s temperament, because both 323edo and 2023edo have a bad 11th harmonic.
Subgroup: 2.3.5.7
Comma list: -21 11 10 -7, 31 28 -24 -7
Mapping: 17 10 31 9, 0 14 7 32
Mapping generators: ~25/24, ~6125/5832
Optimal tuning (CTE): ~6125/5832 = 85.427
Vals: 323, 1700, 2023
2.3.5.7.13 subgroup
Subgroup: 2.3.5.7.13
Comma list: 1990656/1990625, 3502727631/3500000000, 134521003125/134296804096
Sval mapping:
Sval maping generators: ~25/24, ~1024/975
Optimal tuning (CTE): ~1024/975 = ...
2.3.5.7.13.17 subgroup
9 periods and 2 generators correspond to 17/13.
Subgroup:
Comma list: 57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000
Sval mapping: 17 10 31 9 98 107, 0 14 7 32 -29 -31
Sval mapping generators: ~25/24, ~765/728
Optimal tuning (CTE): ~765/728 = 85.424
Tritonopod
Period-35, 17 generators are equal to 7/5, 18 generators are equal to 10/7.
Possibly rank-3?
Playing cards
Work in progress