14/13: Difference between revisions

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

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 small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable [[EDO|EDO]]s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.

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 small comma (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.

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.)

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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.

See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]] [[Category:13-limit]]

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

[[Category:13-limit]]

[[Category:interval]]

[[Category:just_interval]]

[[Category:ratio]]

[[Category:second]]

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 [[File:jid_14_13_pluck_adu_dr220.mp3]] [[:File:jid_14_13_pluck_adu_dr220.mp3|sound sample]]
-/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 small comma (5/4)/(14/13)^3 = 10985/10976 is tempered out in such notable [[EDO|EDO]]s as 46, 84, 94, 103, 111, 121, 130, 224, 270, 494 and 764, leading to a variety of temperaments in which three trienthirds make up a major third.
+/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 small comma (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.
 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.)
@@ Line 12: / Line 12: @@
 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.
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
+See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
+[[Category:13-limit]]
 [[Category:interval]]
 [[Category:just_interval]]
 [[Category:ratio]]
 [[Category:second]]