Spogg wrote:Maybe this is all about semantics
Sensory perception plays a big part too, I think. In my earlier example, I showed how two detuned oscillators can sound the same as a single oscillator being amplitude modulated, and vice versa. But if the separation in frequency is big enough (or, equivalently, the modulation frequency is high enough), we do perceive two separate tones. I don't know of any experiments into where the point lies at which our "description" would change, nor how consistent it is between different listeners; but my hunch is that it's where the partial frequencies are separated far enough to fall into different "bins" in an internal, biological/neural "FFT analyser" (the spiral of the cochlea in the inner ear acts as a kind of physical frequency separator, so it may not be entirely down to the brain).
Two sine waves is only the very simplest case, of course - more commonly we're working with waveforms where there are a multitude of partials interacting, so it's maybe not surprising that there are effects which are difficult to describe unambiguously, and even some we might call "auditory illusions" (e.g. rising/falling shepard tones). This is a big part of my fascination for DSP; even processes which are well known and mathematically simple can produce interesting perceptual effects if you just happen to throw the right combination together.
In the case of tula's thought experiment: if the modulation speed were high enough, and contained suitable harmonic content (and was aliasing-free!), it might well be
perceived by most people as a kind of morphing rather than AM/cross-fading - in the same way that FM synths don't usually sound like a bunch of discrete oscillators with lots of vibrato applied. Whether "morphing" should be considered an accurate description in a
technical sense is an open question, I think - personally, I lean more towards Martin's definition (PWM being possibly the simplest form), but I don't think it's written in stone.
(PS: Thanks for the lovely welcomes back - though I'm not sure that living in a "Yellow submarine" would be too pleasant in the dingy, peat-stained, industrially-polluted waters of Bradford Beck! I may well have been in some other place where "the sun doesn't shine" [metaphorically or otherwise], however!
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