14/13: Difference between revisions

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Included the name of the comma that acts as the difference between a stack of three 14/13 intervals and a 5/4 Major 3rd.
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'''14/13'''
{{Infobox Interval
|1 0 0 1 0 -1>
| Icon =
| Ratio = 14/13
| Monzo = 1 0 0 1 0 -1
| Cents = 128.29824
| Name = tridecimal 2/3-tone, <br>trienthird
| Color name =
| FJS name = M2<sup>7</sup><sub>13</sub>
| Sound = jid_14_13_pluck_adu_dr220.mp3
}}


128.29824 cents
'''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]]. The cantonisma – (5/4)/(14/13)<sup>3</sup> = 10985/10976 – is tempered out in such notable [[EDO|EDO]]s as {{EDOs|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.


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


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.
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.


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.)
== See also ==
* [[13/7]] – its [[octave complement]]
* [[Gallery of just intervals]]


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]]
[[Category:13-limit]]
[[Category:interval]]
[[Category:Interval]]
[[Category:just_interval]]
[[Category:Just interval]]
[[Category:ratio]]
[[Category:Ratio]]
[[Category:second]]
[[Category:Second]]
[[Category:Neutral second]]
[[Category:Semitone]]

Revision as of 11:03, 20 September 2020

Interval information
Ratio 14/13
Factorization 2 × 7 × 13-1
Monzo [1 0 0 1 0 -1⟩
Size in cents 128.2982¢
Names tridecimal 2/3-tone,
trienthird
FJS name [math]\displaystyle{ \text{M2}^{7}_{13} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.50779
Weil height (log2 max(n, d)) 7.61471
Wilson height (sopfr(nd)) 22

[sound info]
Open this interval in xen-calc

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. The cantonisma – (5/4)/(14/13)3 = 10985/10976 – is tempered out in such notable EDOs 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 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.

See also

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