What is the maximum temporal duration over which a semi-tonal transformation (IC 1) can still be recognised?
Intervallic SpaceTime (or time-space) – the physics of frequency and temporal perception
In the following 4 examples (of 5, 10, 20, & 40 seconds duration),
a sine wave is smoothly transposed/transformed by a semtone (IC1) from PC A4 (440Hz) to Bb (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 the transposition/transition becomes, and the lengths one would need to go to make the transition unnoticeable (i.e., meaningless) would be dependent on a range of subjective factors relating to hearing “ability”. For arguments sake, one would expect the perception of the following descending (rather than ascending) example (v), from PC A4 (440Hz) to G#4 (415.30Hz) to be as cognitively relevant as iv.
Example v (A to G# – 40 seconds):
Although the dynamics of all examples i-vi are constant, our experiential familiarity with the Doppler effect and auditory object location might suggest that we perceive the dynamics of the ascending example iv to increase with “awareness” over time, and decrease when listening to example v, as in the following combined example:
Example vi (A to Bb to A):
Aside from a means of portraying cosmological expansion in relation to the centrality of our perceptual experience, 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) pitches?
Do we consequently experience descending arpeggios as being temporally stretched, and ascending ones as being temporally contracted, or visa versa? Similarly, are descending entries and ascending exits (a) counter intuitive, and/or (b) relative to the emergent nature of space-time (or time-space)?
In other words, is intervallic awareness (a correlation between the vertical/harmonic and temporal/horizontal) intrinsic to the nature of space-time?
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. > frequency = > energy = > entropy. However, with sound, the proportion of intervallic potential is regarded as constant, dependent on octave equivalence.
Perhaps the musical interval needs to be thought of as a topographical vector of sorts, an auditory and energetic space. Not least in 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”
( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2629434/ )
What if space-time is discrete rather than continuous (see causal Set Theory), and time is atomized?
( https://www.quantamagazine.org/physicists-discover-geometry-underlying-particle-physics-20130917/ )