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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.15604 bits
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 8211/8192 (about four cents) away. In the same region ('flat tritone'), we have 25/18 at 3213/3200 down and 7/5 at 256/255 up.

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.