7/5
| Ratio | 7/5 |
| Factorization | 5-1 × 7 |
| Monzo | [0 0 -1 1⟩ |
| Size in cents | 582.51219¢ |
| Names | narrow tritone, lesser septimal tritone, Huygens' tritone |
| Color name | zg5, zogu 5th |
| FJS name | [math]\text{d5}^{7}_{5}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 5.12928 |
| Weil height (log2 max(n, d)) | 5.61471 |
| Wilson height (sopfr (nd)) | 12 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.13095 bits |
[sound info] | |
| open this interval in xen-calc | |
In 7-limit just intonation, 7/5 is a narrow tritone (or Huygens' tritone) measuring about 582.5¢. It is a noticeable 17.5¢ away from the 600¢ half-octave (square root of 2) tritone of 12edo and every even-numbered EDO. It represents the difference between 7/4 and 5/4. While in the context of the harmonic seventh chord, it is rightly recognized as a type of diminished fifth, it can also be argued on the basis of the fact that 7/5 interval is smaller than 600 cents that it acts more as a type of augmented fourth than a diminished fifth- an analysis that is required in cases where this interval occurs in a heptatonic scale that demonstrates Rothenberg propriety. This is one of the reasons why 7/4 can be argued to be a type of "sinth"- a cross between a sixth and a seventh- as opposed to merely a subminor seventh.
7/5 is notable for its low harmonic entropy, and is often reported to sound more consonant than the half-octave tritone; indeed it appears in the 4:5:6:7 tetrad that forms the basis of consonance in 7-limit JI. Its inversion is 10/7, which measures about 617.5¢, and these two septimal tritones differ by the superparticular interval 50/49, about 35.0¢. Systems which temper out 50/49 will equate 7/5 and 10/7, usually to the 600¢ half-octave.
Another just tritone is the 3-limit 729/512, 611.7¢, and this is literally a tri-tone, since it is (9/8)3, or three "whole tones". Yet another is 45/32, about 590.2¢, which appears in the 5-limit (inversion is 64/45). See also 13/9, 18/13, 17/12, 24/17, 25/18 and 36/25.