297/256
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Ratio | 297/256 |
Factorization | 2^{-8} × 3^{3} × 11 |
Monzo | [-8 3 0 0 1⟩ |
Size in cents | 257.18294¢ |
Name | Alpharabian ultramajor second |
Color name | L1o2, lalo 2nd |
FJS name | [math]\text{M2}^{11}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 16.2143 |
Weil height (log_{2} max(n, d)) | 16.4286 |
Wilson height (sopfr (nd)) | 36 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~4.54373 bits |
open this interval in xen-calc |
297/256, the Alpharabian ultramajor second, is the basic ultramajor second in the 2.3.11 subgroup. It differs from the 22/19 undevicesimal semifourth by 513/512, and differs from 7/6 by 896/891. As suggested by its name, it is reached by tacking a 33/32 quartertone onto 9/8.
In tonal music, it is a useful paradiatonic interval, as a 1/1-27/22-16/11-512/297 chord can be built on top of a note situated at this distance from the Tonic, and this chord can lead into a 1/1-6/5-3/2 triad built on the note located at 5/4 above the Tonic.