Ditonmic family: Difference between revisions

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{{Mapping|legend=1| 1 6 3 | 0 -13 -2 }}
{{Mapping|legend=1| 1 6 3 | 0 -13 -2 }}
: mapping generators: ~2, ~15625/12288


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~15625/12288 = 407.534
* [[CTE]]: ~2 = 1200.000{{c}}, ~15625/12288 = 407.534{{c}}
: [[error map]]: {{val| 0.000 +0.099 -1.382 }}
: [[error map]]: {{val| 0.000 +0.099 -1.382 }}
* [[POTE]]: ~2 = 1200.000, ~15625/12288 = 407.574
* [[POTE]]: ~2 = 1200.000{{c}}, ~15625/12288 = 407.574{{c}}
: error map: {{val| 0.000 -0.416 -1.462 }}
: error map: {{val| 0.000 -0.416 -1.462 }}


Line 29: Line 30:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~1225/972 = 407.642
* [[CTE]]: ~2 = 1200.000{{c}}, ~1225/972 = 407.642{{c}}
: [[error map]]: {{val| 0.000 -1.298 -1.597 +1.921 }}
: [[error map]]: {{val| 0.000 -1.298 -1.597 +1.921 }}
* [[POTE]]: ~2 = 1200.000, ~1225/972 = 407.690
* [[POTE]]: ~2 = 1200.000{{c}}, ~1225/972 = 407.690{{c}}
: error map: {{val| 0.000 -1.921 -1.693 +0.483 }}
: error map: {{val| 0.000 -1.921 -1.693 +0.483 }}


Line 46: Line 47:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~1225/972 = 407.688
* CTE: ~2 = 1200.000{{c}}, ~1225/972 = 407.688{{c}}
* POTE: ~2 = 1200.000, ~1225/972 = 407.741
* POTE: ~2 = 1200.000{{c}}, ~1225/972 = 407.741{{c}}


{{Optimal ET sequence|legend=0| 50, 53, 103 }}
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
Line 61: Line 62:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~325/256 = 407.691
* CTE: ~2 = 1200.000{{c}}, ~325/256 = 407.691{{c}}
* POTE: ~2 = 1200.000, ~325/256 = 407.736
* POTE: ~2 = 1200.000{{c}}, ~325/256 = 407.736{{c}}


{{Optimal ET sequence|legend=0| 50, 53, 103 }}
{{Optimal ET sequence|legend=0| 50, 53, 103 }}
Line 76: Line 77:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~242/189 = 407.528
* CTE: ~2 = 1200.000{{c}}, ~242/189 = 407.528{{c}}
* POTE: ~2 = 1200.000, ~242/189 = 407.567
* POTE: ~2 = 1200.000{{c}}, ~242/189 = 407.567{{c}}


{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
{{Optimal ET sequence|legend=0| 3de, 50e, 53 }}
Line 91: Line 92:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~242/189 = 407.514
* CTE: ~2 = 1200.000{{c}}, ~242/189 = 407.514{{c}}
* POTE: ~2 = 1200.000, ~33/26 = 407.541
* POTE: ~2 = 1200.000{{c}}, ~33/26 = 407.541{{c}}


{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}
{{Optimal ET sequence|legend=0| 3def, 50eff, 53 }}
Line 108: Line 109:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 407.922
* [[CTE]]: ~2 = 1200.000{{c}}, ~2625/2048 = 407.922{{c}}
: [[error map]]: {{val| 0.000 -4.939 -2.157 -10.388 }}
: [[error map]]: {{val| 0.000 -4.939 -2.157 -10.388 }}
* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 407.954
* [[POTE]]: ~2 = 1200.000{{c}}, ~2625/2048 = 407.954{{c}}
: error map: {{val| 0.000 -5.353 -2.221 -9.751 }}
: error map: {{val| 0.000 -5.353 -2.221 -9.751 }}


Line 125: Line 126:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/11 = 407.930
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 407.930{{c}}
* POTE: ~2 = 1200.000, ~14/11 = 407.892
* POTE: ~2 = 1200.000{{c}}, ~14/11 = 407.892{{c}}


{{Optimal ET sequence|legend=0| 3, 47, 50 }}
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
Line 140: Line 141:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~14/11 = 407.933
* CTE: ~2 = 1200.000{{c}}, ~14/11 = 407.933{{c}}
* POTE: ~2 = 1200.000, ~14/11 = 407.887
* POTE: ~2 = 1200.000{{c}}, ~14/11 = 407.887{{c}}


{{Optimal ET sequence|legend=0| 3, 47, 50 }}
{{Optimal ET sequence|legend=0| 3, 47, 50 }}
Line 147: Line 148:
Badness (Smith): 0.054997
Badness (Smith): 0.054997


== Notes ==
== References ==


[[Category:Ditonmic family| ]] <!-- main article -->
[[Category:Ditonmic family| ]] <!-- main article -->

Revision as of 07:42, 21 September 2026

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]]

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

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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