14/13: Difference between revisions
Split off most of the information about the cantonisma onto its own page |
Carmen14edo (talk | contribs) m I remember people talking about possible names for this interval months back and multiple people agreed on the "coffee interval" so I wanted it to catch on. I hope this edit is ok, considering that's the first agreed-upon nickname for this interval to my knowledge. |
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| Monzo = 1 0 0 1 0 -1 | | Monzo = 1 0 0 1 0 -1 | ||
| Cents = 128.29824 | | Cents = 128.29824 | ||
| Name = tridecimal 2/3-tone, <br>trienthird | | Name = tridecimal 2/3-tone, <br>trienthird, <br>coffee interval | ||
| Color name = | | Color name = | ||
| FJS name = M2<sup>7</sup><sub>13</sub> | | FJS name = M2<sup>7</sup><sub>13</sub> | ||
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}} | }} | ||
'''14/13''', the '''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]]. | '''14/13''', the '''2/3-tone''' or '''trienthird''' (one-third third), nicknamed the '''coffee interval''', 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). | 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). | ||
Revision as of 18:29, 16 January 2021
| Interval information |
trienthird,
coffee interval
reduced
[sound info]
14/13, the 2/3-tone or trienthird (one-third third), nicknamed the coffee interval, 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).
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.