EDONOI is short for "equal divisions of non-octave intervals".
Examples include the equal-tempered Bohlen-Pierce scale (a.k.a. the 13th root of 3), Carlos Alpha, Carlos Beta, Carlos Gamma, the 19th root of 3, the 6th root of 3:2 , 88cET and the square root of 13:10 .
Some EDONOI contain an interval close to a 2:1 that might function like a stretched or squashed octave. They can thus be considered variations on EDOs.
Other EDONOI contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional redundancy, that of octave equivalence, and thus require special attention.