Mint temperaments: Difference between revisions

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{{Mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}
{{Mapping|legend=1| 1 1 2 2 | 0 3 2 4 }}
: mapping generators: ~2, ~7/6
: mapping generators: ~2, ~7/6


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 231.845
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 231.845{{c}}
: [[error map]]: {{val| 0.000 -6.421 +77.376 -41.447 }}
: [[error map]]: {{val| 0.000 -6.421 +77.376 -41.447 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 239.977
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 239.977{{c}}
: error map: {{val| 0.000 +17.976 +93.640 -8.918 }}
: error map: {{val| 0.000 +17.976 +93.640 -8.918 }}


{{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }}
{{Optimal ET sequence|legend=1| 1bd, …, 4bcd, 5 }}


[[Badness]] (Sintel): 1.1864
[[Badness]] (Sintel): 1.19


== Progression ==
== Progression ==
Line 49: Line 48:


{{Mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}
{{Mapping|legend=1| 1 1 2 2 | 0 5 3 7 }}
: mapping generators: ~2, ~15/14
: mapping generators: ~2, ~15/14


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~15/14 = 138.611
* [[CTE]]: ~2 = 1200.000{{c}}, ~15/14 = 138.611{{c}}
: [[error map]]: {{val| 0.000 -8.900 +29.519 +1.451 }}
: [[error map]]: {{val| 0.000 -8.900 +29.519 +1.451 }}
* [[POTE]]: ~2 = 1200.000, ~15/14 = 140.927
* [[POTE]]: ~2 = 1200.000{{c}}, ~15/14 = 140.927{{c}}
: error map: {{val| 0.000 +2.680 +36.467 +17.663 }}
: error map: {{val| 0.000 +2.680 +36.467 +17.663 }}


{{Optimal ET sequence|legend=1| 8d, 9, 17c }}
{{Optimal ET sequence|legend=1| 8d, 9, 17c }}


[[Badness]] (Sintel): 1.2237
[[Badness]] (Sintel): 1.22


=== 11-limit ===
=== 11-limit ===
Line 70: Line 68:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~12/11 = 138.556
* CTE: ~2 = 1200.000{{c}}, ~12/11 = 138.556{{c}}
* POTE: ~2 = 1200.000, ~12/11 = 140.747
* POTE: ~2 = 1200.000{{c}}, ~12/11 = 140.747{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness (Sintel): 0.8612
Badness (Sintel): 0.861


=== 13-limit ===
=== 13-limit ===
Line 85: Line 83:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.741
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.741{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 140.751
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.751{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17c }}
{{Optimal ET sequence|legend=0| 8d, 9, 17c }}


Badness (Sintel): 0.7503
Badness (Sintel): 0.750


=== 17-limit ===
=== 17-limit ===
Line 100: Line 98:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.649
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.649{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 141.404
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 141.404{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness (Sintel): 0.8529
Badness (Sintel): 0.853


=== 19-limit ===
=== 19-limit ===
Line 115: Line 113:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/12 = 138.750
* CTE: ~2 = 1200.000{{c}}, ~13/12 = 138.750{{c}}
* POTE: ~2 = 1200.000, ~13/12 = 140.479
* POTE: ~2 = 1200.000{{c}}, ~13/12 = 140.479{{c}}


{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}
{{Optimal ET sequence|legend=0| 8d, 9, 17cg }}


Badness (Sintel): 1.0244
Badness (Sintel): 1.02


== Subklei ==
== Subklei ==
Line 130: Line 128:


{{Mapping|legend=1| 1 3 4 4 | 0 -6 -7 -5 }}
{{Mapping|legend=1| 1 3 4 4 | 0 -6 -7 -5 }}
: mapping generators: ~2, ~7/6
: mapping generators: ~2, ~7/6


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~7/6 = 284.986
* [[CTE]]: ~2 = 1200.000{{c}}, ~7/6 = 284.986{{c}}
: [[error map]]: {{val| 0.000 -11.870 +18.785 +6.245 }}
: [[error map]]: {{val| 0.000 -11.870 +18.785 +6.245 }}
* [[POTE]]: ~2 = 1200.000, ~7/6 = 284.219
* [[POTE]]: ~2 = 1200.000{{c}}, ~7/6 = 284.219{{c}}
: error map: {{val| 0.000 -7.268 +24.154 +10.080 }}
: error map: {{val| 0.000 -7.268 +24.154 +10.080 }}


