"...Please don't believe me, dive into some books and check it out for
yourself: multiple researchers have come to the conclusion that the human
ear cannot discern less than 1 Hz increments when it comes to a single
tone..."What do you mean by "a single tone", a sine wave? If so, this is
not something we meet in harpsichord notes. Please give us your references.
Which pages of which books?
David

Dear David,
In the meanwhile, I find this penchant of yours for faux obtuseness boring
and obnoxious, and I will not help you bait me into another useless
discussion where everything is mixed into a 'Macaroni casserole' (pun
intended).

Seen you are evidently unable to use the Internet, here are just a few
examples that you could easily have found yourself - if you were truly
interested in a real discussion:

"What is the minimum audible change in frequency? I created two .wav files:
case #1 was a series of 1/2 second tone bursts, all at a frequency of 800
Hz; for case #2 the bursts alternated between 800 and 805 Hz. I can
reliably distinguish between these two cases in a double-blind test. This
difference in frequency is less than 1/100 of an octave. I could also
distinguish between 400 and 402 Hz. According to *Jourdain *(page 18) this
is about normal for a young person; at age 61 I'm not supposed to be able
to detect a difference of less than about 8 Hz at 400 Hz. But I can. (I
repeated this test at age 67, and I still can do it)..."

www.silcom.com

Besides the sound pressure level-dependent sensitivity of hearing, humans
also can differentiate very fine changes in frequency. Below frequencies of
500 Hz, the ear can differentiate tone bursts with a frequency difference
of approximately 1 Hz. Above 500 Hz, the barely-noticeable difference is
proportional to the frequency (0.002 x *f *).

www.zone.ni.com

Need I add that this formula means at 880 Hz the frequency differentiation
is 1.76 Hz?

The just noticeable difference in *pitch *must be expressed as a ratio
or *musical
interval *since the human ear tends to respond equally to equal ratios of
frequencies. It is convenient to express the just noticeable
difference in *cents
*since that notation was developed to express musical intervals. Although
research reveals *variations*, a reasonable estimate of the JND is about
five cents. One of the *advantages **of the cents notation *is that it
expresses the same musical interval, regardless of the frequency range.

http://hyperphysics.phy-astr.gsu.edu/hbase/music/cents.html#c4

Need I add that around 440 Hz 5 cents = more than 1 Hz ???


About the ear:
"..The eardrum is a very durable and tightly stretched membrane that
vibrates...As shown below, a compression forces the eardrum inward and a
rarefaction forces the eardrum outward, thus vibrating the eardrum at the
same frequency of the sound wave.

http://www.physicsclassroom.com/class/sound/Lesson-2/The-Human-Ear

Note the last sentence...And read the rest of it.

Theodore

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