Mint family: Difference between revisions
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Switch to Sintel's badness, WE & CWE tunings, per community consensus |
m Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families" |
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}} | ||
: error map: {{val| 0.000 -6.708 +14.813 +20.543 }} | : error map: {{val| 0.000 -6.708 +14.813 +20.543 }} | ||
{{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }} | {{Optimal ET sequence|legend=1| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }} | ||
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* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}} | * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}} | ||
: error map: {{val| 0.000 -13.956 +4.914 +15.945 +15.908 }} | : error map: {{val| 0.000 -13.956 +4.914 +15.945 +15.908 }} | ||
{{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | {{Optimal ET sequence|legend=1| 7, 9, 12, 21, 28 }} | ||
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* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}} | * WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}} | ||
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}} | * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}} | ||
{{Optimal ET sequence|legend=0| 7, 9, 12f, 16, 21, 28, 37b }} | {{Optimal ET sequence|legend=0| 7, 9, 12f, 16, 21, 28, 37b }} | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Mint family| ]] <!-- main article --> | [[Category:Mint family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 12:17, 27 November 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The mint family of rank-3 temperaments tempers out 36/35, identifying both 7/6 with 6/5 and 5/4 with 9/7.
Mint
Subgroup: 2.3.5.7
Comma list: 36/35
Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]
- mapping generators: ~2, ~3, ~5
- WE: ~2 = 1196.3575 ¢, ~3/2 = 696.5144 ¢, ~5/4 = 403.0537 ¢
- error map: ⟨-3.643 -9.083 +9.455 +13.864]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 695.2474 ¢, ~5/4 = 401.1263 ¢
- error map: ⟨0.000 -6.708 +14.813 +20.543]
Optimal ET sequence: 4, 5, 7, 8d, 9, 12, 41cd, 53cdd
Badness (Sintel): 0.281
Nickel
Subgroup: 2.3.5.7.11
Comma list: 36/35, 45/44
Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 2 2], ⟨0 0 1 -1 1]]
- WE: ~2 = 1198.7814 ¢, ~3/2 = 688.1375 ¢, ~5/4 = 391.4822 ¢
- error map: ⟨-1.219 -15.036 +2.731 +13.530 +14.002]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 687.9993 ¢, ~5/4 = 391.2274 ¢
- error map: ⟨0.000 -13.956 +4.914 +15.945 +15.908]
Optimal ET sequence: 7, 9, 12, 21, 28
Badness (Sintel): 0.557
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 27/26, 36/35, 45/44
Mapping: [⟨1 0 0 2 -2 -1], ⟨0 1 0 2 2 3], ⟨0 0 1 -1 1 0]]
Optimal tunings:
- WE: ~2 = 1199.6174 ¢, ~3/2 = 684.7864 ¢, ~5/4 = 390.1319 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 684.7716 ¢, ~5/4 = 390.0622 ¢
Optimal ET sequence: 7, 9, 12f, 16, 21, 28, 37b
Badness (Sintel): 0.605