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 | 252.68038¢ |
| 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{n\cdot d}[/math]) |
~4.54804 bits |
[sound info] | |
| open this interval in xen-calc | |
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.