{{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }}
{{Optimal ET sequence|legend=1| 4, 13cd, 17c, 21, 38c }}


[[Badness]] (Sintel): 1.5463
[[Badness]] (Sintel): 1.55


=== 11-limit ===
=== 11-limit ===
Line 151: Line 148:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.265
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.265{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.253
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.253{{c}}


{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}
{{Optimal ET sequence|legend=0| 4e, …, 13cdee, 17c }}


Badness (Sintel): 1.4761
Badness (Sintel): 1.48


==== 13-limit ====
==== 13-limit ====
Line 166: Line 163:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 283.918
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 283.918{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 282.856
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 282.856{{c}}


{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}
{{Optimal ET sequence|legend=0| 4ef, …, 13cdeef, 17c }}


Badness (Sintel): 1.3357
Badness (Sintel): 1.34


=== Subkla ===
=== Subkla ===
Line 181: Line 178:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.870
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.870{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.822
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.822{{c}}


{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce }}
{{Optimal ET sequence|legend=0| 4, 17c, 21, 38ce }}


Badness (Sintel): 1.5620
Badness (Sintel): 1.56


==== 13-limit ====
==== 13-limit ====
Line 196: Line 193:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/6 = 284.758
* CTE: ~2 = 1200.000{{c}}, ~7/6 = 284.758{{c}}
* POTE: ~2 = 1200.000, ~7/6 = 283.882
* POTE: ~2 = 1200.000{{c}}, ~7/6 = 283.882{{c}}


{{Optimal ET sequence|legend=0| 4, 17c, 38ce }}
{{Optimal ET sequence|legend=0| 4, 17c, 38ce }}


Badness (Sintel): 1.5166
Badness (Sintel): 1.52


== Naian ==
== Naian ==
Line 211: Line 208:


{{Mapping|legend=1| 1 5 5 7 | 0 -9 -7 -11 }}
{{Mapping|legend=1| 1 5 5 7 | 0 -9 -7 -11 }}
: mapping generators: ~2, ~98/75
: mapping generators: ~2, ~98/75


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~98/75 = 456.494
* [[CTE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.494{{c}}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }}
: [[error map]]: {{val| 0.000, -10.401, +18.228, +9.740 }}
* [[CWE]]: ~2 = 1200.000, ~98/75 = 456.012
* [[CWE]]: ~2 = 1200.000{{c}}, ~98/75 = 456.012{{c}}
: error map: {{val| 0.000, -6.059, +21.606, +15.047 }}
: error map: {{val| 0.000, -6.059, +21.606, +15.047 }}


{{Optimal ET sequence|legend=1| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=1| 8d, 13b, 21 }}


[[Badness]] (Sintel): 2.8912
[[Badness]] (Sintel): 2.89


=== 11-limit ===
=== 11-limit ===
Line 232: Line 228:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~77/60 = 456.625
* CTE: ~2 = 1200.000{{c}}, ~77/60 = 456.625{{c}}
* CWE: ~2 = 1200.000, ~77/60 = 455.798
* CWE: ~2 = 1200.000{{c}}, ~77/60 = 455.798{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.9522
Badness (Sintel): 1.95


=== 13-limit ===
=== 13-limit ===
Line 247: Line 243:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/10 = 456.767
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.767{{c}}
* CWE: ~2 = 1200.000, ~13/10 = 455.730
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.730{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.5538
Badness (Sintel): 1.55


=== 17-limit ===
=== 17-limit ===
Line 262: Line 258:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~13/10 = 456.821
* CTE: ~2 = 1200.000{{c}}, ~13/10 = 456.821{{c}}
* CWE: ~2 = 1200.000, ~13/10 = 455.732
* CWE: ~2 = 1200.000{{c}}, ~13/10 = 455.732{{c}}


{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}
{{Optimal ET sequence|legend=0| 8d, 13b, 21 }}


Badness (Sintel): 1.4332
Badness (Sintel): 1.43


== Slurpee ==
== Slurpee ==
Line 277: Line 273:


