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The hemi-fourth interval (around 250 cents) when taken as a generator, and an octave is taken as the generator, a 9-note scale is possible:


It is an MOS scale, of type "unfair bug", with SEVEN triads, subminor or supermajor. Holy holes. If the generator is around 248-250 cents, we might take this as representing a MOS in barbados temperament.

The family

A map of 3 levels of the scale tree between g=1/5 and 1/4


So, to the right of 2/9 lie "fair" 9-note scales, and to the left lie the "unfair" ones. The easy way to think about this: if the generator is closer to 5 in the denominator, then the 5 intervals will be bigger.


voice-leading sketch in 24-EDO's flavor of hemifourths[9]

qt mode chord prog.mp3


Entropy, the Grandfather of Wind (broken link. 2011-03-04) in 14-EDO's flavor of hemifourths[9] [dead link]