15/13: Difference between revisions

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{{Infobox Interval

| ~~Icon =~~

| Name = tridecimal semifourth

~~| Ratio~~ = ~~15/13~~

| Color name = 3uy2, thuyo 2nd

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

~~| Cents = 247.74105~~

~~| Name~~ = ~~tredecimal super second~~, ~~or ~ sub third~~

| Sound = jid_15_13_pluck_adu_dr220.mp3

~~| Color name =~~

}}

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 [[13-limit]] [[Just Intonation]], 15/13 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 "ultra second" as it is even sharper than 8/7 which is often called a "super major second".~~

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 ==

* [[Gallery of ~~Just Intervals~~]],

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

* [[13/10]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[The Archipelago]]

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

[[Category:~~13-limit~~]]

[[Category:Interseptimal intervals]]

[[Category:~~Interval~~]]

[[Category:Semifourth]]

[[Category:~~interseptimal~~]]

[[Category:Third]]

[[Category:third]]

[[Category:Subminor third]]

[[Category:~~second~~]]

[[Category:Second]]

[[Category:~~supermajor]]~~

[[Category:Supermajor second]]

~~[[Category:ultra]]~~

~~[[Category:whole_tone~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = tridecimal semifourth
-| Ratio = 15/13
+| Color name = 3uy2, thuyo 2nd
-| Monzo = 0 1 1 0 0 -1
-| Cents = 247.74105
-| Name = tredecimal super second, or ~ sub third
 | Sound = jid_15_13_pluck_adu_dr220.mp3
-| Color name =
 }}
+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 [[13-limit]] [[Just Intonation]], 15/13 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 "ultra second" as it is even sharper than 8/7 which is often called a "super major second".
+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 ==
-* [[Gallery of Just Intervals]],
+* [[26/15]] – its [[octave complement]]
+* [[13/10]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
 * [[The Archipelago]]
-* [[26/15]] its [[octave complement]]
-[[Category:13-limit]]
+[[Category:Interseptimal intervals]]
-[[Category:Interval]]
+[[Category:Semifourth]]
-[[Category:interseptimal]]
+[[Category:Third]]
-[[Category:third]]
+[[Category:Subminor third]]
-[[Category:second]]
+[[Category:Second]]
-[[Category:supermajor]]
+[[Category:Supermajor second]]
-[[Category:ultra]]
-[[Category:whole_tone]]