Aberschismic temperaments: Difference between revisions

m Status update
Ketchup: replace 19- and 23-limit with no-19 23-limit, which is more natural
Line 206: Line 206:


== Ketchup ==
== Ketchup ==
Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its ploidacot is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.  
Ketchup may be described as the {{nowrap| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 258: Line 258:
Subgroup: 2.3.5.7.11.13.17
Subgroup: 2.3.5.7.11.13.17


Comma list: 289/288, 325/324, 352/351, 385/384, 561/560
Comma list: 289/288, 325/324, 352/351, 385/384, 442/441


Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 | 0 4 15 -9 -2 -14 4 }}
Line 270: Line 270:
Badness (Sintel): 0.845
Badness (Sintel): 0.845


=== 19-limit ===
=== 2.3.5.7.11.13.17.23 subgroup ===
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.23


Comma list: 190/189, 209/208, 289/288, 352/351, 385/384, 561/560
Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390


Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 -12 }}
Mapping: {{mapping| 2 3 4 6 7 8 8 9 | 0 4 15 -9 -2 -14 4 1 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~17/12 = 600.1639{{c}}, ~66/65 = 25.6669{{c}}
* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6597{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}


{{Optimal ET sequence|legend=0| 46, 94, 140h }}
{{Optimal ET sequence|legend=0| 46, 94, 140 }}
 
Badness (Sintel): 1.11
 
=== 23-limit ===
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384
 
Mapping: {{mapping| 2 3 4 6 7 8 8 9 9 | 0 4 15 -9 -2 -14 4 -12 1 }}
 
Optimal tunings:
* WE: ~17/12 = 600.1777{{c}}, ~66/65 = 25.6682{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6605{{c}}
 
{{Optimal ET sequence|legend=0| 46, 94, 140h }}


Badness (Sintel): 1.00
Badness (Sintel): 0.772


== Undecental ==
== Undecental ==