{{Mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}
{{Mapping|legend=1| 1 2 3 3 | 0 -7 -11 -3 }}
: mapping generators: ~2, ~21/20
: mapping generators: ~2, ~21/20


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~21/20 = 72.776
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 72.776{{c}}
: [[error map]]: {{val| 0.000 -11.385 +13.153 +12.847 }}
: [[error map]]: {{val| 0.000 -11.385 +13.153 +12.847 }}
* [[POTE]]: ~2 = 1200.000, ~21/20 = 72.303
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 72.303{{c}}
: error map: {{val| 0.000 -8.075 +18.355 +14.265 }}
: error map: {{val| 0.000 -8.075 +18.355 +14.265 }}


{{Optimal ET sequence|legend=1| 16, 17c, 33 }}
{{Optimal ET sequence|legend=1| 16, 17c, 33 }}


[[Badness]] (Sintel): 2.9070
[[Badness]] (Sintel): 2.91


=== 11-limit ===
=== 11-limit ===
Line 298: Line 293:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 72.681
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.681{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 72.297
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.297{{c}}


{{Optimal ET sequence|legend=0| 16, 17c, 33 }}
{{Optimal ET sequence|legend=0| 16, 17c, 33 }}


Badness (Sintel): 1.6700
Badness (Sintel): 1.67


=== 13-limit ===
=== 13-limit ===
Line 313: Line 308:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000, ~21/20 = 72.653
* CTE: ~2 = 1200.000{{c}}, ~21/20 = 72.653{{c}}
* POTE: ~2 = 1200.000, ~21/20 = 72.409
* POTE: ~2 = 1200.000{{c}}, ~21/20 = 72.409{{c}}


{{Optimal ET sequence|legend=0| 16, 17c, 33 }}
{{Optimal ET sequence|legend=0| 16, 17c, 33 }}


Badness (Sintel): 1.3678
Badness (Sintel): 1.37


== Shallowtone ==
== Shallowtone ==
Line 332: Line 327:


[[Optimal tuning]]s:
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~3/2 = 681.278
* [[CTE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.278{{c}}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }}
: [[error map]]: {{val| 0.000 -20.677 +0.906 +6.510 }}
* [[CWE]]: ~2 = 1200.000, ~3/2 = 681.245
* [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 681.245{{c}}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}
: error map: {{val| 0.000 -20.710 +1.239 +6.110 }}


{{Optimal ET sequence|legend=1| 7, 30b, 37b }}
{{Optimal ET sequence|legend=1| 7, 30b, 37b }}


[[Badness]] (Sintel): 7.7857
[[Badness]] (Sintel): 7.79


=== 11-limit ===
=== 11-limit ===
Line 349: Line 344:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 681.254
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.254{{c}}
* CWE: ~2 = 1200.000, ~3/2 = 681.327
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.327{{c}}


{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness (Sintel): 4.2942
Badness (Sintel): 4.29


=== 13-limit ===
=== 13-limit ===
Line 364: Line 359:


Optimal tunings:
Optimal tunings:
* CTE: ~2 = 1200.000, ~3/2 = 681.237
* CTE: ~2 = 1200.000{{c}}, ~3/2 = 681.237{{c}}
* CWE: ~2 = 1200.000, ~3/2 = 681.267
* CWE: ~2 = 1200.000{{c}}, ~3/2 = 681.267{{c}}


{{Optimal ET sequence|legend=0| 7, 30b, 37b }}
{{Optimal ET sequence|legend=0| 7, 30b, 37b }}


Badness (Sintel): 3.1927
Badness (Sintel): 3.19


== Notes ==
== References ==


[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Mint temperaments| ]] <!-- main article -->
[[Category:Mint temperaments| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 07:05, 10 March 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.

This is a collection of low complexity, high error, temperaments which temper out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. These temperaments equate 6/5 with 7/6, 5/4 with 9/7, and 7/4 with 9/5, so minor and major thirds and sixths are intervals of 5 and 7 at the same time.

Temperaments discussed elsewhere include

Penta

For the 5-limit version, see Syntonic–diatonic equivalence continuum #University.

