14/13: Difference between revisions
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. |
m add another name for this interval category |
||
| Line 12: | Line 12: | ||
'''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]]. | '''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). 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. | 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. | ||
Revision as of 18:42, 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). 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.