Reversed meantone: Difference between revisions
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'''Reversed meantone''' is a temperament which tempers out the 41-limit comma [[82/81]]. | '''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 [[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. | Related to this idea, [[162/161]] is a 23-limit comma (specifically 161 = 7 × 23), and [[163/162]] being prime would indeed be ridiculous. | ||
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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> | ||
[[Category: | === Other tunings === | ||
[[Category: | * [[DKW theory|DKW]] (2.3.41): ~2 = 1\1, ~3/2 = 706.8411 (~4/3 = 493.1589) | ||
* DKW (2.3.6561/160<ref>Mathematically identical to [[meantone]], but optimized for the "retroptolemaic" thirds, [[2560/2187]] and [[6561/5120]], rather than 6/5 and 5/4</ref>): ~2 = 1\1, ~3/2 = 706.8984 (~4/3 = 493.1016) | |||
[[Category:Reversed meantone| ]] <!-- main article --> | |||
[[Category:Subgroup temperaments]] | |||
[[Category:Rank-2 temperaments]] | |||