11/9

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Interval information
Ratio 11/9
Factorization 3-2 × 11
Monzo [0 -2 0 0 1
Size in cents 347.4079¢
Names undecimal neutral third,
Alpharabian artoneutral third
Color name 1o3, ilo 3rd
FJS name [math]\displaystyle{ \text{m3}^{11} }[/math]
Special properties reduced
Tenney height (log2 nd) 6.62936
Weil height (log2 max(n, d)) 6.91886
Wilson height (sopfr(nd)) 17

[sound info]
Open this interval in xen-calc

In 11-limit just intonation, 11/9 is a neutral third of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but it is only one of many, of which others include 16/13, 27/22, 39/32, 49/40 and 60/49. As this is the smaller of the two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian artoneutral third in Alpharabian tuning. Since it is nearly halfway between two intervals of 12edo, it implies that it is both very xenharmonic and well-represented in 24edo. It is approximated even more closely in 31edo and 38edo, where the slight flatness of the fifth creates two near perfect 11/9's when divided in half, making the neutral triad particularly stable sounding in these tunings.

In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the 11th harmonic and the 9th harmonic. A triad can also be built with 3/2 and 11/9, and the chord formed is 18:22:27. This introduces a second neutral third, 27/22, which is the difference between 3/2 and 11/9. Many temperaments, including 7edo, 10edo, 17edo, 24edo, 31edo, 41edo, 58edo, miracle, harry, and sesquart, conflate these two neutral thirds. The interval which represents both neutral thirds can then be stacked twice to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of these commas leads to the 11-limit rank three temperament jove.

See also