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closeDo equivalencies occur at factors of two?
Posted by MrVibrating on 29 Jan 2013 at 21:31 GMT
There seems good basis to surmise that the equivalencies between frequencies in factor-of-two relationships that characterise auditory spatial processing are not unique to audition - that rather, the percept of 'pitch class' is borne of a systemic channel convergence, a form of fundamental metamery intrinsic to multicellular information processing...
...it thus follows that similar subjective equivalencies would occur in other modalities that depend on frequency analysis.
In short, one prediction of resonant olfaction - and a key indicator - would be matched properties of stimuli in factor-of-two synchrony - so an odorant with a fundamental component at 25Hz would have similarities with another at 50 or 100 or 200Hz, for example, while still maintaining distinct individual properties - to wit; octaves should, in some respect, smell "the same" as one another...
Conversely, those in a 'dissonant' relationship - such as a tritone - would smell maximally different, with little in common.
One wonders whether these possibilities have hitherto been addressed with respect to this research?
RE: Do equivalencies occur at factors of two?
lucaturin replied to MrVibrating on 30 Jan 2013 at 09:17 GMT
In hearing the octave relationship is due to the fact that the timbre of sounds emitted by physical objects, either because of standing waves with an integer number of nodes or because of nonlinearities in the eleastic constants, have a spectrum consisting of a fundamental and some harmonics, or partials when the "octave" is not exactly 2-fold. As Bill Sethares http://sethares.engr.wisc... has shown conclusively, and despite 2000 years of Pythagorean maunderings, there is in fact nothing special about the octave itself that makes it more harmonious. Note also that in color vision there is no folding over of the spectrum, otherwise the rainbow spectrum would be red or purple at both ends.However, molecules _do_ exhibit overtones and combination bands when probed in the IR, due to nonlinearities in the bond stretch elastic constants. It is unclear as yet whether overtones can be perceived by a tunnelling spectroscope. The IETS spectra I have seen so far appeared to consist only of fundamentals.
RE: RE: Do equivalencies occur at factors of two?
MrVibrating replied to lucaturin on 30 Jan 2013 at 13:06 GMT
Thanks for your thoughts. I'm familiar with Sethare's work, however the concept that interests me is the equivalence of pure tones in octave relationships (2x, 4x etc.) - octave stretch phenomena notwithstanding, there is indeed a significant property, which is this perceived equivalence. Specifically, the key point is that while absolute pitch perception is maintained (the two tones are clearly at very different pitches), the 'difference' in their relationship registers as zero.
What's important is that we have here a valuation of metadata - an objective zero point, if you like, that is more fundamental than audition itself. All multicellular nervous systems are subject to this equivalence percept, and all bandwidths of all sensory modalities are constrained by it - the olfactory bulb has a two-octave range, likewise the entire peripheral nervous system, and importantly the thalamocortical network. Visiospatial bandwidth, as you note, neatly falls within one octave, and as you suggest it is compelling to suppose that were it any larger, erroneous information would result - from this we can surmise that no animal with have optical bandwidths exceeding one octave. Visuotemporal bandwidth is one octave (per the wagonwheel effect and related phenomenon). Some species of bat have been shown to separate navigational and communicative bandwidths into higher and lower octaves, respectively. The list goes on - it's obviously beyond the scope of the quick reply format here...
There's a lot of confusing and dubious ideas and concepts in current psychoacoustics research, but don't let that distract you - the equivalence of octaves is not cultural, or even learned in any sense, but an innate, intrinsic and inherent limit in how we process and relate information... i believe it's a key element in the solution of the binding problem.
I'd implore you to ignore the psychomusicologists on this one and concentrate on the informational implications. A conclusive test for equivalence could be incorporated into future investigations without much extra work.. and a positive result would be strong evidence of vibrational weighting...
Maybe just.. keep it in mind..?
Highest regards,
V.
RE: RE: RE: Do equivalencies occur at factors of two?
MrVibrating replied to MrVibrating on 30 Jan 2013 at 13:29 GMT
NB - incidently, Sethare's 'atonal octaves' are themselves examples of metamery, or channel convergence, as noted in my initial reply. Timbre also significantly muddies the waters - pure tone stimuli should be the objective measure of harmonic properties. And his key 'insights' into this field were inspired by novel divisions of the octave - far from 'debunking' equivalence, his work is entirely dependent upon it, even where trying to thwart it.
And FWIW, Diana Deutsch's earlier work on the phenomenon considers the mechanisms of the metamery, but then neglects to question it's significance within the broader informational framework - as indeed everyone does...
Sorry to bang on, just trying to pre-empt common objections and drive the point across..
Many thanks,
V.
RE: RE: RE: RE: Do equivalencies occur at factors of two?
lucaturin replied to MrVibrating on 30 Jan 2013 at 20:45 GMT
At this point I get a strong feeling we need to have a couple of beers so you can explain to me all this stuff I have never given any thought to properly. Maybe Bill Sethares can join us too, and that way I will learn even more. Where in the world are you ?
RE: RE: RE: RE: RE: Do equivalencies occur at factors of two?
MrVibrating replied to lucaturin on 01 Feb 2013 at 03:23 GMT
lol i'm in London, howeveri discussed this briefly with Sethares many years ago and failed to make much of an impression - in retrospect i could've been more tactful.. although i don't think this challenges his work, it does challenge any casual conclusions downplaying the significance of the equivalence. From my persepctive, harmonic consonance is but degrees of equivalence, because maximum consonance IS equivalence. Or to put it the other way, dissonance is the degree of inequivalence... and the corresponding impulse rate and connective entropies are the stuff of information. That is, the equivalence correlates to minimum connective and impulse rate equilibria.
(NB. some suggest that the unity, at 1:1, is the most consonant interval, however it's an interval of zero - no interval - and thus not in the realm of harmonic relations, instead having only amplitude and phase relations... they might cancel, or add 2db, but they don't engage harmonic processing... hence, 'pure' consonance = factor-of-two equivalence)
To me this doesn't seem so much controversial as axiomatic - it's the same basic formalism, just a slight shift of focus..
Anyhoo my email address is my username at gmail.com if you wanted to discuss it further..!
Regards,
V.