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Gamelismic clan: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings, per community consensus (4/)
Switch to Sintel's badness, WE & CWE tunings, per community consensus (5/)
Line 1,397: Line 1,397:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 77.878{{c}}
* [[WE]]: ~2 = 1200.0749{{c}}, ~21/20 = 77.8687{{c}}
: [[error map]]: {{val| +0.075 -1.062 +3.179 -2.207 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 77.8673{{c}}
: error map: {{val| 0.000 -1.149 +3.023 -2.428 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~21/20 = 77.878{{c}}
: [[error map]]: {{val| 0.000 -1.057 +3.074 -2.459 }}
: [[error map]]: {{val| 0.000 -1.057 +3.074 -2.459 }}
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 77.864{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~21/20 = 77.864{{c}}
: error map: {{val| 0.000 -1.181 +3.005 -2.417 }}
: error map: {{val| 0.000 -1.181 +3.005 -2.417 }} -->


[[Minimax tuning]]:
[[Minimax tuning]]:
Line 1,412: Line 1,416:
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.  
[[Algebraic generator]]: smaller root of ''x''<sup>2</sup> - 89''x'' + 92, or (89 - sqrt (7553))/2, at 77.8616 cents.  


{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185, 262cd }}
{{Optimal ET sequence|legend=1| 15, 31, 46, 77, 185 }}


[[Badness]] (Smith): 0.031056
[[Badness]] (Sintel): 0.786


=== 11-limit ===
=== 11-limit ===
Line 1,422: Line 1,426:


Mapping: {{mapping| 1 1 2 3 3 | 0 9 5 -3 7 }}
Mapping: {{mapping| 1 1 2 3 3 | 0 9 5 -3 7 }}
: mapping generators: ~2, ~21/20


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.963{{c}}
* WE: ~2 = 1200.3890{{c}}, ~22/21 = 77.9065{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.881{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.9007{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.963{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.881{{c}} -->


Minimax tuning:
Minimax tuning:
Line 1,436: Line 1,440:
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.
Algebraic generator: positive root of 4''x''<sup>3</sup> + 15''x''<sup>2</sup> - 21, or else Gontrand2, the smallest positive root of 4''x''<sup>7</sup> - 8''x''<sup>6</sup> + 5.


{{Optimal ET sequence|legend=0| 15, 31, 46, 77, 262cdee, 339cdeee }}
{{Optimal ET sequence|legend=0| 15, 31, 46, 77 }}


Badness (Smith): 0.016687
Badness (Sintel): 0.552


==== Valentino ====
==== Valentino ====
Line 1,448: Line 1,452:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.968{{c}}
* WE: ~2 = 1200.1967{{c}}, ~22/21 = 77.9708{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.958{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.9594{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.968{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.958{{c}} -->


{{Optimal ET sequence|legend=0| 15f, 31, 46, 77 }}
{{Optimal ET sequence|legend=0| 15f, 31, 46, 77 }}


Badness (Smith): 0.020665
Badness (Sintel): 0.854


===== 17-limit =====
===== 17-limit =====
Line 1,463: Line 1,469:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/21 = 78.003{{c}}
* WE: ~2 = 1200.0404{{c}}, ~22/21 = 78.0055{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 78.003{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 78.0029{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/21 = 78.003{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 78.003{{c}} -->


{{Optimal ET sequence|legend=0| 15f, 31, 46, 77, 123e }}
{{Optimal ET sequence|legend=0| 15f, 31, 46, 77, 123e }}


Badness (Smith): 0.016768
Badness (Sintel): 0.854


==== Lupercalia ====
==== Lupercalia ====
Line 1,478: Line 1,486:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.694{{c}}
* WE: ~2 = 1199.9143{{c}}, ~22/21 = 77.7039{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.709{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 77.7049{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/21 = 77.694{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 77.709{{c}} -->


{{Optimal ET sequence|legend=0| 15, 31 }}
{{Optimal ET sequence|legend=0| 15, 31 }}


