What is the maximum temporal duration over which a semitonal transformation (IC 1) can still be recognised?
In the following 4 examples (using durations of 5, 10, 20, and 40 seconds), a sine wave is smoothly transposed by a semtone (IC1) from PC A4 (440Hz) to B♭4 (466.16Hz).
Example i (5 seconds):
Example ii (10 seconds):
Example iii (20 seconds):
Example iv (40 seconds):
Obviously, the longer the duration, the less noticable (i.e., meaningful) the glissando becomes. As the following descending example (v), from PC A4 (440Hz) to G♯4 (415.30Hz) has durational and intervallic equivalence with the ascending example (iv) above, one might expect it to be perceived similarly, but is it?
Example v (A to G♯ – 40 seconds):
Although the dynamics of all examples (i-v) are constant, our familiarity with the Doppler effect and experitise regarding auditory object location (perhaps related to the “looming threat”) suggests that we perceive the dynamics of the ascending example (iv) to increase and vice versa when listening to example v.
As decreasing frequency = lengthening wave length (time), and vice versa, this raises some interesting musical questions. Over a given temporal frame, are more ascending (higher) pitches (frequencies) required in order to be as meaningful as fewer descending (lower) ones? Do we experience descending arpeggios as being temporally stretched and ascending ones as being temporally contracted? Similarly, are descending entries and ascending exits counter-intuitive?
It is interesting that the frequency range of the piano keyboard, and the range of traditional musical output in general, utilises less than a third of human hearing potential (20Hz to 20000 Hz approx.); and all at the lower end of the spectrum. Might this help to explain a tendency towards accelerando with ascending arpeggios, a need to (literally) rush to the top, like air/pressure bubbles in a stream?
In physics, “all” short/faster wavelengths are said to be more energetic than long/slower wavelengths; where > frequency = > energy = > entropy.
If the up/down “directional” placement of auditory objects contributes to their perception, then why is octave equivalence (OE) deemed to be exempt?
Perhaps “all” musical intervals need to be thought of with regard to energetic temporal distance, not least that “pitch combinations give rise to emergent properties not present in the component notes” (McDermott and Oxenham, 2008, p. 452) and music “provides a powerful stimulus with which to discover interesting auditory phenomena; these may in turn reveal auditory mechanisms that would otherwise go unnoticed or underappreciated” (ibid.).
McDermott, J.H. and Oxenham, A.J. (2008) ‘Music perception, pitch, and the auditory system’, Current opinion in neurobiology, 18(4), pp. 452-463. doi: 10.1016/j.conb.2008.09.005.