81/64: Difference between revisions

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{{Infobox Interval

~~| Ratio = 81/64~~

| Name = Pythagorean major third, ditone

~~| Monzo = -6 4~~

~~| Cents = 407.82000~~

| Name = Pythagorean major third

| Color name = Lw3, lawa 3rd

~~| FJS name = M3~~

| Sound = jid_81_64_pluck_adu_dr220.mp3

}}

The '''Pythagorean major third''', '''81/64''', may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s. 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 ==

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* [[Pythagorean tuning]]

~~[[Category:3-limit]]~~

[[Category:Third]]

[[Category:Major third]]

~~{{todo|expand}}~~

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 {{Infobox Interval
-| Ratio = 81/64
+| Name = Pythagorean major third, ditone
-| Monzo = -6 4
-| Cents = 407.82000
-| Name = Pythagorean major third
 | Color name = Lw3, lawa 3rd
-| FJS name = M3
 | Sound = jid_81_64_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Ditone}}
-The '''Pythagorean major third''', '''81/64''', may be reached by stacking four perfect fifths ([[3/2]]), and reducing by two [[octave]]s.  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 ==
@@ Line 17: / Line 13: @@
 * [[Pythagorean tuning]]
-[[Category:3-limit]]
 [[Category:Third]]
 [[Category:Major third]]
-{{todo|expand}}