Reversed meantone: Difference between revisions
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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. | 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]] with the numerator 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. | 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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Reversed meantone may be extended to the 2.3.23.25.41 subgroup by mapping 32/25 and 23/18 to the major third, resulting in the '''shrub''' temperament. | Reversed meantone may be extended to the 2.3.23.25.41 subgroup by mapping 32/25 and 23/18 to the major third, resulting in the '''shrub''' temperament. | ||
A temperament in a simpler subgroup that has tunings around this range is [[supra]]. | |||
== Tunings == | == Tunings == | ||