Subgroup: 2.3.5.7

Comma list: 28/25, 36/35

Mapping: [⟨1 1 2 2], ⟨0 3 2 4]]

mapping generators: ~2, ~7/6

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 231.845 ¢
error map: ⟨0.000 -6.421 +77.376 -41.447]
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 239.977 ¢
error map: ⟨0.000 +17.976 +93.640 -8.918]

Optimal ET sequence: 1bd, …, 4bcd, 5

Badness (Sintel): 1.19

Progression

Not to be confused with Progress.
For the 5-limit version, see Miscellaneous 5-limit temperaments #Lafayette.

Progression, named by Gene Ward Smith in 2011[1] can be described as the 8d & 9 temperament, and 17edo is an obvious tuning for it.

Subgroup: 2.3.5.7

Comma list: 36/35, 392/375

Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]

mapping generators: ~2, ~15/14

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~15/14 = 138.611 ¢
error map: ⟨0.000 -8.900 +29.519 +1.451]
  • POTE: ~2 = 1200.000 ¢, ~15/14 = 140.927 ¢
error map: ⟨0.000 +2.680 +36.467 +17.663]

Optimal ET sequence: 8d, 9, 17c

Badness (Sintel): 1.22

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 77/75

Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~12/11 = 138.556 ¢
  • POTE: ~2 = 1200.000 ¢, ~12/11 = 140.747 ¢

Optimal ET sequence: 8d, 9, 17c

Badness (Sintel): 0.861

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3], ⟨0 5 3 7 4 6]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~13/12 = 138.741 ¢
  • POTE: ~2 = 1200.000 ¢, ~13/12 = 140.751 ¢

Optimal ET sequence: 8d, 9, 17c

Badness (Sintel): 0.750

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 26/25, 36/35, 51/50, 56/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4], ⟨0 5 3 7 4 6 1]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~13/12 = 138.649 ¢
  • POTE: ~2 = 1200.000 ¢, ~13/12 = 141.404 ¢

Optimal ET sequence: 8d, 9, 17cg

Badness (Sintel): 0.853

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65

Mapping: [⟨1 1 2 2 3 3 4 4], ⟨0 5 3 7 4 6 1 2]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~13/12 = 138.750 ¢
  • POTE: ~2 = 1200.000 ¢, ~13/12 = 140.479 ¢

Optimal ET sequence: 8d, 9, 17cg

Badness (Sintel): 1.02

Subklei

For the 5-limit version, see Miscellaneous 5-limit temperaments #Delorean.

Subgroup: 2.3.5.7

Comma list: 36/35, 1029/1000

Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]

mapping generators: ~2, ~7/6

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 284.986 ¢
error map: ⟨0.000 -11.870 +18.785 +6.245]
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 284.219 ¢
error map: ⟨0.000 -7.268 +24.154 +10.080]

Optimal ET sequence: 4, 13cd, 17c, 21, 38c

Badness (Sintel): 1.55

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 77/75, 352/343

Mapping: [⟨1 3 4 4 7], ⟨0 -6 -7 -5 -15]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 284.265 ¢
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 283.253 ¢

Optimal ET sequence: 4e, …, 13cdee, 17c

Badness (Sintel): 1.48

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 36/35, 66/65, 352/343

Mapping: [⟨1 3 4 4 7 7], ⟨0 -6 -7 -5 -15 -14]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 283.918 ¢
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 282.856 ¢

Optimal ET sequence: 4ef, …, 13cdeef, 17c

Badness (Sintel): 1.34

Subkla

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1000

Mapping: [⟨1 3 4 4 3], ⟨0 -6 -7 -5 2]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 284.870 ¢
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 283.822 ¢

Optimal ET sequence: 4, 17c, 21, 38ce

Badness (Sintel): 1.56

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 56/55, 66/65, 640/637

Mapping: [⟨1 3 4 4 3 3], ⟨0 -6 -7 -5 2 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~7/6 = 284.758 ¢
  • POTE: ~2 = 1200.000 ¢, ~7/6 = 283.882 ¢

Optimal ET sequence: 4, 17c, 38ce

Badness (Sintel): 1.52

Naian

For the 5-limit version, see Miscellaneous 5-limit temperaments #Naian.

