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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~343/320 = 116.291 ¢
Optimal ET sequence: 10, 21, 31, 134, 165, 196, 227, 485d, 712d, 1197dd
Countermiracle
The countermiracle temperament (31 & 145) tempers out the trimyna, 50421/50000 and the quince comma, 823543/819200.
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Todo: expand
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 = 1200.0000 ¢, ~343/320 = 115.9169 ¢
Optimal ET sequence: 31, 114, 145, 176, 559cc, 735cc
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.9158 ¢
Optimal ET sequence: 31, 114e, 145, 176
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.8803 ¢
Optimal ET sequence: 31, 83e, 114e, 145, 321ceff
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.8756 ¢
Optimal ET sequence: 31, 83e, 114e, 145
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.9335 ¢
Optimal ET sequence: 31, 114ef, 145f, 176, 207, 383c, 590cc
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.9391 ¢
Optimal ET sequence: 31, 114efg, 145fg, 176, 207
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.8898 ¢
Optimal ET sequence: 145, 176, 321ce
Badness (Smith): 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 = 1200.0000 ¢, ~77/72 = 115.8832 ¢
Optimal ET sequence: 145, 321ce
Badness (Smith): 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 = 1200.0000 ¢, ~343/320 = 115.9192 ¢
Optimal ET sequence: 31, 114, 145e, 176e
Badness (Smith): 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 = 1200.0000 ¢, ~273/256 = 115.8624 ¢
Optimal ET sequence: 31, 83, 114, 145e
Badness (Smith): 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 = 1200.0000 ¢, ~91/85 = 115.8527 ¢
Optimal ET sequence: 31, 83, 114, 145e
Badness (Smith): 0.044043
Subgroup extensions
Mercy (2.5.7.13)
Subgroup: 2.5.7.13
Comma list: 343/338, 640/637
Subgroup-val mapping: [⟨1 3 3 4], ⟨0 -7 -2 -3]]
Gencom mapping: [⟨1 0 3 3 0 4], ⟨0 0 -7 -2 0 -3]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~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
Subgroup-val 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~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
Subgroup-val 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~14/13 = 115.716 ¢