Reversed meantone: Difference between revisions

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~~=REVERSE MEANTONE!=~~

'''Reverse meantone''' or '''reversed meantone''' is a temperament which tempers out the 41-limit comma [[82/81]].

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.

== 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.

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.

[[Category:41-limit]]

[[Category:Temperaments]]

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-=REVERSE MEANTONE!=
+'''Reverse meantone''' or '''reversed meantone''' is a temperament which tempers out the 41-limit comma [[82/81]].
-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.
+== 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.
+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.
+[[Category:41-limit]]
+[[Category:Temperaments]]