357/256

Interval information

Ratio

357/256

Factorization

2^-8 × 3 × 7 × 17

Monzo

[-8 1 0 1 0 0 1⟩

Size in cents

575.7363¢

Names

merry tritone,
octave-reduced 357th harmonic

Color name

17oz5, sozo 5th

FJS name

[math]\displaystyle{ \text{d5}^{7,17} }[/math]

Special properties

reduced,
reduced harmonic

Tenney height (log₂ nd)

16.4798

Weil height (log₂ max(n, d))

16.9596

Wilson height (sopfr(nd))

43

Open this interval in xen-calc

The merry tritone, 357/256, is a close approximation to 12\25, hence the name. It is also a rather good approximation to 32/23 at about four cents (or 8211/8192) away.

Terminology and notation

Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.

For 357/256 specifically:

In Functional Just System, it is a diminished fifth, separated by 4131/4096 from the Pythagorean diminished fifth (1024/729) less a 64/63
In Helmholtz-Ellis notation, it is an augmented fourth, separated by 2187/2176 from the Pythagorean augmented fourth (729/512) less a 64/63.

The term merry tritone omits the distinction and only describes its melodic property i.e. the size.