297/256

Interval information

Ratio	297/256
Factorization	2-8 × 33 × 11
Monzo	[-8 3 0 0 1⟩
Size in cents	257.1829¢
Name	Alpharabian ultramajor second
Color name	L1o2, lalo 2nd
FJS name	[math]\displaystyle{ \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
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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. In addition, Kyle Gann had reason to use this interval in his music in a different context- specifically in the piece "Custer and Sitting Bull" as part of a pair of scales that, together, were used to represent General George Armstrong Custer.

See also

• 512/297 – its octave complement
• Gallery of just intervals