Keegic temperaments
- 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.
Keegic rank two temperaments temper out the keega, [-3 1 -3 3⟩ = 1029/1000, the difference three 7/5s and perfect eleventh 8/3.
Temperaments discussed elsewhere include antitonic, kangaroo, keemun, liese, progress, subklei, triton, trisected, and xenia.
Quinkee
Quinkee has a period of 1/5 octave and tempers out the keega (1029/1000), from which it derives its name. It may be described as the 15 & 55 temperament. It was named by Xenllium in 2021.
Subgroup: 2.3.5.7
Comma list: 1029/1000, 6144/6125
Mapping: [⟨5 0 9 14], ⟨0 3 1 0]]
- mapping generators: ~8/7, ~10/7
- WE: ~8/7 = 240.0512 ¢, ~10/7 = 633.5744 ¢ (~25/24 = 86.5794 ¢)
- error map: ⟨+0.256 -1.232 +7.722 -8.108]
- CWE: ~8/7 = 240.0000 ¢, ~10/7 = 633.4834 ¢ (~25/24 = 86.5160 ¢)
- error map: ⟨0.000 -1.505 +7.170 -8.826]
Optimal ET sequence: 15, 40, 55
Badness (Sintel): 4.66
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 176/175, 1029/1000
Mapping: [⟨5 0 9 14 12], ⟨0 3 1 0 2]]
Optimal tunings:
- WE: ~8/7 = 240.0916 ¢, ~10/7 = 633.6802 ¢ (~22/21 = 86.5947 ¢)
- CWE: ~8/7 = 240.0000 ¢, ~10/7 = 633.5204 ¢ (~22/21 = 86.4796 ¢)
Optimal ET sequence: 15, 40, 55
Badness (Sintel): 2.16
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 105/104, 121/120, 637/625
Mapping: [⟨5 9 12 14 18 20], ⟨0 3 1 0 2 4]]
Optimal tunings:
- WE: ~8/7 = 240.0392 ¢, ~10/7 = 632.9013 ¢ (~22/21 = 87.2162 ¢)
- CWE: ~8/7 = 240.0000 ¢, ~10/7 = 632.8351 ¢ (~22/21 = 87.1649 ¢)
Optimal ET sequence: 15, 40, 55
Badness (Sintel): 2.00
Aurora
- For the 5-limit version, see Diaschismic–gothmic equivalence continuum #Goldis.
The aurora temperament (13 & 21) is very strongly related to the golden oneirotonic tuning (generator: (3 - sqrt(5))/2 octave = 458.3592135001 cents). It has a temperament structure superficially similar to father, with extremely flat fourths (sub-fourths/ultra-major third) or sharp fifths (super-fifths/ultra-minor sixths). However, unlike father, 12 of these bad fourths reach a more in tune fifth, which is useful for creating resolutions when using a large enough gamut, such as the 13L 8s mos which has two good major & minor chords.
Subgroup: 2.3.5.7
Comma list: 1029/1000, 28672/28125
Mapping: [⟨1 -3 5 7], ⟨0 12 -7 -11]]
POTE generator: ~21/16 = 458.348
Optimal ET sequence: 8bd, 13, 21, 34, 55, 89d, 144cdd
Badness: 0.242134
11-limit
Subgroup: 2.3.5.7.11
Comma list: 56/55, 1029/1000, 5632/5625
Mapping: [⟨1 -3 5 7 5], ⟨0 12 -7 -11 -4]]
POTE generator: ~21/16 = 458.413
Optimal ET sequence: 8bd, 13, 21, 34, 55e, 89dee
Badness: 0.116654
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 56/55, 105/104, 512/507, 637/625
Mapping: [⟨1 -3 5 7 5 6], ⟨0 12 -7 -11 -4 -6]]
POTE generator: ~13/10 = 458.444
Optimal ET sequence: 8bd, 13, 21, 34, 55e, 89deef
Badness: 0.066541
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 56/55, 105/104, 170/169, 221/220, 375/374
Mapping: [⟨1 -3 5 7 5 6 6], ⟨0 12 -7 -11 -4 -6 -5]]
POTE generator: ~13/10 = 458.444
Optimal ET sequence: 8bd, 13, 21, 34, 55e, 89deef
Badness: 0.044148
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 56/55, 76/75, 105/104, 170/169, 190/187, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5], ⟨0 12 -7 -11 -4 -6 -5 -2]]
POTE generator: ~13/10 = 458.444
Optimal ET sequence: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.037621
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 56/55, 76/75, 105/104, 161/160, 170/169, 190/187, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5 3], ⟨0 12 -7 -11 -4 -6 -5 -2 4]]
POTE generator: ~13/10 = 458.430
Optimal ET sequence: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.030236
29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 56/55, 76/75, 105/104, 116/115, 145/143, 161/160, 170/169, 221/220
Mapping: [⟨1 -3 5 7 5 6 6 5 3 6], ⟨0 12 -7 -11 -4 -6 -5 -2 4 -3]]
POTE generator: ~13/10 = 458.426
Optimal ET sequence: 8bd, 13, 21, 34, 55eh, 89deefhh
Badness: 0.025201