297/256

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Interval information
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{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.

See also