Mint family: Difference between revisions

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m Units & misc. cleanup
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Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}
Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}


{{Optimal ET sequence|legend=1| 7, 9, 12f, 16, 21, 28 }}
{{Optimal ET sequence|legend=0| 7, 9, 12f, 16, 21, 28 }}


Badness (Smith): 0.647 × 10<sup>-3</sup>
Badness (Smith): 0.647 × 10<sup>-3</sup>
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[[Category:Pages with mostly numerical content]]
[[Category:Pages with mostly numerical content]]
[[Category:Mint family| ]] <!-- main article -->
[[Category:Mint family| ]] <!-- main article -->
[[Category:Mint| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]

Revision as of 13:03, 19 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]]

Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 698.6351 ¢, ~5/4 = 404.2809 ¢

Optimal ET sequence4, 5, 7, 8d, 9, 12

Badness (Smith): 0.0637 × 10-3

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]]

Optimal tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 688.8370 ¢, ~5/4 = 391.8801 ¢

Optimal ET sequence7, 9, 12, 21, 28

Badness (Smith): 0.463 × 10-3

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 tuning (POTE): ~2 = 1200.0000 ¢, ~3/2 = 685.0048 ¢, ~5/4 = 390.2563 ¢

Optimal ET sequence: 7, 9, 12f, 16, 21, 28

Badness (Smith): 0.647 × 10-3