51/40: Difference between revisions

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{{Infobox Interval

~~| Ratio = 51/40~~

| Name = diatismic major third

~~| Monzo = -8 1 -1 0 0 0 1~~

~~| Cents = 420.59670~~

| Name = ~~septendecimal~~ major third

| Color name = 17og4, sogu 4th

~~| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3~~

}}

In [[17-limit]] [[just intonation]], '''51/40''' is the '''~~septendecimal~~ major third'''. ~~Although technically a type of supermajor third, there's already a septendecimal supermajor third in~~ the ~~form of~~ [[22/17]]~~, while this interval is the~~ [[~~fifth complement]] of [[20~~/17]], ~~which is~~ the ~~septendecimal minor third~~.

In [[17-limit]] [[just intonation]], '''51/40''' is the '''diatismic major third'''. It exceeds the [[81/64|Pythagorean major third (81/64)]] by a [[136/135|diatisma (136/135)]], hence the name.

It is approximated by:

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* [[3edo|1\3]] ([[12edo|4\12]]) (400 cents)

* [[17edo|6\17]] ([[34edo|12\34]]) (423.529 cents)

* [[37edo|13\37]] (421.622 cents)

== See also ==

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* [[Gallery of just intervals]]

~~[[Category:17-limit]]~~

[[Category:Third]]

[[Category:Major third]]

[[Category:Supermajor third]]

~~{{todo|expand}}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 51/40
+| Name = diatismic major third
-| Monzo = -8 1 -1 0 0 0 1
-| Cents = 420.59670
-| Name = septendecimal major third
 | Color name = 17og4, sogu 4th
-| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3
 }}
-In [[17-limit]] [[just intonation]], '''51/40''' is the '''septendecimal major third'''.  Although technically a type of supermajor third, there's already a septendecimal supermajor third in the form of [[22/17]], while this interval is the [[fifth complement]] of [[20/17]], which is the septendecimal minor third.
+In [[17-limit]] [[just intonation]], '''51/40''' is the '''diatismic major third'''.  It exceeds the [[81/64|Pythagorean major third (81/64)]] by a [[136/135|diatisma (136/135)]], hence the name.
 It is approximated by:
@@ Line 14: / Line 10: @@
 * [[3edo|1\3]] ([[12edo|4\12]]) (400 cents)
 * [[17edo|6\17]] ([[34edo|12\34]]) (423.529 cents)
+* [[37edo|13\37]] (421.622 cents)
 == See also ==
@@ Line 20: / Line 17: @@
 * [[Gallery of just intervals]]
-[[Category:17-limit]]
 [[Category:Third]]
 [[Category:Major third]]
 [[Category:Supermajor third]]
-{{todo|expand}}