Badness (Smith): 0.021328
Badness (Sintel): 0.881


==== Dwynwen ====
==== Dwynwen ====
Line 1,493: Line 1,503:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~22/21 = 78.243{{c}}
* WE: ~2 = 1200.1306{{c}}, ~22/21 = 78.2273{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 78.219{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~22/21 = 78.2241{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~22/21 = 78.243{{c}}
* POTE: ~2 = 1200.000{{c}}, ~22/21 = 78.219{{c}} -->


{{Optimal ET sequence|legend=0| 15, 31f, 46 }}
{{Optimal ET sequence|legend=0| 15, 31f, 46 }}


Badness (Smith): 0.023461
Badness (Sintel): 0.969


==== Semivalentine ====
==== Semivalentine ====
Line 1,506: Line 1,518:


Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}
Mapping: {{mapping| 2 2 4 6 6 7 | 0 9 5 -3 7 3 }}
: mapping generators: ~55/39, ~22/21
: mapping generators: ~55/39, ~22/21


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.000{{c}}, ~22/21 = 77.997{{c}}
* WE: ~55/39 = 600.3497{{c}}, ~22/21 = 77.8845{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~22/21 = 77.839{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~22/21 = 77.8715{{c}}
<!-- * CTE: ~55/39 = 600.000{{c}}, ~22/21 = 77.997{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~22/21 = 77.839{{c}} -->


{{Optimal ET sequence|legend=0| 16, 30, 46, 62, 108ef }}
{{Optimal ET sequence|legend=0| 16, 30, 46, 62, 108ef }}


Badness (Smith): 0.032749
Badness (Sintel): 1.35


==== Hemivalentine ====
==== Hemivalentine ====
Line 1,523: Line 1,536:


Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}
Mapping: {{mapping| 1 1 2 3 3 4 | 0 18 10 -6 14 -9 }}
: mapping generators: ~2, ~40/39
: mapping generators: ~2, ~40/39


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~40/39 = 39.014{{c}}
* WE: ~2 = 1199.6529{{c}}, ~40/39 = 39.0323{{c}}
* POTE: ~2 = 1200.000{{c}}, ~40/39 = 39.044{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~40/39 = 39.0383{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~40/39 = 39.014{{c}}
* POTE: ~2 = 1200.000{{c}}, ~40/39 = 39.044{{c}} -->


{{Optimal ET sequence|legend=0| 30, 31, 61, 92f }}
{{Optimal ET sequence|legend=0| 30, 31, 61, 92f }}


Badness (Smith): 0.047059
Badness (Sintel): 1.94


==== Demivalentine ====
==== Demivalentine ====
Line 1,540: Line 1,554:


Mapping: {{mapping| 1 -8 -3 6 -4 -16 | 0 18 10 -6 14 37 }}
Mapping: {{mapping| 1 -8 -3 6 -4 -16 | 0 18 10 -6 14 37 }}
: mapping generators: ~2, ~13/9
: mapping generators: ~2, ~13/9


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~13/9 = 638.964{{c}}
* WE: ~2 = 1200.3929{{c}}, ~13/9 = 639.1320{{c}}
* CWE: ~2 = 1200.000{{c}}, ~13/9 = 638.932{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/9 = 638.9325{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~13/9 = 638.964{{c}} -->


{{Optimal ET sequence|legend=0| 15, 47ef, 62, 77 }}
{{Optimal ET sequence|legend=0| 15, 47ef, 62, 77 }}


Badness (Smith): 0.0349
Badness (Sintel): 1.44


=== Hemivalentino ===
=== Hemivalentino ===
Line 1,559: Line 1,573:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~45/44 = 38.928{{c}}
* WE: ~2 = 1200.0816{{c}}, ~45/44 = 38.9236{{c}}
* POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.921{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9228{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~45/44 = 38.928{{c}}
* POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.921{{c}} -->


{{Optimal ET sequence|legend=0| 31, 92e, 123, 154, 185 }}
{{Optimal ET sequence|legend=0| 31, 92e, 123, 154, 185 }}


