Quince clan
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The quince clan tempers out the quince comma, [-15 0 -2 7⟩ = 823543/819200. Quince temperaments include:
- Casablanca (+126/125) → Starling temperaments
- Miracle (+225/224) → Gamelismic clan
- Quincy (+4375/4374) → Ragismic microtemperaments
- Birds (+3136/3125) → 31st-octave temperaments
- Octowerck (+321489/320000 or 420175/419904) → Varunismic temperaments
- Cotoneum (+10976/10935) → Garischismic clan
Mercy
Mercy is the no-3 version of miracle. It can be thought of as a way to conceptualize the 2.5.7.13.17.19 subgroup of 31edo. Two generators make an 8/7; five generators make a 7/5.
Subgroup: 2.5.7
Comma list: 823543/819200
Subgroup-val mapping: [⟨1 3 3], ⟨0 -7 -2]]
- mapping generators: ~2, ~343/320
Gencom mapping: [⟨1 0 3 3], ⟨0 0 -7 -2]]
- gencom: [2 343/320; 823543/819200]
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 116.291
Optimal ET sequence: 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd
2.5.7.13 subgroup
Subgroup: 2.5.7.13
Comma list: 343/338, 640/637
Sval mapping: [⟨1 3 3 4], ⟨0 -7 -2 -3]]
Gencom mapping: [⟨1 0 3 3 0 4], ⟨0 0 -7 -2 0 -3]]
- gencom: [2 14/13; 343/338 640/637]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 116.094
Optimal ET sequence: 10, 21, 31
2.5.7.13.17 subgroup
Subgroup: 2.5.7.13.17
Comma list: 170/169, 224/221, 640/637
Sval mapping: [⟨1 3 3 4 4], ⟨0 -7 -2 -3 1]]
Gencom mapping: [⟨1 0 3 3 0 4 4], ⟨0 0 -7 -2 0 -3 1]]
- gencom: [2 14/13; 170/169 224/221 640/637]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.769
Optimal ET sequence: 10, 21, 31
2.5.7.13.17.19 subgroup
Subgroup: 2.5.7.13.17.19
Comma list: 170/169, 343/338, 640/637, 16384/16055
Sval mapping: [⟨1 3 3 4 4 3], ⟨0 -7 -2 -3 1 13]]
Gencom mapping: [⟨1 0 3 3 0 4 4 3], ⟨0 0 -7 -2 0 -3 1 13]]
- gencom: [2 14/13; 170/169 343/338 640/637 16384/16055]
Optimal tuning (POTE): ~2 = 1\1, ~14/13 = 115.716
Optimal ET sequence: 10, 21, 31, 52f
Countermiracle
The countermiracle temperament (31 & 145) tempers out the trimyna, 50421/50000 and the quince comma, 823543/819200.
|
Todo: explain relationship to miracle
There's clearly some relationship, since the extensions are named the same way, but the nature of that relationship isn't obvious from looking at this page. |
Subgroup: 2.3.5.7
Comma list: 6144/6125, 50421/50000
Mapping: [⟨1 4 3 3], ⟨0 -25 -7 -2]]
- Mapping generators: ~2, ~343/320
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9169
Optimal ET sequence: 31, 114, 145, 176, 559cc, 735cc
Badness: 0.102326
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 6144/6125
Mapping: [⟨1 4 3 3 8], ⟨0 -25 -7 -2 -47]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9158
Optimal ET sequence: 31, 114e, 145, 176
Badness: 0.039162
Countermiraculous
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 1001/1000, 6144/6125
Mapping: [⟨1 4 3 3 8 1], ⟨0 -25 -7 -2 -47 28]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8803
Optimal ET sequence: 31, 83e, 114e, 145, 321ceff
Badness: 0.039271
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 1001/1000, 1225/1224
Mapping: [⟨1 4 3 3 8 1 1], ⟨0 -25 -7 -2 -47 28 32]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8756
Optimal ET sequence: 31, 83e, 114e, 145
Badness: 0.029496
Counterbenediction
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 3146/3125, 3584/3575
Mapping: [⟨1 4 3 3 8 -2], ⟨0 -25 -7 -2 -47 59]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9335
Optimal ET sequence: 31, 114ef, 145f, 176, 207, 383c, 590cc
Badness: 0.045569
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 441/440, 561/560, 1632/1625, 3146/3125
Mapping: [⟨1 4 3 3 8 -2 -2], ⟨0 -25 -7 -2 -47 59 63]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.9391
Optimal ET sequence: 31, 114efg, 145fg, 176, 207
Badness: 0.036289
Countermanna
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 3388/3375, 6144/6125
Mapping: [⟨1 4 3 3 8 15], ⟨0 -25 -7 -2 -47 -117]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8898
Optimal ET sequence: 145, 176, 321ce
Badness: 0.053409
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 364/363, 441/440, 595/594, 1632/1625, 3388/3375
Mapping: [⟨1 4 3 3 8 15 15], ⟨0 -25 -7 -2 -47 -117 -113]]
Optimal tuning (POTE): ~2 = 1\1, ~77/72 = 115.8832
Optimal ET sequence: 145, 321ce
Badness: 0.040898
Counterrevelation
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 50421/50000
Mapping: [⟨1 4 3 3 5], ⟨0 -25 -7 -2 -16]]
Optimal tuning (POTE): ~2 = 1\1, ~343/320 = 115.9192
Optimal ET sequence: 31, 114, 145e, 176e
Badness: 0.064070
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 176/175, 196/195, 13750/13689
Mapping: [⟨1 4 3 3 5 1], ⟨0 -25 -7 -2 -16 28]]
Optimal tuning (POTE): ~2 = 1\1, ~273/256 = 115.8624
Optimal ET sequence: 31, 83, 114, 145e
Badness: 0.057497
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 176/175, 196/195, 10647/10625
Mapping: [⟨1 4 3 3 5 1 1], ⟨0 -25 -7 -2 -16 28 32]]
Optimal tuning (POTE): ~2 = 1\1, ~91/85 = 115.8527
Optimal ET sequence: 31, 83, 114, 145e
Badness: 0.044043