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, 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]]

mapping generators: ~2, ~15625/12288

Optimal tunings:

• 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]]

Optimal tunings:

• 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]]

Optimal tunings:

• 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