Badness (Smith): 0.061275
Badness (Sintel): 2.03


==== 13-limit ====
==== 13-limit ====
Line 1,574: Line 1,590:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~45/44 = 38.944{{c}}
* WE: ~2 = 1199.8782{{c}}, ~45/44 = 38.9440{{c}}
* POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.948{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9472{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~45/44 = 38.944{{c}}
* POTE: ~2 = 1200.000{{c}}, ~45/44 = 38.948{{c}} -->


{{Optimal ET sequence|legend=0| 31, 123, 154 }}
{{Optimal ET sequence|legend=0| 31, 123, 154 }}


Badness (Smith): 0.057919
Badness (Sintel): 2.39


==== Hemivalentoid ====
==== Hemivalentoid ====
Line 1,589: Line 1,607:


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~40/39 = 38.946{{c}}
* WE: ~2 = 1199.3614{{c}}, ~45/44 = 38.9721{{c}}
* POTE: ~2 = 1200.000{{c}}, ~40/39 = 38.993{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~45/44 = 38.9839{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~40/39 = 38.946{{c}}
* POTE: ~2 = 1200.000{{c}}, ~40/39 = 38.993{{c}} -->


{{Optimal ET sequence|legend=0| 31, 92ef }}
{{Optimal ET sequence|legend=0| 31, 92ef }}


Badness (Smith): 0.057931
Badness (Sintel): 2.39


== Superkleismic ==
== Superkleismic ==
Line 1,602: Line 1,622:
Superkleismic tempers out the keema, [[875/864]], and can be described as the {{nowrap| 15 & 26 }} temperament. It splits the ~7/4 into three ~6/5 generators of around 322 cents. This is noticeably sharper than the [[kleismic]] generator, hence the name. Its [[ploidacot]] is wau-enneacot. In the 11-limit, two generator steps can be identified with ~16/11, and in the 13-limit, the same step can be treated as ~13/9. The [[S-expression]]-based comma list of 13-limit superkleismic is {[[875/864|S5/S6]], [[1029/1024|S7/S8]], [[100/99|S10]], [[144/143|S12]], ([[441/440|S21]])}. Through careful observation of the equivalences therein one can derive the mapping of the full 13-limit.
Superkleismic tempers out the keema, [[875/864]], and can be described as the {{nowrap| 15 & 26 }} temperament. It splits the ~7/4 into three ~6/5 generators of around 322 cents. This is noticeably sharper than the [[kleismic]] generator, hence the name. Its [[ploidacot]] is wau-enneacot. In the 11-limit, two generator steps can be identified with ~16/11, and in the 13-limit, the same step can be treated as ~13/9. The [[S-expression]]-based comma list of 13-limit superkleismic is {[[875/864|S5/S6]], [[1029/1024|S7/S8]], [[100/99|S10]], [[144/143|S12]], ([[441/440|S21]])}. Through careful observation of the equivalences therein one can derive the mapping of the full 13-limit.


Superkleismic also sets two intervals of [[21/20]] equal to [[10/9]]; as {{nowrap| 10/9 {{=}} ([[20/19]])⋅([[19/18]]) }}, we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out {{nowrap| S19 {{=}} [[361/360]] }} and {{nowrap| S20 {{=}} [[400/399]] }}.  
Superkleismic also sets two intervals of [[21/20]] equal to [[10/9]]; as {{nowrap| 10/9 {{=}} ([[20/19]])⋅([[19/18]]) }}, we can identify 21/20, 20/19, and 19/18 together to add prime 19, tempering out [[361/360]] ({{S|19}}) and [[400/399]] ({{S|20}}).  


41edo gives an obvious tuning in all the subgroups.  
41edo gives an obvious tuning in all the subgroups.  
Line 1,610: Line 1,630:
[[Comma list]]: 875/864, 1029/1024
[[Comma list]]: 875/864, 1029/1024


{{Mapping|legend=1| 1 4 5 2 | 0 -9 -10 3 }}
{{Mapping|legend=1| 1 -5 -5 5 | 0 9 10 -3 }}
 
