7/5

Interval information

Ratio	7/5
Factorization	5-1 × 7
Monzo	[0 0 -1 1⟩
Size in cents	582.5122¢
Name	Huygens tritone
FJS name	[math]\displaystyle{ \text{d5}^{7}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	5.12928
Weil norm (log2 max(n, d))	5.61471
Wilson norm (sopfr(nd))	12
[sound info]
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In 7-limit Just Intonation, 7/5 is a narrow 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.

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.

See also Gallery of Just Intervals