Subgroup: 2.3.5.7

Comma list: 36/35, 9604/9375

Mapping: [⟨1 5 5 7], ⟨0 -9 -7 -11]]

mapping generators: ~2, ~98/75

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~98/75 = 456.494 ¢
error map: ⟨0.000, -10.401, +18.228, +9.740]
  • CWE: ~2 = 1200.000 ¢, ~98/75 = 456.012 ¢
error map: ⟨0.000, -6.059, +21.606, +15.047]

Optimal ET sequence: 8d, 13b, 21

Badness (Sintel): 2.89

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 2541/2500

Mapping: [⟨1 5 5 7 5], ⟨0 -9 -7 -11 -4]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~77/60 = 456.625 ¢
  • CWE: ~2 = 1200.000 ¢, ~77/60 = 455.798 ¢

Optimal ET sequence: 8d, 13b, 21

Badness (Sintel): 1.95

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 56/55, 66/65, 507/500

Mapping: [⟨1 5 5 7 5 6], ⟨0 -9 -7 -11 -4 -6]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~13/10 = 456.767 ¢
  • CWE: ~2 = 1200.000 ¢, ~13/10 = 455.730 ¢

Optimal ET sequence: 8d, 13b, 21

Badness (Sintel): 1.55

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 36/35, 51/50, 56/55, 66/65, 170/169

Mapping: [⟨1 5 5 7 5 6 6], ⟨0 -9 -7 -11 -4 -6 -5]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~13/10 = 456.821 ¢
  • CWE: ~2 = 1200.000 ¢, ~13/10 = 455.732 ¢

Optimal ET sequence: 8d, 13b, 21

Badness (Sintel): 1.43

Slurpee

For the 5-limit version, see Miscellaneous 5-limit temperaments #Slurpee.

Subgroup: 2.3.5.7

Comma list: 36/35, 51200/50421

Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]

mapping generators: ~2, ~21/20

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~21/20 = 72.776 ¢
error map: ⟨0.000 -11.385 +13.153 +12.847]
  • POTE: ~2 = 1200.000 ¢, ~21/20 = 72.303 ¢
error map: ⟨0.000 -8.075 +18.355 +14.265]

Optimal ET sequence: 16, 17c, 33

Badness (Sintel): 2.91

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 121/120, 352/343

Mapping: [⟨1 2 3 3 4], ⟨0 -7 -11 -3 -9]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~21/20 = 72.681 ¢
  • POTE: ~2 = 1200.000 ¢, ~21/20 = 72.297 ¢

Optimal ET sequence: 16, 17c, 33

Badness (Sintel): 1.67

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 36/35, 66/65, 143/140, 352/343

Mapping: [⟨1 2 3 3 4 4], ⟨0 -7 -11 -3 -9 -5]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~21/20 = 72.653 ¢
  • POTE: ~2 = 1200.000 ¢, ~21/20 = 72.409 ¢

Optimal ET sequence: 16, 17c, 33

Badness (Sintel): 1.37

Shallowtone

For the 5-limit version, see Syntonic–chromatic equivalence continuum #Shallowtone (5-limit).

Subgroup: 2.3.5.7

Comma list: 36/35, 295245/262144

Mapping: [⟨1 0 18 -16], ⟨0 1 -10 12]]

mapping generators: ~2, ~3

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3/2 = 681.278 ¢
error map: ⟨0.000 -20.677 +0.906 +6.510]
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 681.245 ¢
error map: ⟨0.000 -20.710 +1.239 +6.110]

Optimal ET sequence: 7, 30b, 37b

Badness (Sintel): 7.79

11-limit

Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 72171/65536

Mapping: [⟨1 0 18 -16 16], ⟨0 1 -10 12 -8]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3/2 = 681.254 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 681.327 ¢

Optimal ET sequence: 7, 30b, 37b

Badness (Sintel): 4.29

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 16731/16384

Mapping: [⟨1 0 18 -16 16 -1], ⟨0 1 -10 12 -8 3]]

Optimal tunings:

  • CTE: ~2 = 1200.000 ¢, ~3/2 = 681.237 ¢
  • CWE: ~2 = 1200.000 ¢, ~3/2 = 681.267 ¢

Optimal ET sequence: 7, 30b, 37b

Badness (Sintel): 3.19

References

  1. ↑ Yahoo! Tuning Group | Progression temperament
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