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Sensamagic family: Difference between revisions

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=== Overview to extensions ===
=== Overview to extensions ===
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]). Considered below are undecimal sensamagic, sensawer, octarod, shrusus, bisector and sensigh.  
The second comma in the comma list defines which [[11-limit]] family member we are looking at. Undecimal sensamagic adds [[385/384]], sensawer adds [[441/440]], octarod adds [[100/99]], shrusus adds [[176/175]]. These temperaments use the same generators as sensamagic. Bisector adds [[121/120]] with a half-octave period.
 
Temperaments discussed elsewhere include [[supernatural]] (→ [[Keemic family #Supernatural|Keemic family]]) and [[sensigh]] (→ [[Sengic family #Sensigh|Sengic family]]). The rest are considered below.  


== Undecimal sensamagic ==
== Undecimal sensamagic ==
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Comma list: 245/243, 352/351, 364/363
Comma list: 245/243, 352/351, 364/363


Mapping: {{mapping| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}
{{Mapping|legend=0| 1 0 0 0 7 12 | 0 1 1 2 -2 -5 | 0 0 2 -1 -1 -1 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 196/195, 245/243, 352/351
Comma list: 196/195, 245/243, 352/351


Mapping: {{mapping| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}
{{Mapping|legend=0| 1 0 0 0 -3 2 | 0 1 1 2 5 2 | 0 0 2 -1 -4 -4 }}


Optimal tunings:  
Optimal tunings:  
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: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }}
: error map: {{val| 0.000 +2.570 -3.230 +0.944 +5.801 }}


{{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e }} *
{{Optimal ET sequence|legend=1| 14c, 19, 22, 27e, 41, 90e, 131e}}*


<nowiki/>[[optimal patent val]]: [[104edo|104]]
<nowiki/>*[[Optimal patent val]]: [[104edo|104]]


[[Badness]] (Sintel): 0.698
[[Badness]] (Sintel): 0.698
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Comma list: 91/90, 176/175, 245/243
Comma list: 91/90, 176/175, 245/243


Mapping: {{mapping| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}
{{Mapping|legend=0| 1 0 0 0 -4 1 | 0 1 1 2 4 1 | 0 0 2 -1 3 3 }}


Optimal tunings:  
Optimal tunings:  
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[[Badness]] (Sintel): 1.31
[[Badness]] (Sintel): 1.31


== Sensigh ==
[[Category:Sensamagic family| ]] <!-- main article -->
Sensigh uses the same mapping as 7-limit [[sensi]] with an independent generator for prime 11.
 
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 126/125, 245/243
 
{{Mapping|legend=1| 1 -1 -1 -2 3 | 0 7 9 13 0 | 0 0 0 0 1 }}
: mapping generators: ~2, ~9/7, ~11
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.7081{{c}}, ~9/7 = 443.2748{{c}}, ~11/8 = 552.1736{{c}}
: [[error map]]: {{val| -0.2919 +1.2608 +3.4518 -5.6691 -0.0202 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/7 = 443.3493{{c}}, ~11/8 = 551.8069{{c}}
: error map: {{val| 0.0000 +1.4899 +3.8297 -5.2854 +0.4890 }}
 
{{Optimal ET sequence|legend=1| 27e, 38df, 46, 111d }}
 
[[Badness]] (Sintel): 1.48
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 91/90, 126/125, 169/168
 
Mapping: {{mapping| 1 -1 -1 -2 3 0 | 0 7 9 13 0 10 | 0 0 0 0 1 0 }}
 
Optimal tunings:
* WE: ~2 = 1200.0000{{c}}, ~9/7 = 443.4379{{c}}, ~11/8 = 550.3462{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3581{{c}}, ~11/8 = 550.7092{{c}}
 
{{Optimal ET sequence|legend=0| 27e, 38df, 46, 111df }}
 
Badness (Sintel): 0.878
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 91/90, 126/125, 154/153, 169/168
 
Mapping: {{mapping| 1 -1 -1 -2 3 0 4 | 0 7 9 13 0 10 -1 | 0 0 0 0 1 0 1 }}
 
Optimal tunings:
* WE: ~2 = 1200.2286{{c}}, ~9/7 = 443.4291{{c}}, ~11/8 = 549.2790{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~9/7 = 443.3707{{c}}, ~11/8 = 549.5775{{c}}
 
{{Optimal ET sequence|legend=0| 27eg, 38df, 46 }}
 
Badness (Sintel): 0.917
 
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Catalogs of rank-3 temperaments]]
[[Category:Sensamagic family| ]] <!-- main article -->
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Sensamagic_family"