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Badness (Sintel): 1.19
Badness (Sintel): 1.19


== Darkstone ==
== Brightstone ==
Darkstone (16 & 19d) is a low-accuacy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles. In [http://www.tonalsoft.com/enc/m/magic.aspx ''Encyclopedia of Microtonal Music Theory'', Tonalsoft], this temperament is given a name ''witch''.
Brightstone tempers out 64/63 and may be described as {{nowrap| 22 & 25 }}. 22edo itself is a good tuning, in which case it is identical to magic. Brightstone can be extended to the 11- and 13-limit in a similar way to muggles.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 1875/1792
[[Comma list]]: 64/63, 3125/3024


{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}
{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.7458{{c}}, ~5/4 = 377.2996{{c}}
* [[WE]]: ~2 = 1198.1701{{c}}, ~5/4 = 381.3741{{c}}
: [[error map]]: {{val| +1.746 -15.457 -5.523 +26.870 }}
: error map: {{val| -1.830 +4.915 -8.599 +6.454 }}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.9630{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 381.9562{{c}}
: error map: {{val| 0.000 -17.140 -9.351 +23.841 }}
: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}


{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}
{{Optimal ET sequence|legend=1| 3, 19d, 22 }}


[[Badness]] (Sintel): 2.13
[[Badness]] (Sintel): 2.23


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 36/35, 45/44, 363/343
Comma list: 55/54, 64/63, 625/616


Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}
Mapping: {{mapping| 1 0 2 6 -1 | 0 5 1 -10 14 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* WE: ~2 = 1198.5372{{c}}, ~5/4 = 381.7556{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.1943{{c}}


{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}
{{Optimal ET sequence|legend=0| 22, 69b }}


Badness (Sintel): 1.55
Badness (Sintel): 1.85


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 27/26, 36/35, 45/44, 363/343
Comma list: 40/39, 55/54, 64/63, 625/616


Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}
Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 14 -4 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* WE: ~2 = 1197.2300{{c}}, ~5/4 = 381.6164{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.4690{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 47bff }}
 
Badness (Sintel): 1.99


{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}
== Darkstone ==
Darkstone (16 & 19d) is a low-accuracy temperament which tempers out 36/35 and 1875/1792. It makes the major third and the fifth even flatter than those of muggles.


Badness (Sintel): 1.58
This temperament is known as ''witch'' in [http://www.tonalsoft.com/enc/m/magic.aspx Tonalsoft Encyclopedia].  


== Brightstone ==
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 64/63, 3125/3024
[[Comma list]]: 36/35, 1875/1792


{{Mapping|legend=1| 1 0 2 6 | 0 5 1 -10 }}
{{Mapping|legend=1| 1 0 2 0 | 0 5 1 9 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1198.1701{{c}}, ~5/4 = 381.3741{{c}}
* [[WE]]: ~2 = 1201.7458{{c}}, ~5/4 = 377.2996{{c}}
: error map: {{val| -1.830 +4.915 -8.599 +6.454 }}
: [[error map]]: {{val| +1.746 -15.457 -5.523 +26.870 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~5/4 = 381.9562{{c}}
* [[CWE]]: ~2 = 1200.000{{c}}, ~5/4 = 376.9630{{c}}
: error map: {{val| 0.000 +7.826 -4.358 +11.613 }}
: error map: {{val| 0.000 -17.140 -9.351 +23.841 }}


{{Optimal ET sequence|legend=1| 3, 19d, 22 }}
{{Optimal ET sequence|legend=1| 3d, …, 13b, 16 }}


[[Badness]] (Sintel): 2.23
[[Badness]] (Sintel): 2.13


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Comma list: 55/54, 64/63, 625/616
Comma list: 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 -1 | 0 5 1 -10 14 }}
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.5372{{c}}, ~5/4 = 381.7556{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.1943{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}


{{Optimal ET sequence|legend=0| 22, 69b }}
{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}


Badness (Sintel): 1.85
Badness (Sintel): 1.55


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Comma list: 40/39, 55/54, 64/63, 625/616
Comma list: 27/26, 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 14 -4 }}
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1197.2300{{c}}, ~5/4 = 381.6164{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 382.4690{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}


{{Optimal ET sequence|legend=0| 22f, 47bff }}
{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}


Badness (Sintel): 1.99
Badness (Sintel): 1.58


== Hocum ==
== Hocum ==
Retrieved from "https://en.xen.wiki/w/Magic_family"