Lehmerismic temperaments: Difference between revisions

Switch to Sintel's badness, WE & CWE tunings
- tyr (moved to landscape family)
Line 14: Line 14:
* ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo|Hemifamity family]]
* ''[[Kapo]]'' (+5120/5103) → [[Hemifamity family #Kapo|Hemifamity family]]


Considered below are tyr, skadi, ganesha, hanuman, lux, and galaxy. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].  
Considered below are skadi, ganesha, hanuman, lux, and galaxy, in the order of increasing badness. For the rank-4 temperament, see [[Rank-4 temperament #Lehmerismic (3025/3024)]].  
 
== Tyr ==
{{See also| Landscape family }}
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 3025/3024, 102487/102400
 
{{Mapping|legend=1| 3 0 0 4 8 | 0 2 0 -4 1 | 0 0 1 2 0 }}
: mapping generators: ~63/50, ~400/231, ~5
 
[[Optimal tuning]]s:
* [[WE]]: ~63/50 = 400.0162{{c}}, ~400/231 = 950.9828{{c}}, ~5/4 = 386.2400{{c}}
: [[error map]]: {{val| +0.049 +0.011 +0.024 -0.017 -0.205 }}
* [[CWE]]: ~63/50 = 400.0000{{c}}, ~400/231 = 950.9591{{c}}, ~5/4 = 386.2764{{c}}
: error map: {{val| 0.000 -0.037 -0.037 -0.109 -0.359 }}
 
{{Optimal ET sequence|legend=1| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}
 
[[Badness]] (Sintel): 0.311
 
=== Borneo ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 676/675, 1001/1000, 3025/3024
 
Mapping: {{mapping| 3 0 0 4 8 -3 | 0 2 0 -4 1 3 | 0 0 1 2 0 1 }}
 
Optimal tunings:
* WE: ~63/50 = 400.0002{{c}}, ~26/15 = 951.0850{{c}}, ~5/4 = 386.5817{{c}}
* CWE: ~63/50 = 400.0000{{c}}, ~26/15 = 951.0846{{c}}, ~5/4 = 386.5821{{c}}
 
{{Optimal ET sequence|legend=0| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}
 
Badness (Sintel): 0.514
 
Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7


== Skadi ==
== Skadi ==