15/13: Difference between revisions

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In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢~~. In the language~~ of ~~[[Margo Schulter]], 15/13 is an instance~~ of an [[~~interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8~~/~~7]] and the small minor third [[7/6]]. (15/13)×([[13/10~~]]~~) =~~ [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".

In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢, wherein two instances of this fall short of [[4/3]] by [[676/675]].

In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root.

When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second". In extended [[Pythagorean tuning]] it is extremely close to {{Monzo|43 -27}}.

== Approximation ==

== See also ==

* [[26/15]] – its [[octave complement]]

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-In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢. In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root. When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second".
+In [[13-limit]] [[just intonation]], '''15/13''', the '''tridecimal semifourth''' is an interval measuring about 247.7¢, wherein two instances of this fall short of [[4/3]] by [[676/675]].
+In the language of [[Margo Schulter]], 15/13 is an instance of an [[interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes – namely the large major second [[8/7]] and the small minor third [[7/6]]. (15/13)×([[13/10]]) = [[3/2]], which implies that 15/13 and 13/10 make a 3/2 perfect fifth. Thus you can make a [[List of root-3rd-P5 triads in JI|root-3rd-P5]] triad that goes 26:30:39, with a 15/13 ''inframinor third'' up from the root.
+When being used as type of second, it is given the name ''ultramajor second'' as it is even sharper than 8/7 which is often called a "supermajor second". In extended [[Pythagorean tuning]] it is extremely close to {{Monzo|43 -27}}.
+== Approximation ==
+{{Interval edo approximation|15/13}}
 == See also ==
 * [[26/15]] – its [[octave complement]]