Mint family: Difference between revisions
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<div style="line-height:1.6;">Technical data</div> | <div style="line-height:1.6;">Technical data</div> | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 36/35 | [[Comma list]]: 36/35 | ||
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<div style="line-height:1.6;">Technical data</div> | <div style="line-height:1.6;">Technical data</div> | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, [[45/44]] | Comma list: 36/35, [[45/44]] | ||
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<div style="line-height:1.6;">Technical data</div> | <div style="line-height:1.6;">Technical data</div> | ||
<div class="mw-collapsible-content"> | <div class="mw-collapsible-content"> | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: [[27/26]], 36/35, 45/44 | Comma list: [[27/26]], 36/35, 45/44 | ||
Revision as of 13:14, 3 March 2021
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
Period: 1\1
Optimal (POTE) generators: ~3/2 = 698.6351, ~5/4 = 404.2809
EDO generators: (2, 1)\4, (3, 2)\5, (7, 4)\12
Scales:
Subgroup: 2.3.5.7
Comma list: 36/35
Mapping: [⟨1 0 0 2], ⟨0 1 0 2], ⟨0 0 1 -1]]
Badness: 0.0637 × 10-3
Nickel
Period: 1\1
Optimal (POTE) generators: ~3/2 = 688.8370, ~5/4 = 391.8801
EDO generators: (4, 2)\7, (5, 3)\9, (7, 4)\12
Scales:
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]]
Badness: 0.463 × 10-3
13-limit
Period: 1\1
Optimal (POTE) generators: ~3/2 = 685.0048, ~5/4 = 390.2563
EDO generators: (4, 2)\7, (5, 3)\9, (7, 4)\12
Scales:
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]]
Badness: 0.647 × 10-3