14/13: Difference between revisions

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~~'''14~~/~~13'''~~

{{Infobox Interval

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

| Name = tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic

| Color name = 3uz2, thuzo 2nd

| Sound = jid_14_13_pluck_adu_dr220.mp3

}}

128.~~29824 cents~~

'''14/13''', the '''tridecimal 2/3-tone''' or '''trienthird''' (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].

[[~~File~~:~~jid_14_13_pluck_adu_dr220~~.~~mp3~~]] [[~~:File:jid_14_13_pluck_adu_dr220.mp3|sound sample~~]]

The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called '''sinaics''' by [[Zhea Erose]]. It may be called the '''tridecimal supraminor second''' as well, analogous to [[21/13]] being the ''tridecimal supraminor sixth''.

14/13, the ~~2/3-tone or trienthird (one-~~third ~~third) interval is a somewhat exotic~~ 13~~-limit interval which, measuring about 128.3¢, is almost exactly 1~~/~~3 of a~~ major third of [[5/4|5/4]]~~. The cantonisma- (5~~/4)/(14/13~~)^3 = 10985~~/~~10976- is tempered out in such notable~~ [[~~EDO|EDO~~]]~~s as 46, 84, 94, 103, 111, 121, 130, 159, 224, 270, 494~~ and ~~764~~, ~~leading to a variety of temperaments~~ in ~~which three trienthirds make up a major third~~.

In [[13-limit]] [[just intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

~~The trienthird was a favorite interval of~~ [~~http:~~/~~/en.wikipedia.org/wiki/Avicenna Avicenna~~] ~~(Ibn Sina) for his scale constructions, and may be considered a smaller size~~ of ~~neutral second (a second between major and minor.)~~

== See also ==

* [[13/7]] – its [[octave complement]]

* [[Gallery of just intervals]]

In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11|13/11]] and tridecimal supermajor third of [[14/11|14/11]]. It is also the difference between [[13/10|13/10]] and [[7/5|7/5]]; [[13/12|13/12]] and [[7/6|7/6]]; [[13/9|13/9]] and [[14/9|14/9]], and of course [[13/8|13/8]] and [[7/4|7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.

[[Category:Second]]

[[Category:Neutral second]]

~~See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]~~

[[Category:Supraminor second]]

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

[[Category:Semitone]]

[[Category:~~interval~~]]

[[Category:~~just_interval]]~~

~~[[Category:ratio~~]]

[[Category:~~second~~]]

@@ Line 1: / Line 1: @@
-'''14/13'''
+{{Infobox Interval
-|1 0 0 1 0 -1&gt;
+| Name = tridecimal 2/3-tone, trienthird, tridecimal supraminor second, sinaic
+| Color name = 3uz2, thuzo 2nd
+| Sound = jid_14_13_pluck_adu_dr220.mp3
+}}
-.29824 cents
+'''14/13''', the '''tridecimal 2/3-tone''' or '''trienthird''' (one-third third) is a somewhat exotic 13-limit interval measuring about 128.3¢, which is almost exactly 1/3 of a [[5/4]] major third- a stack of three trienthirds falling short of a 5/4 major third by a [[10985/10976|cantonisma]].
-[[File:jid_14_13_pluck_adu_dr220.mp3]] [[:File:jid_14_13_pluck_adu_dr220.mp3|sound sample]]
+The trienthird was a favorite interval of [[Wikipedia:Avicenna|Avicenna]] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor). Thus intervals close in size to it have been called '''sinaics''' by [[Zhea Erose]]. It may be called the '''tridecimal supraminor second''' as well, analogous to [[21/13]] being the ''tridecimal supraminor sixth''.
-/13, the 2/3-tone or trienthird (one-third third) interval is a somewhat exotic 13-limit interval which, measuring about 128.3¢, is almost exactly 1/3 of a major third of [[5/4|5/4]]. The cantonisma- (5/4)/(14/13)^3 = 10985/10976- is tempered out in such notable [[EDO|EDO]]s as 46, 84, 94, 103, 111, 121, 130, 159, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.
+In [[13-limit]] [[just intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11]] and undecimal major third of [[14/11]]. It is also the difference between [[13/10]] and [[7/5]]; [[13/12]] and [[7/6]]; [[13/9]] and [[14/9]], and of course [[13/8]] and [[7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.
-The trienthird was a favorite interval of [http://en.wikipedia.org/wiki/Avicenna Avicenna] (Ibn Sina) for his scale constructions, and may be considered a smaller size of neutral second (a second between major and minor.)
+== See also ==
+* [[13/7]] – its [[octave complement]]
+* [[Gallery of just intervals]]
-In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 14/13 represents the difference in size between the tridecimal minor third of [[13/11|13/11]] and tridecimal supermajor third of [[14/11|14/11]]. It is also the difference between [[13/10|13/10]] and [[7/5|7/5]]; [[13/12|13/12]] and [[7/6|7/6]]; [[13/9|13/9]] and [[14/9|14/9]], and of course [[13/8|13/8]] and [[7/4|7/4]] and the inversions of the above. As it combines the primes 7 and 13, it appears in JI subgroup tunings involving those primes.
+[[Category:Second]]
+[[Category:Neutral second]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+[[Category:Supraminor second]]
-[[Category:13-limit]]
+[[Category:Semitone]]
-[[Category:interval]]
-[[Category:just_interval]]
-[[Category:ratio]]
-[[Category:second]]