357/256
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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]\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]\sqrt{nd}[/math])
~4.15604 bits
open this interval in xen-calc
| Interval information |
octave-reduced 357th harmonic
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
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, 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.