: mapping generators: ~2, ~5/3
: mapping generators: ~2, ~6/5


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.798{{c}}
* [[WE]]: ~2 = 1200.7640{{c}}, ~5/3 = 878.6289{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~6/5 = 321.930{{c}}
: [[error map]]: {{val| +0.764 +1.885 +3.844 -0.893 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/3 = 878.1077{{c}}
: error map: {{val| 0.000 +1.014 -5.237 -3.149 }}
<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~5/3 = 878.202{{c}}
* [[POTE]]: ~2 = 1200.000{{c}}, ~5/3 = 878.070{{c}} -->


{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}
{{Optimal ET sequence|legend=1| 11c, 15, 26, 41 }}


[[Badness]]:
[[Badness]] (Sintel): 1.21
* Smith: 0.0479
* Sintel: 1.21


=== 11-limit ===
=== 11-limit ===
Line 1,629: Line 1,650:
Comma list: 100/99, 245/242, 385/384
Comma list: 100/99, 245/242, 385/384


Mapping: {{mapping| 1 4 5 2 4 | 0 -9 -10 3 -2 }}
Mapping: {{mapping| 1 -5 -5 5 2 | 0 9 10 -3 2 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.815{{c}}
* WE: ~2 = 1200.1691{{c}}, ~5/3 = 878.2772{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.847{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.1606{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.185{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.153{{c}} -->


{{Optimal ET sequence|legend=0| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}
{{Optimal ET sequence|legend=0| 11c, 15, 26, 41, 179cde, 220cde, 261ccdee }}


Badness:
Badness (Sintel): 0.848
* Smith: 0.0257
* Sintel: 0.848


==== 2.3.5.7.11.19 subgroup ====
==== 2.3.5.7.11.19 subgroup ====
Line 1,648: Line 1,669:
Comma list: 100/99, 133/132, 190/189, 385/384
Comma list: 100/99, 133/132, 190/189, 385/384


Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -14}}
Mapping: {{mapping| 1 -5 -5 5 2 -6 | 0 9 10 -3 2 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.779{{c}}
* WE: ~2 = 1200.2289{{c}}, ~5/3 = 878.3409{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.827{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.1840{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.221{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.173{{c}} -->


Optimal ET sequence: {{Optimal ET sequence| 11c, 15, 26, 41, 138e, 179cde, 220cdeh }}
{{Optimal ET sequence|legend=0| 11c, 15, 26, 41, 138e }}


Badness (Sintel): 0.692
Badness (Sintel): 0.692
Line 1,665: Line 1,688:
Comma list: 100/99, 105/104, 144/143, 245/242
Comma list: 100/99, 105/104, 144/143, 245/242


Mapping: {{mapping| 1 4 5 2 4 8 | 0 -9 -10 3 -2 -16 }}
Mapping: {{mapping| 1 -5 -5 5 2 -8 | 0 9 10 -3 2 16 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.986{{c}}
* WE: ~2 = 1200.0261{{c}}, ~5/3 = 878.0252{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.994{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.0073{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.014{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.006{{c}} -->


{{Optimal ET sequence|legend=0| 11cf, 15, 26, 41 }}
{{Optimal ET sequence|legend=0| 11cf, 15, 26, 41 }}


Badness:
Badness (Sintel): 0.887
* Smith: 0.0215
* Sintel: 0.887


==== 17-limit ====
==== 17-limit ====
Line 1,682: Line 1,705:
Comma list: 100/99, 105/104, 120/119, 144/143, 245/242
Comma list: 100/99, 105/104, 120/119, 144/143, 245/242


Mapping: {{mapping| 1 4 5 2 4 8 10 | 0 -9 -10 3 -2 -16 -22 }}
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 | 0 9 10 -3 2 16 22 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 322.136{{c}}
* WE: ~2 = 1200.0488{{c}}, ~5/3 = 877.8872{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 322.149{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 877.8537{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 877.864{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 877.851{{c}} -->


{{Optimal ET sequence|legend=0| 11cfg, 15g, 26, 41 }}
{{Optimal ET sequence|legend=0| 11cfg, 15g, 26, 41 }}


