Reversed meantone: Difference between revisions
Undo. The data added are simply meantone and the "non-octave" section doesn't make much sense. Tag: Undo |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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[[TOP tuning|TOP generator]]s: ~2 = 1199.6961, ~4/3 = 494.3834 | [[TOP tuning|TOP generator]]s: ~2 = 1199.6961, ~4/3 = 494.3834 | ||
{{Optimal ET sequence|legend=1| 5, 12, 17 }} | |||
</div></div> | </div></div> | ||
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[[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029 | [[TOP tuning|TOP generator]]s: ~2 = 1197.2342, ~4/3 = 488.9029 | ||
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 49 }} | |||
</div></div> | </div></div> | ||
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[[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454 | [[TOP tuning|TOP generator]]s: ~2 = 1197.9683, ~4/3 = 491.3454 | ||
{{Optimal ET sequence|legend=1| 5, 12, 17, 22, 39d }} | |||
</div></div> | </div></div> | ||
Revision as of 16:26, 7 May 2023
Reversed meantone is a temperament which tempers out the 41-limit comma 82/81.
Properties
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. As a very high limit interval, however, that 41/32 is far less recognizable as an interval than meantone’s 5/4, and would more likely be heard as a flat 9/7. Additionally, the 41st is very delicate, 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.
Temperament data
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
Optimal ET sequence: 5, 12, 17
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
Subgroup: 2.3.7.11.41
Comma list: 64/63, 82/81, 99/98
Gencom: [2 4/3; 64/63 82/81 99/98]
Sval mapping: [⟨1 2 2 1 7], ⟨0 -1 2 6 -4]]
POTE generator: ~4/3 = 492.1787
TOP generators: ~2 = 1197.9683, ~4/3 = 491.3454