297/256
| Interval information |
reduced harmonic
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
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, which approaches a delta-rational 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 same Tonic. Furthermore, Margo Schulter has stated that it is useful as a large interseptimal interval in a Neo-Medieval European setting as a substitute for 7/6, and is closer to the likeliest interpretation- such as that of Jay Rahn- of Marcheto (or Marchettus or Marchetto) of Padua in 1318 than her own older septimal interpretation of the same interval.
In addition to all this, 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.
Among the more reasonably sized large EDOs that represent this interval and other intervals in its class- such as 2673/2048, 891/512 and 8019/4096- with a pretty good level of accuracy include 159edo.