Bisection of tonal intervals larger than an octave.

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Abstract
For auditory intervals smaller than an octave the midpoint lies at the geometrical mean, no matter whether the intervals are perceived as auditory distances or musical qualities. This fact has been attested by the bulk of experimental work on the bisection of intervals and the direct comparison of intervals. The apparent size of intervals which extend beyond the ra ge of an octave has been a matter of dispute. Stumpf gave it as his opinion that the apparent size of the same interval increases with increase of pitch. The results of the present experiment indicate that if an auditory distance larger than an octave is taken as a musical interval the midpoint still remains near the geometrical mean, but that if it is taken as a given separation of auditory qualities the midpoint moves up toward the arithmetical mean. (PsycINFO Database Record (c) 2006 APA, all rights reserved)

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