11/9
| Ratio | 11/9 |
| Factorization | 3-2 × 11 |
| Monzo | [0 -2 0 0 1⟩ |
| Size in cents | 347.40794¢ |
| Names | undecimal neutral third, Alpharabian artoneutral third |
| Color name | 1o3, ilo 3rd |
| FJS name | [math]\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 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.59093 bits |
[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 of course, only one of many (others include 16/13, 27/22, 39/32, 49/40 and 60/49). As this is the smaller of two 11-limit neutral thirds obtained by modifying Pythagorean intervals by 33/32, it is dubbed the Alpharabian artoneutral third in Alpharabian tuning. It is nearly halfway between two intervals of 12edo, implying 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 5th 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 harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including 17edo, 24edo, 31edo, 41edo, 58edo, 72edo, 130edo, 202edo, miracle, harry, and sesquart, conflate these two neutral thirds, allowing either interval to be stacked on top of itself 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 them leads to the 11-limit rank three temperament jove.