81/64: Difference between revisions

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The '''Pythagorean major third''', '''81/64''' may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s. It is also known as the '''ditone''', as it may be reached by stacking two (Pythagorean whole) [[tone]]s ([[9/8]]). In contrast to the more typical [[5/4]]~~—with~~ which it is conflated in [[meantone]]~~—this~~ interval is a bit more ~~dissonant when not bridged by a stack of 3/2 intervals within in a chord~~, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]]. Thus, some would argue that it is functionally an imperfect dissonance.

The '''Pythagorean major third''', '''81/64''' may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s. It is also known as the '''ditone''', as it may be reached by stacking two (Pythagorean whole) [[tone]]s ([[9/8]]). In contrast to the more typical [[5/4]]—with which it is conflated in [[meantone]]—this interval is a bit more discordant on its own, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]]. Thus, some would argue that it is functionally an imperfect dissonance.

== See also ==

* [[128/81]] ~~— Its~~ [[octave complement]]

* [[128/81]] – its [[octave complement]]

* [[32/27]] ~~– Its~~ [[fifth complement]]

* [[32/27]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[Pythagorean tuning]]

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[[Category:Third]]

[[Category:Major third]]

~~{{todo|expand}}~~

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 {{Wikipedia|Ditone}}
-The '''Pythagorean major third''', '''81/64''' may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s. It is also known as the '''ditone''', as it may be reached by stacking two (Pythagorean whole) [[tone]]s ([[9/8]]). In contrast to the more typical [[5/4]]&mdash;with which it is conflated in [[meantone]]&mdash;this interval is a bit more dissonant when not bridged by a stack of 3/2 intervals within in a chord, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]]. Thus, some would argue that it is functionally an imperfect dissonance.
+The '''Pythagorean major third''', '''81/64''' may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s. It is also known as the '''ditone''', as it may be reached by stacking two (Pythagorean whole) [[tone]]s ([[9/8]]). In contrast to the more typical [[5/4]]—with which it is conflated in [[meantone]]—this interval is a bit more discordant on its own, with a [[harmonic entropy]] level somewhere between that of [[9/8]] and that of [[8/7]]. Thus, some would argue that it is functionally an imperfect dissonance.
 == See also ==
-* [[128/81]] &mdash; Its [[octave complement]]
+* [[128/81]] – its [[octave complement]]
-* [[32/27]] &ndash; Its [[fifth complement]]
+* [[32/27]] – its [[fifth complement]]
 * [[Gallery of just intervals]]
 * [[Pythagorean tuning]]
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 [[Category:Third]]
 [[Category:Major third]]
-{{todo|expand}}