Hi Theodore,
With respect, your propositions about hearing and psychoacoustics are incorrect. The ear/brain is perfectly capable of perceiving pitches that are expressed as decimal fractions in Hertz, e,g, 415.3. Frequency measured in Hertz is simply the number of cycles in an arbitrary time period, for Hertz, the second. As Rodney has pointed out, the ear/brain system does not have a clock that ticks at one second intervals. Further the mechanism of pitch perception does not depend on having to wait for a full acoustic cycle to complete to be able to assign pitch. That is a very odd idea, and I have seen nothing in the literature to suggest that. As to how the brain perceives pitch, which is not related to frequency in a linear way, by the way, it is the subject of immensely subtle research, and it is still not entirely clear what is going on, and there are conflicting views in psychoacoustics.
As to 415 versus 415.3, this is a furphy. The psychoacoustic experiments that have accumulated over the last 100 years tend to indicate that the population as a whole can discriminate signals separated by about 1-3Hz from about 100Hz to 500-1000Hz. From 500Hz to 2000-4000Hz Weber’s Law takes over, which means that the Just Noticeable Difference (and) becomes larger as the frequency increases (and the Weber fraction is roughly constant), so by the time you are at 4K you can really only discriminate about 10-12Hz, if you are good (as we are on this list :-))
The reason I say this is a furphy is that we are not comparing 415 to 415.3 anyway. It’s just that 415.3 is the arithmetic exact ET semitone down from 440.0. But you can certainly hear fractional pitches. If not, you would not be able to hear much at all!
Finally, in psychoacoustics, while frequency is measured in Hertz, pitch is not, as it is not equivalent to frequency, and is measured in mels, in a non linear relation, not Hertz as you assert.
For those who are interested, here is a chart of what is the called the difference limen for frequency, which is what we are talking about, based on experimental data.
http://www.open.edu/openlearn/science-maths-technology/science/biology/hearing/content-section-11.2
Note that intensity affects these results. But soon I suppose this had better shift to a mailing list on psychoacoustics!
Andrew
On 8 February 2016 at 05:35:06, T. Diehl ([log in to unmask]) wrote:
Nonetheless, this inward/outward motion in a second is how we are able to
define pitch as Hz.
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