Ditonmic family: Difference between revisions
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Latest revision as of 00:29, 24 June 2025
- 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 (ratio: 1220703125/1207959552, monzo: [-27 -2 13⟩).
Ditonic
Named by Petr Pařízek in 2011[1], ditonic can be described as the 50 & 53 temperament. It splits ~8/5 in two for a generator, which happens to be an interval very close in size to the ditone, ~81/64. Note that the ditone itself is 52 generator steps away.
Subgroup: 2.3.5
Comma list: 1220703125/1207959552
Mapping: [⟨1 6 3], ⟨0 -13 -2]]
- CTE: ~2 = 1200.000, ~15625/12288 = 407.534
- error map: ⟨0.000 +0.099 -1.382]
- POTE: ~2 = 1200.000, ~15625/12288 = 407.574
- error map: ⟨0.000 -0.416 -1.462]
Optimal ET sequence: 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc
Badness (Smith): 0.167086
Coditone
Subgroup: 2.3.5.7
Comma list: 225/224, 2125764/2100875
Mapping: [⟨1 6 3 13], ⟨0 -13 -2 -30]]
- CTE: ~2 = 1200.000, ~1225/972 = 407.642
- error map: ⟨0.000 -1.298 -1.597 +1.921]
- POTE: ~2 = 1200.000, ~1225/972 = 407.690
- error map: ⟨0.000 -1.921 -1.693 +0.483]
Optimal ET sequence: 3d, 50, 53, 103, 156
Badness (Smith): 0.064356
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 78408/78125
Mapping: [⟨1 6 3 13 -3], ⟨0 -13 -2 -30 19]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~1225/972 = 407.688
- POTE: ~2 = 1200.000, ~1225/972 = 407.741
Optimal ET sequence: 50, 53, 103
Badness (Smith): 0.044329
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 351/350, 385/384, 847/845
Mapping: [⟨1 6 3 13 -3 2], ⟨0 -13 -2 -30 19 5]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~325/256 = 407.691
- POTE: ~2 = 1200.000, ~325/256 = 407.736
Optimal ET sequence: 50, 53, 103
Badness (Smith): 0.024352
Coditonic
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 6655/6561
Mapping: [⟨1 6 3 13 15], ⟨0 -13 -2 -30 -34]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~242/189 = 407.528
- POTE: ~2 = 1200.000, ~242/189 = 407.567
Optimal ET sequence: 3de, 50e, 53
Badness (Smith): 0.063876
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 176/175, 325/324, 847/845
Mapping: [⟨1 6 3 13 15 20], ⟨0 -13 -2 -30 -34 -48]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~242/189 = 407.514
- POTE: ~2 = 1200.000, ~33/26 = 407.541
Optimal ET sequence: 3def, 50eff, 53
Badness (Smith): 0.043989
Diton
This extension is known as ditonic in Graham Breed's temperament finder.
Subgroup: 2.3.5.7
Comma list: 126/125, 8751645/8388608
Mapping: [⟨1 6 3 -4], ⟨0 -13 -2 20]]
- CTE: ~2 = 1200.000, ~2625/2048 = 407.922
- error map: ⟨0.000 -4.939 -2.157 -10.388]
- POTE: ~2 = 1200.000, ~2625/2048 = 407.954
- error map: ⟨0.000 -5.353 -2.221 -9.751]
Optimal ET sequence: 3, 47, 50
Badness (Smith): 0.242101
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 245/242, 2079/2048
Mapping: [⟨1 6 3 -4 -3], ⟨0 -13 -2 20 19]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~14/11 = 407.930
- POTE: ~2 = 1200.000, ~14/11 = 407.892
Optimal ET sequence: 3, 47, 50
Badness (Smith): 0.100884
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 126/125, 245/242, 1287/1280
Mapping: [⟨1 6 3 -4 -3 2], ⟨0 -13 -2 20 19 5]]
Optimal tunings:
- CTE: ~2 = 1200.000, ~14/11 = 407.933
- POTE: ~2 = 1200.000, ~14/11 = 407.887
Optimal ET sequence: 3, 47, 50
Badness (Smith): 0.054997