Octave (interval region): Difference between revisions

A '''perfect octave''' ('''P8''') or '''octave''' ('''8ve''') is an [[interval]] that is approximately 1200 [[cent]]s in [[interval size measure|size]]. While a rough tuning range for octaves is sharper than 1170 cents according to [[Margo Schulter]]'s theory of interval regions, the term ''octave'' tends to imply a function within music that only works with intervals that corresponding to a [[just]] [[ratio]] of [[2/1]] or a close approximation thereof, usually preferred to be sharp-tempered if tempered. Other intervals are also classified as octaves, sometimes called '''wolf octaves''' or '''imperfect octaves''', if they are reasonably mapped to 7\7 and [[24edo|24＼24]] (precisely seven steps of the diatonic scale and twelve steps of the chromatic scale). The use of 24edo's 24＼24 as the mapping criteria here rather than [[12edo]]'s 12＼12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]].