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Diaschismic rank-3 family: Difference between revisions

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* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}
: error map: {{val| 0.000 +3.003 +3.769 +2.469 }}
: error map: {{val| 0.000 +3.003 +3.769 +2.469 }}
<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->


{{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}
{{Optimal ET sequence|legend=1| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}
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[[Badness]] (Sintel): 1.95
[[Badness]] (Sintel): 1.95


== Julius a.k.a. varda ==
== Varda ==
Varda tempers out 176/175, 896/891 as well as 9801/9800, and is the main extension of rank-3 diaschismic to the 11-limit. Notice the identity {{nowrap| 2048/2025 {{=}} (176/175)⋅(896/891) }}. In the natural 13-limit extension, 351/350, 352/351 and 364/363 are further tempered out, and in the 17-limit, 136/135, 256/255 and 289/288.  
 
[[Subgroup]]: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


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* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}
* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}
: error map: {{val| 0.000 +2.703 +4.371 +3.153 +2.031 }}
: error map: {{val| 0.000 +2.703 +4.371 +3.153 +2.031 }}
<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->


[[Minimax tuning]]:  
[[Minimax tuning]]:  
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; Scales
; Scales
* Julius[22] [[hobbit]] [[transversal]]:
* Varda[22] [[hobbit]] [[transversal]]:
: 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2
: 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2
* Julius[24] hobbit transversal
* Varda[24] hobbit transversal
: 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2
: 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2


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


Comma list: 176/175, 351/350, 364/363
Comma list: 176/175, 351/350, 364/363


Mapping: {{mapping| 2 0 11 0 14 24 | 0 1 -2 0 -4 -7 | 0 0 0 1 1 1 }}
{{Mapping|legend=0| 2 0 11 0 14 24 | 0 1 -2 0 -4 -7 | 0 0 0 1 1 1 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 136/135, 176/175, 256/255, 351/350
Comma list: 136/135, 176/175, 256/255, 351/350


Mapping: {{mapping| 2 0 11 0 14 24 5 | 0 1 -2 0 -4 -7 1 | 0 0 0 1 1 1 0 }}
{{Mapping|legend=0| 2 0 11 0 14 24 5 | 0 1 -2 0 -4 -7 1 | 0 0 0 1 1 1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 92: Line 92:
Comma list: 176/175, 325/324, 896/891
Comma list: 176/175, 325/324, 896/891


Mapping: {{mapping| 2 0 11 0 14 -18 | 0 1 -2 0 -4 8 | 0 0 0 1 1 0 }}
{{Mapping|legend=0| 2 0 11 0 14 -18 | 0 1 -2 0 -4 8 | 0 0 0 1 1 0 }}


Optimal tunings:  
Optimal tunings:  
Line 107: Line 107:
Comma list: 136/135, 176/175, 256/255, 325/324
Comma list: 136/135, 176/175, 256/255, 325/324


Mapping: {{mapping| 2 0 11 0 14 -18 5 | 0 1 -2 0 -4 8 1 | 0 0 0 1 1 0 0 }}
{{Mapping|legend=0| 2 0 11 0 14 -18 5 | 0 1 -2 0 -4 8 1 | 0 0 0 1 1 0 0 }}


Optimal tunings:  
Optimal tunings:  
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Comma list: 136/135, 176/175, 190/189, 256/255, 286/285
Comma list: 136/135, 176/175, 190/189, 256/255, 286/285


Mapping: {{mapping| 2 0 11 0 14 -18 5 -13 | 0 1 -2 0 -4 8 1 5 | 0 0 0 1 1 0 0 1 }}
{{Mapping|legend=0| 2 0 11 0 14 -18 5 -13 | 0 1 -2 0 -4 8 1 5 | 0 0 0 1 1 0 0 1 }}


Optimal tunings:  
Optimal tunings:  
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[[Badness]] (Sintel): 2.37
[[Badness]] (Sintel): 2.37


[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Diaschismic rank-3 family| ]] <!-- main article -->
[[Category:Diaschismic rank-3 family| ]] <!-- main article -->
[[Category:Diaschismic| ]] <!-- key article -->
[[Category:Diaschismic| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]
Retrieved from "https://en.xen.wiki/w/Diaschismic_rank-3_family"