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Misty family: Difference between revisions

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Switch to Sintel's badness, WE & CWE tunings
Move back subgroup extensions since they're still septimal misty extensions
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{{Main| Misty }}
{{Main| Misty }}


=== 7-limit ===
[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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[[Badness]] (Sintel): 0.931
[[Badness]] (Sintel): 0.931
==== 2.3.5.7.17-subgroup ====
The [[S-expression]]-based comma list for this extension is {([[5120/5103|S8/S9]]), [[2025/2023|S15/S17]], [[256/255|S16]], [[1701/1700|S18/S20]], ([[2500/2499|S50]])}, and for the 2.3.5.7.17.19-subgroup extension, {([[5120/5103|S8/S9]]), [[256/255|S16]], [[324/323|S18]], [[400/399|S20]], [[1445/1444|S17/S19]], ([[2500/2499|S50]])}.
Subgroup: 2.3.5.7.17
Comma list: 256/255, 1701/1700, 2025/2023
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 | 0 1 -4 -10 3 }}
: mapping generators: ~34/27, ~3
Optimal tunings:
* WE: ~34/27 = 399.8023{{c}}, ~3/2 = 702.6087{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 702.9837{{c}}
<!-- * CTE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.0963{{c}} -->
{{Optimal ET sequence|legend=0| 12, 87, 99, 309cdg, 408cdgg, 507cdggg }}
Badness (Sintel): 0.688
==== 2.3.5.7.17.19 subgroup ====
Subgroup: 2.3.5.7.17.19
Comma list: 256/255, 324/323, 400/399, 476/475
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}
Optimal tunings:
* WE: ~24/19 = 399.7556{{c}}, ~3/2 = 702.4862{{c}}
* CWE: ~24/19 = 400.0000{{c}}, ~3/2 = 702.9418{{c}}
<!-- * CTE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.0778{{c}} -->
{{Optimal ET sequence|legend=0| 12, 87, 99, 210gh, 309cdghh }}
Badness (Sintel): 0.637


=== Undecimal misty ===
=== Undecimal misty ===
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Badness (Sintel): 1.70
Badness (Sintel): 1.70
== Subgroup extensions ==
=== Misty (2.3.5.7.17) ===
The [[S-expression]]-based comma list for this extension is {([[5120/5103|S8/S9]]), [[2025/2023|S15/S17]], [[256/255|S16]], [[1701/1700|S18/S20]], ([[2500/2499|S50]])}, and for the 2.3.5.7.17.19-subgroup extension, {([[5120/5103|S8/S9]]), [[256/255|S16]], [[324/323|S18]], [[400/399|S20]], [[1445/1444|S17/S19]], ([[2500/2499|S50]])}.
Subgroup: 2.3.5.7.17
Comma list: 256/255, 1701/1700, 2025/2023
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 | 0 1 -4 -10 3 }}
: mapping generators: ~34/27, ~3
Optimal tunings:
* WE: ~34/27 = 399.8023{{c}}, ~3/2 = 702.6087{{c}}
* CWE: ~34/27 = 400.0000{{c}}, ~3/2 = 702.9837{{c}}
<!-- * CTE: ~34/27 = 400.0000{{c}}, ~3/2 = 703.0963{{c}} -->
{{Optimal ET sequence|legend=0| 12, 87, 99, 309cdg, 408cdgg, 507cdggg }}
Badness (Sintel): 0.688
==== 2.3.5.7.17.19 subgroup ====
Subgroup: 2.3.5.7.17.19
Comma list: 256/255, 324/323, 400/399, 476/475
Subgroup-val mapping: {{mapping| 3 0 26 56 -2 8 | 0 1 -4 -10 3 1 }}
Optimal tunings:
* WE: ~24/19 = 399.7556{{c}}, ~3/2 = 702.4862{{c}}
* CWE: ~24/19 = 400.0000{{c}}, ~3/2 = 702.9418{{c}}
<!-- * CTE: ~24/19 = 400.0000{{c}}, ~3/2 = 703.0778{{c}} -->
{{Optimal ET sequence|legend=0| 12, 87, 99, 210gh, 309cdghh }}
Badness (Sintel): 0.637


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Misty family| ]] <!-- main article -->
[[Category:Misty family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Misty_family"