14/13: Difference between revisions

Line 6:

[[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, 159, 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 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.

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 6: / Line 6: @@
 [[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, 159, 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 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.
 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.)