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First off, the (unrolled) length of our cochlea maps out frequencies such that high frequency sounds cause excitation (neural signals) from the front part of the cochlea, and low frequencies result in neural signals from the end part of the cochlea. Thus we can associate the neurons at each position along the cochlea with a specific frequency.

The aspect is that I'm unsure of is whether a sinusoidal wave will cause the neural signals from the regions that correspond to the harmonics of the wave's frequency. I.e. when a person listens to a 440Hz sine wave, the neurons corresponding 880,1320,1760... are activated. I seem to recall this idea from somewhere, and this claim is made in this video, but it is unsubstantiated.

Basically, I'd like to know how (and by whom) this phenomenon has been studied, in order to better understand the physiological basis for the sensations of harmony.

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    A very interesting question. What do you hope to gain from this? Is there an application to this knowledge, or more of a curiosity? My thoughts are that we don't really perceive the harmonics of other sounds so much as they influence how we perceive the fundamental, such as tone and being able to identify the instrument. So even if a sine wave would trigger some sort of harmonic stimulation, the way we perceive it is as a tone without harmonics. I guess my thought is more based on the psychology/neurology side of things. – Basstickler Dec 30 '14 at 17:29
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When you use a pure sinusoidal excitation (at reasonably low levels) you will only excite the basilar membrane at a relatively small area and only the neurons associated with that area will be active. At higher levels the middle ear can become non-linear by itself so you will see some harmonics and the according neural activity as well.

Establishing a one to one relationship between specific neurons and pitch perception is overly simplistic. The mechanical properties of the basilar membrane don't allow for as much frequency selectivity than humans actually have. There are a fair bit of other physiological, neurological and cognitive processes involved as well.

If you want to deep dive, I suggest starting with the work of Georg von Bekesy (http://en.wikipedia.org/wiki/Georg_von_B%C3%A9k%C3%A9sy) who pioneered this field of research and actually got a Nobel Price for it. A quick summary of his work can be found here http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3449028/

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Well, the excitation of the receptors happens according to their sinoidal components, and as long as no significant of energy is being dissipated in the hearing organs and attenuation responses (like the coupling in the middle ear) happen on a larger time scale than the vibration itself, the response of the various ear mechanics is essentially linear. And that means that the sensory receptors for 880Hz... will not get triggered.

With regard to following neural path ways, signals are highly correlated with their harmonics, so the following processing pathways will likely get coexcited. If you are looking at a partially obstructed circle, your brain will complete the picture of the circle and actual neurons usually related with the obstructed circle path will also fire.

Now some stuff will obviously not fire. Locating the source of a sinoid signal is actually pretty hard since the wavefronts of the harmonics and the different behavior when turning the head and the auricle are used for location pointers. But without a good sense of location, neural signals will be inconclusive in some respect.

The respective neurons will be tuned to be "trigger-happy", but there is no concrete signal that would make them fire in an information-carrying pattern in connection with the neurons triggered by the fundamental.

  • I think it's worth noting that when the neurons are tuned 'trigger-happy', all it takes is a hint of imagination to actually set some of them off and the mind (or at least part of it) is unaware of the difference. While not a normal feature of consciousness this type of auditory hallucination is extremely common (studies among college-aged participants reveal around a 50% rate of experiencing some form) and white-noise experiments have been conducted for many, many decades in which imagined perceptions are explored. – Darren Ringer Dec 31 '14 at 1:15
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Re. the "by whom this has been studied": As I recall the local deity is Sethares. Do a search on the Alternate Tuning Yahoo Mailing List (https://groups.yahoo.com/neo/groups/tuning/info) for his name, 'cochlea', 'ERB', or a related concept 'harmonic entropy', and you'll find more babbling than you'll ever want to read about it.

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Yes for loud enough sounds. Fundamentals of Muscial Acoustics (A. Benade 1975) describes this in Chpt. 14. The bare bones study involves presenting a loud sinusoidal sound to the subject at a given frequency, and then adding in a (sinusoidal) search tone. When the search tone is close to one of the harmonics of the main tone, beating between the search tone and the induced harmonic are heard by the subject. More careful experiments by J. Goldstein in the late 60's early 70's allowed for the estimation of the effective amplitude of these components as a function of the strength of the original tone.

This book also cites (as a note) "A good survey of heterodyne phenomena in the ear can be found in four papers by Donald D. Greenwood: "Aural Combination Tones and Auditory Masking" J. Acoust. Soc. Am 50 (1971): 502-43; and three that appear together in J. Acoust. Soc. Am. 52 (1972): 1137-67: "Masking by Narrow Bands of Noise in Proximity to More Intense Pure Tones of Higher Frequency", "Masking by Combination Bands;" and "Combination Bands of Even Order".

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