15/13: Difference between revisions

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'''15/13'''

{{Infobox Interval

~~|0 1 1 0 0 -1>~~

| Name = tridecimal semifourth

| Color name = 3uy2, thuyo 2nd

| Sound = jid_15_13_pluck_adu_dr220.mp3

}}

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]].

~~247~~.~~74105 cents~~

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.

[[~~File:jid_15_13_pluck_adu_dr220.mp3~~]] ~~[[:File:jid_15_13_pluck_adu_dr220~~.~~mp3|sound sample]]~~

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}}.

~~In [[13-limit~~|~~13-limit]] [[Just_intonation|Just Intonation]],~~ 15/13 ~~is an interval measuring about 247.7¢. In the language of~~ [[~~Margo_Schulter|Margo Schulter~~]]~~, 15/13 is an instance of an~~ [[~~Interseptimal|interseptimal~~]] ~~interval, as it falls in an ambiguous zone between two septimal extremes -- namely the large major second~~ [[8/~~7|8/7~~]] ~~and the small minor third~~ [[~~7/6|7/6~~]]~~. (15/13)~~*([[~~13/10|13/10~~]])=[[~~3/2|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".

== Approximation ==

== See also ==

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

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

* [[Gallery of just intervals]]

* [[The Archipelago]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[The_Archipelago|The Archipelago]]~~ [[Category:~~13-limit~~]]

[[Category:Interseptimal intervals]]

[[Category:~~interseptimal~~]]

[[Category:Semifourth]]

[[Category:~~second~~]]

[[Category:Third]]

[[Category:~~supermajor~~]]

[[Category:Subminor third]]

[[Category:~~ultra~~]]

[[Category:Second]]

[[Category:~~whole_tone~~]]

[[Category:Supermajor second]]

@@ Line 1: / Line 1: @@
-'''15/13'''
+{{Infobox Interval
-|0 1 1 0 0 -1&gt;
+| Name = tridecimal semifourth
+| Color name = 3uy2, thuyo 2nd
+| Sound = jid_15_13_pluck_adu_dr220.mp3
+}}
+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]].
-.74105 cents
+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.
-[[File:jid_15_13_pluck_adu_dr220.mp3]] [[:File:jid_15_13_pluck_adu_dr220.mp3|sound sample]]
+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}}.
-In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 15/13 is an interval measuring about 247.7¢. In the language of [[Margo_Schulter|Margo Schulter]], 15/13 is an instance of an [[Interseptimal|interseptimal]] interval, as it falls in an ambiguous zone between two septimal extremes -- namely the large major second [[8/7|8/7]] and the small minor third [[7/6|7/6]]. (15/13)*([[13/10|13/10]])=[[3/2|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".
+== Approximation ==
+{{Interval edo approximation|15/13}}
+== See also ==
+* [[26/15]] – its [[octave complement]]
+* [[13/10]] – its [[fifth complement]]
+* [[Gallery of just intervals]]
+* [[The Archipelago]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[The_Archipelago|The Archipelago]]      [[Category:13-limit]]
+[[Category:Interseptimal intervals]]
-[[Category:interseptimal]]
+[[Category:Semifourth]]
-[[Category:second]]
+[[Category:Third]]
-[[Category:supermajor]]
+[[Category:Subminor third]]
-[[Category:ultra]]
+[[Category:Second]]
-[[Category:whole_tone]]
+[[Category:Supermajor second]]