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 as such, 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.
This raises some other interesting musical questions. As decreasing frequency = lengthening wave length (time), and visa versa.
Over a given temporal frame, are more ascending (higher) pitches (frequencies) required, to be as meaningful as fewer descending (lower) ones? Do we consequently 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 – C0 (16.35Hz) – F8 (5587.65Hz), and the range of traditional musical output in general, utilizes less than a third of human hearing potential, 20Hz to 20000 Hz, and all at the lower end of the spectrum. Is this why frequencies 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 (EO) deemed to be exempt?
Perhaps “all” musical interval’s 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” and that 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” (McDermott and Oxenham, 2008 – https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2629434/ ).