10/7
| Ratio | 10/7 |
| Factorization | 2 × 5 × 7-1 |
| Monzo | [1 0 1 -1⟩ |
| Size in cents | 617.48781¢ |
| Names | high tritone, greater septimal tritone, Euler's tritone |
| Color name | ry4, ruyo 4th |
| FJS name | [math]\text{A4}^{5}_{7}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 6.12928 |
| Weil height (log2 max(n, d)) | 6.64386 |
| Wilson height (sopfr (nd)) | 14 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.56876 bits |
[sound info] | |
| open this interval in xen-calc | |
In 7-limit just intonation, 10/7 is a high tritone (or Euler's tritone) measuring about 617.5¢. It has a similar sound to its inversion, 7/5, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (5/4) appears above the harmonic seventh (7/4), such as 4:6:7:10- This particular chord is well-approximated in 88cET, which has a good approximation of 10/7, but no 7/5. While in the context of the harmonic seventh chord, it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth- an analysis that is required in cases where this interval occurs in a heptatonic scale that demonstrates Rothenberg propriety.