Magic family: Difference between revisions

- CTE & POTE tunings
BudjarnLambeth (talk | contribs)
 
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Badness (Sintel): 1.05
Badness (Sintel): 1.05


====== 19-limit ======
====== Magicus ======
Subgroup: 2.3.5.7.11.13.17.19
Subgroup: 2.3.5.7.11.13.17.19


Line 237: Line 237:


Badness (Sintel): 1.07
Badness (Sintel): 1.07
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 52/51, 65/64, 78/77, 91/90, 100/99
Mapping: {{mapping| 1 0 2 -1 6 4 6 | 0 5 1 12 -8 -1 -6 }}
Optimal tunings:
* WE: ~2 = 1200.4822{{c}}, ~5/4 = 380.8818{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7356{{c}}
{{Optimal ET sequence|legend=0| 19, 22 }}
Badness (Sintel): 1.21
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 52/51, 65/64, 78/77, 91/90, 100/99, 133/132
Mapping: {{mapping| 1 0 2 -1 6 4 6 9 | 0 5 1 12 -8 -1 -6 -15 }}
Optimal tunings:
* WE: ~2 = 1200.6684{{c}}, ~5/4 = 380.8328{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6212{{c}}
{{Optimal ET sequence|legend=0| 19, 22 }}
Badness (Sintel): 1.41


==== Necromancy ====
==== Necromancy ====
Line 297: Line 267:


Badness (Sintel): 1.12
Badness (Sintel): 1.12
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 100/99, 120/119, 133/132, 154/153, 209/208, 225/224
Mapping: {{mapping| 1 0 2 -1 6 11 6 9 | 0 5 1 12 -8 -23 -6 -15 }}
Optimal tunings:
* WE: ~2 = 1199.6176{{c}}, ~5/4 = 380.6981{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7355{{c}}
{{Optimal ET sequence|legend=0| 19f, 22, 41 }}
Badness (Sintel): 1.28


==== Soothsaying ====
==== Soothsaying ====
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Badness (Sintel): 1.05
Badness (Sintel): 1.05
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 55/54, 65/64, 85/84, 91/90, 99/98
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 | 0 5 1 12 14 -1 16 }}
Optimal tunings:
* WE: ~2 = 1202.5560{{c}}, ~5/4 = 381.4295{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7843{{c}}
{{Optimal ET sequence|legend=0| 19eg, 22, 41efg }}
Badness (Sintel): 1.03
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 55/54, 57/56, 65/64, 76/75, 85/84, 99/98
Mapping: {{mapping| 1 0 2 -1 -1 4 -1 2 | 0 5 1 12 14 -1 16 7 }}
Optimal tunings:
* WE: ~2 = 1203.4043{{c}}, ~5/4 = 381.5989{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7353{{c}}
{{Optimal ET sequence|legend=0| 19egh, 22, 41efghh }}
Badness (Sintel): 1.16


==== Intuition ====
==== Intuition ====
Line 432: Line 357:


Badness (Sintel): 1.08
Badness (Sintel): 1.08
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
Comma list: 55/54, 66/65, 85/84, 99/98, 105/104
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 | 0 5 1 12 14 18 16 }}
Optimal tunings:
* WE: ~2 = 1201.3593{{c}}, ~5/4 = 381.0356{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.7204{{c}}
{{Optimal ET sequence|legend=0| 19eg, 22f }}
Badness (Sintel): 1.03
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 55/54, 66/65, 77/76, 85/84, 99/98, 105/104
Mapping: {{mapping| 1 0 2 -1 -1 -2 -1 -4 | 0 5 1 12 14 18 16 26 }}
Optimal tunings:
* WE: ~2 = 1201.5266{{c}}, ~5/4 = 381.0019{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.6275{{c}}
{{Optimal ET sequence|legend=0| 19egh, 22fh }}
Badness (Sintel): 1.19


=== Horcrux ===
=== Horcrux ===
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Badness (Sintel): 1.06
Badness (Sintel): 1.06
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 105/104, 133/132, 154/153, 170/169, 171/169, 196/195
Mapping: {{mapping| 1 0 2 -1 -7 -2 -7 -4 | 0 5 1 12 33 18 35 26 }}
Optimal tunings:
* WE: ~2 = 1201.2528{{c}}, ~5/4 = 380.5518{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 380.2052{{c}}
{{Optimal ET sequence|legend=0| 19egh, 41, 60eh }}
Badness (Sintel): 1.13


=== Divination ===
=== Divination ===
Line 793: Line 673:
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: 64/63, 100/99, 605/588
Comma list: 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 6 | 0 5 1 -10 -8 }}
Mapping: {{mapping| 1 0 2 0 0 | 0 5 1 9 11 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1198.8032{{c}}, ~5/4 = 381.3145{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.7119{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.9735{{c}}


{{Optimal ET sequence|legend=0| 3, 19d, 22 }}
{{Optimal ET sequence|legend=0| 3de, 13be, 16 }}


Badness (Sintel): 1.57
Badness (Sintel): 1.55


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


Comma list: 64/63, 65/63, 100/99, 169/165
Comma list: 27/26, 36/35, 45/44, 363/343


Mapping: {{mapping| 1 0 2 6 6 4 | 0 5 1 -10 -8 -1 }}
Mapping: {{mapping| 1 0 2 0 0 -1 | 0 5 1 9 11 15 }}


Optimal tunings:  
Optimal tunings:  
* WE: ~2 = 1199.9726{{c}}, ~5/4 = 381.7271{{c}}
* WE: ~2 = 1201.7428{{c}}, ~5/4 = 377.3134{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 381.7362{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~5/4 = 376.4221{{c}}
 
{{Optimal ET sequence|legend=0| 3def, 13beff, 16 }}
 
Badness (Sintel): 1.58


{{Optimal ET sequence|legend=0| 3, 22 }}
Scales: [[User:BudjarnLambeth/Volcanic glass]]


Badness (Sintel): 1.64
Music: [https://www.youtube.com/watch?v=oXy_RXrBVWA ''Rain in the crystal mirror caves''] - [[Budjarn Lambeth]] (2026)


== Hocum ==
== Hocum ==
Line 1,014: Line 902:
Comma list: 105/104, 144/143, 245/242, 625/616
Comma list: 105/104, 144/143, 245/242, 625/616


Mapping: {{mapping| 1 5 3 4 5 9 | 0 -20 -4 -7 -9 -31 }}
Mapping: {{mapping| 1 -15 -1 -3 -22 | 0 20 4 7 9 31 }}


Optimal tunings:  
Optimal tunings:  
Line 1,093: Line 981:


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Magic family| ]] <!-- main article -->
[[Category:Magic family| ]] <!-- main article -->
[[Category:Magic| ]] <!-- key article -->
[[Category:Magic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Listen]]
[[Category:Listen]]