297/256
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| Ratio | 297/256 |
| Factorization | 2-8 × 33 × 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 (log2 nd) | 16.2143 |
| Weil height (log2 max(n, d)) | 16.4286 |
| Wilson height (sopfr (nd)) | 36 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.19284 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.