Ditonmic family
- 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 ditonmic family of temperaments tempers out the ditonma (monzo: [-27 -2 13⟩, ratio: 1 220 703 125 / 1 207 959 552).
Ditonic
Named by Petr Pařízek in 2011[1], ditonic splits ~5/2 in two for a generator, which happens to be an interval very close in size to the octave complement of the ditone (i.e. the Pythagorean major third, 81/64). It can be described as 3 & 53, and is part of the schismic–Mercator equivalence continuum with equivalence number n = 13/2. Its ploidacot is eta-13-cot. Note that the ditone itself is 52 generator steps away.
Subgroup: 2.3.5
Comma list: 1220703125/1207959552
Mapping: [⟨1 -7 1], ⟨0 13 2]]
- mapping generators: ~2, ~24576/15625
- WE: ~2 = 1200.2971 ¢, ~24576/15625 = 792.6223 ¢
- error map: ⟨+0.297 +0.055 -0.772]
- CWE: ~2 = 1200.0000 ¢, ~24576/15625 = 792.4403 ¢
- error map: ⟨0.000 -0.231 -1.433]
Optimal ET sequence: 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc
Badness (Sintel): 3.92
Coditone
Subgroup: 2.3.5.7
Comma list: 225/224, 2125764/2100875
Mapping: [⟨1 -7 1 -17], ⟨0 13 2 30]]
- WE: ~2 = 1200.4411 ¢, ~1944/1225 = 792.6016 ¢
- error map: ⟨+0.441 -1.223 -0.669 +1.722]
- CWE: ~2 = 1200.0000 ¢, ~1944/1225 = 792.3270 ¢
- error map: ⟨0.000 -1.704 -1.660 +0.985]
Optimal ET sequence: 50, 53, 103, 156
Badness (Sintel): 1.63
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 78408/78125
Mapping: [⟨1 -7 1 -17 16], ⟨0 13 2 30 -19]]
Optimal tunings:
- WE: ~2 = 1200.8016 ¢, ~198/125 = 792.7878 ¢
- CWE: ~2 = 1200.0000 ¢, ~198/125 = 792.2692 ¢
Optimal ET sequence: 50, 53, 103, 259be, 362bcee
Badness (Sintel): 1.47
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 385/384, 847/845
Mapping: [⟨1 -7 1 -17 16 7], ⟨0 13 2 30 -19 -5]]
Optimal tunings:
- WE: ~2 = 1200.7372 ¢, ~198/125 = 792.7511 ¢
- CWE: ~2 = 1200.0000 ¢, ~198/125 = 792.2715 ¢
Optimal ET sequence: 50, 53, 103, 259be, 362bceef
Badness (Sintel): 1.01
Coditonic
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 6655/6561
Mapping: [⟨1 -7 1 -17 -19], ⟨0 13 2 30 34]]
Optimal tunings:
- WE: ~2 = 1200.3578 ¢, ~189/121 = 792.6693 ¢
- CWE: ~2 = 1200.0000 ¢, ~189/121 = 792.4463 ¢
Optimal ET sequence: 3de, 50e, 53
Badness (Sintel): 2.11
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 325/324, 847/845
Mapping: [⟨1 -7 1 -17 -19 -28], ⟨0 13 2 30 34 48]]
Optimal tunings:
- WE: ~2 = 1200.2797 ¢, ~52/33 = 792.6439 ¢
- CWE: ~2 = 1200.0000 ¢, ~52/33 = 792.4682 ¢
Optimal ET sequence: 3def, 50eff, 53
Badness (Sintel): 1.82
Diton
This low-accuracy temperament was considered the canonical extension of ditonic, and catalogued as so in Graham Breed's Temperament Finder.
Subgroup: 2.3.5.7
Comma list: 126/125, 8751645/8388608
Mapping: [⟨1 -7 1 16], ⟨0 13 2 -20]]
- WE: ~2 = 1201.9455 ¢, ~2048/1323 = 793.3304 ¢
- error map: ⟨+1.946 -2.278 +2.293 -4.305]
- CWE: ~2 = 1200.000 ¢, ~2048/1323 = 792.0527 ¢
- error map: ⟨0.000 -5.270 -2.208 -9.879]
Optimal ET sequence: 3, 47, 50
Badness (Sintel): 6.13
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 2079/2048
Mapping: [⟨1 -7 1 16 16], ⟨0 13 2 -20 -19]]
Optimal tunings:
- WE: ~2 = 1201.6076 ¢, ~11/7 = 793.1692 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 792.1016 ¢
Optimal ET sequence: 3, 47, 50
Badness (Sintel): 3.34
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 245/242, 1287/1280
Mapping: [⟨1 -7 1 16 16 7], ⟨0 13 2 -20 -19 -5]]
Optimal tunings:
- WE: ~2 = 1201.3885 ¢, ~11/7 = 793.0294 ¢
- CWE: ~2 = 1200.0000 ¢, ~11/7 = 792.1096 ¢
Optimal ET sequence: 3, 47, 50
Badness (Sintel): 2.27