Reversed meantone: Difference between revisions
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The more well known [[64/63]] comma equates 9/8 with 8/7 instead of 10/9, which also results in a sharper fifth, and the major third is equivalent to 9/7. | The more well known [[64/63]] comma equates 9/8 with 8/7 instead of 10/9, which also results in a sharper fifth, and the major third is equivalent to 9/7. | ||
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[[Comma list]]: 82/81 | [[Comma list]]: 82/81 | ||
[[Mapping]]: [{{val| 1 2 7 }}, {{val| 0 -1 -4 }}] | [[Gencom]]: [2 4/3; 82/81] | ||
[[Mapping|Sval mapping]]: [{{val| 1 2 7 }}, {{val| 0 -1 -4 }}] | |||
[[POTE generator]]: ~4/3 = 494.5086 | [[POTE generator]]: ~4/3 = 494.5086 | ||
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[[Optimal GPV sequence]]: {{Val list| 5, 12, 17 }} | [[Optimal GPV sequence]]: {{Val list| 5, 12, 17 }} | ||
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<div style="line-height:1.6;">'''Reversed meantone (5&12, 2.3.7.41 subgroup)'''</div> | |||
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Subgroup: 2.3.7.41 | |||
[[Comma list]]: 64/63, 82/81 | |||
[[Gencom]]: [2 4/3; 64/63 82/81] | |||
[[Mapping|Sval mapping]]: [{{val| 1 2 2 7 }}, {{val| 0 -1 2 -4 }}] | |||
[[POTE generator]]: ~4/3 = 490.0323 | |||
[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029 | |||
[[Optimal GPV sequence]]: {{Val list| 5, 12, 17, 22, 49 }} | |||
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[[Category:41-limit]] | [[Category:41-limit]] | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
Revision as of 12:59, 2 March 2022
Reversed meantone is a temperament which tempers out the 41-limit comma 82/81.
REVERSE MEANTONE!
As meantone is based on the syntonic comma, 81/80, tempering the fifth flat, tempering 82/81 instead results in a sharper fifth, and a major third equivalent to the 41st harmonic instead of the 5th, so it might as well be called reverse meantone. The 41st is very delicate however and mistuning by several cents destroys it, so if its use is intended as more than a joke exact quarter comma tempering is best, although 39edo does a fair job.
Related to this idea, 162/161 is a 23-limit comma (specifically 161 = 7 × 23), and 163/162 being prime would indeed be ridiculous.
The more well known 64/63 comma equates 9/8 with 8/7 instead of 10/9, which also results in a sharper fifth, and the major third is equivalent to 9/7.
Subgroup: 2.3.41
Comma list: 82/81
Gencom: [2 4/3; 82/81]
Sval mapping: [⟨1 2 7], ⟨0 -1 -4]]
POTE generator: ~4/3 = 494.5086
TOP generators: ~2 = 1199.6961, ~4/3 = 494.3834
Subgroup: 2.3.7.41
Comma list: 64/63, 82/81
Gencom: [2 4/3; 64/63 82/81]
Sval mapping: [⟨1 2 2 7], ⟨0 -1 2 -4]]
POTE generator: ~4/3 = 490.0323
TOP generators: ~2 = 1197.2342, ~4/3 = 488.9029