14/13: Difference between revisions
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'''14/13''', the '''2/3-tone''' or '''trienthird''' (one-third third), nicknamed the '''sinaic''' (after Ibn Sina who used it in one of his scales), 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]]. | '''14/13''', the '''2/3-tone''' or '''trienthird''' (one-third third), nicknamed the '''sinaic''' (after Ibn Sina who used it in one of his scales) by [[Zhea Erose]], 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]]. | ||
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''. | 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''. | ||
Revision as of 09:53, 16 April 2021
| Interval information |
trienthird,
sinaic
reduced
[sound info]
14/13, the 2/3-tone or trienthird (one-third third), nicknamed the sinaic (after Ibn Sina who used it in one of his scales) by Zhea Erose, 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 cantonisma.
The trienthird was a favorite interval of 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.
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.