Edonoi
An equal division of a non-octave interval (EDONOI) is a tuning obtained by dividing an non-octave interval in a certain number of equal steps. In the broader sense, any equal tuning that is not an integer edo is an edonoi.
Examples include the equal-tempered Bohlen-Pierce scale (i.e. 13 equal divisions of 3), the Phoenix tuning, tunings of Carlos Alpha, Beta, and Gamma, the 19 equal divisions of 3, the 6 equal divisions of 3/2, the 2 equal divisions of 13/10, and 88cET. For a more extensive list see Category:Edonoi.
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.