Badness (Sintel): 1.007
Badness (Sintel): 1.01


==== 19-limit ====
==== 19-limit ====
Line 1,697: Line 1,722:
Comma list: 100/99, 105/104, 120/119, 144/143, 133/132, 190/189
Comma list: 100/99, 105/104, 120/119, 144/143, 133/132, 190/189


Mapping: {{mapping| 1 4 5 2 4 8 10 8 | 0 -9 -10 3 -2 -16 -22 -14 }}
Mapping: {{mapping| 1 -5 -5 5 2 -8 -12 -6 | 0 9 10 -3 2 16 22 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 322.084{{c}}
* WE: ~2 = 1200.2120{{c}}, ~5/3 = 878.0243{{c}}
* CWE: ~2 = 1200.000{{c}}, ~6/5 = 322.121{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 877.8789{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 877.916{{c}} -->


{{Optimal ET sequence|legend=0| 11cfgh, 15g, 26, 41 }}
{{Optimal ET sequence|legend=0| 11cfgh, 15g, 26, 41 }}
Line 1,714: Line 1,740:
Comma list: 100/99, 196/195, 385/384, 441/440
Comma list: 100/99, 196/195, 385/384, 441/440


Mapping: {{mapping| 1 4 5 2 4 -3 | 0 -9 -10 3 -2 25 }}
Mapping: {{mapping| 1 -5 -5 5 2 22 | 0 9 10 -3 2 -25 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.724{{c}}
* WE: ~2 = 1199.8272{{c}}, ~5/3 = 878.1538{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.719{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.2795{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.276{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.281{{c}} -->


{{Optimal ET sequence|legend=0| 15f, 26f, 41, 97, 138e }}
{{Optimal ET sequence|legend=0| 15f, 41, 97, 138e }}


Badness (Sintel): 1.402
Badness (Sintel): 1.40


==== 17-limit ====
==== 17-limit ====
Line 1,729: Line 1,757:
Comma list: 100/99, 154/153, 196/195, 256/255, 273/272
Comma list: 100/99, 154/153, 196/195, 256/255, 273/272


Mapping: {{mapping| 1 4 5 2 4 -3 -1 | 0 -9 -10 3 -2 25 19 }}
Mapping: {{mapping| 1 -5 -5 5 2 22 18 | 0 9 10 -3 2 -25 -19 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.650{{c}}
* WE: ~2 = 1199.5964{{c}}, ~5/3 = 878.0482{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.657{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.3444{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.350{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.343{{c}} -->


{{Optimal ET sequence|legend=0| 15f, 26fg, 41, 56, 97g }}
{{Optimal ET sequence|legend=0| 15f, 41, 56, 97g }}


Badness (Sintel): 1.452
Badness (Sintel): 1.45


==== 19-limit ====
==== 19-limit ====
Line 1,744: Line 1,774:
Comma list: 100/99, 133/132, 154/153, 190/189, 196/195, 256/255
Comma list: 100/99, 133/132, 154/153, 190/189, 196/195, 256/255


Mapping: {{mapping| 1 4 5 2 4 -3 -1 8 | 0 -9 -10 3 -2 25 19 -14 }}
Mapping: {{mapping| 1 -5 -5 5 2 22 18 -6 | 0 9 10 -3 2 -25 -19 14 }}


Optimal tunings:  
Optimal tunings:  
* CTE: ~2 = 1200.000{{c}}, ~6/5 = 321.646{{c}}
* WE: ~2 = 1199.6638{{c}}, ~5/3 = 878.1109{{c}}
* POTE: ~2 = 1200.000{{c}}, ~6/5 = 321.643{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/3 = 878.3566{{c}}
<!-- * CTE: ~2 = 1200.000{{c}}, ~5/3 = 878.364{{c}}
* POTE: ~2 = 1200.000{{c}}, ~5/3 = 878.357{{c}} -->


{{Optimal ET sequence|legend=0| 15f, 26fg, 41, 56, 97g }}
{{Optimal ET sequence|legend=0| 15f, 41, 56, 97g }}


Badness (Sintel): 1.355
Badness (Sintel): 1.36


== Unidec ==
== Unidec ==
Retrieved from "https://en.xen.wiki/w/Gamelismic_clan"