81/70
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Ratio
81/70
Factorization
2-1 × 34 × 5-1 × 7-1
Monzo
[-1 4 -1 -1⟩
Size in cents
252.6804¢
Name
septimal ultramajor second
Color name
rg2, rugu 2nd
FJS name
[math]\text{M2}_{5,7}[/math]
Special properties
reduced
Tenney height (log2 nd)
12.4691
Weil height (log2 max(n, d))
12.6797
Wilson height (sopfr(nd))
26
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.2192 bits
[sound info]
open this interval in xen-calc
| Interval information |
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
81/70, the septimal ultramajor second is a 7-limit interseptimal ratio of about 253 cents. It is sharp of a major second 9/8 by a septimal quartertone 36/35, sharp of a supermajor second 8/7 by a syntonic comma 81/80, and flat of a subminor third 7/6 by a sensamagic comma 245/243.
Notice it is also flat of the just minor third 6/5 by a subminor second 28/27. For this fact it is useful in the sensamagic dominant chord where it functions as a dissonance yet to be resolved up to the minor third. The canou temperament targets this progression and uses it as one of the generators.
Approximation
It is near-perfectly approximated by 19edo (4\19), with an error of 0.05 cents, and hence equally well done by the enneadecal temperament.