Re: Measurement of pitch


<matt271829-news@xxxxxxxxxxx> wrote in message
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Tom Potter wrote:

"OG" <owen@xxxxxxxxxxxxxxxxxxx> wrote in message
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<tdp1001@xxxxxxxxx> wrote in message
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OG wrote:
"John Bailey" <john_bailey@xxxxxxxxxxxxxxxx> wrote in message
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On 4 Dec 2006 16:29:27 -0800, matt271829-news@xxxxxxxxxxx wrote:

Hi

At what time in history were the range of frequencies of audible
sounds
first roughly known? Who made the first scientifically accurate
measurement of the frequency of a sound wave, and when?

"Mersenne's description in his Harmonic universelle (1636) of the
first absolute determination of the frequency of an audible tone
(at
84 Hz) implies that he already demonstrated that the
absolute-frequency ratio of two vibrating strings, radiating a
musical
tone and its octave, is as 1 : 2.

Fascinating

And I found this description of how he did it
"The first major step toward defining pitch into an exact number of
vibrations per second - its frequency - was Mersenne in the 1600s,
who
stretched a brass wire 138 feet and counted its vibrations by eye. He
then
stretched smaller wires until they matched the tuning of an organ
pipe
and
scaled up the numbers from the long wire and correctly calculated its
frequency."
http://digitalcontentproducer.com/mag/avinstall_measure/

Mersenne's method was not as good
as the method used by the Pythagoreans.

Maybe, but the OP's question was regarding the first scientific
measurement of ACTUAL frequency rather than relative frequency, which
was
Pythagoras' work.

Apparently "OG" didn't get the message.

Comparing a frequency directly to a frequency standard
such as middle C, is more precise and more fundamental than
comparing a frequency to an artificial, politically set,
real number, pseudo-frequency such as the second.

As Maxwell pointed out when he formulated Dimensional Analysis,
a measurement consists of two parts,
a reference unit, and a number that represents the number
of these reference units in the quantity to be measured.

The Pythagorians probably used the most stable
instrument available to them, as their reference "atomic clock"
against which to compare all other things that cycled,
vibrated, or could be made to ring,
perhaps including days, months, years, etc.

Hopefully "OG" will explain what "ACTUAL frequency"
really is.

This seems a valid point. To measure frequency you need some reference
time measure, and if huge accuracy is not required then one cycle of a
vibrating string (or pendulum if you like) seems as good as anything.
The string or pendulum in question could no doubt be specified exactly,
but I doubt that it could be made physically perfect enough for
super-precision time measurements. (And I'm also not sure if the
frequency of a string or pendulum doesn't vary very slightly depending
on amplitude, so that would need to be specified too.)

And the question remains: could Pythagoras relate the frequency of his
vibrating string to other phenomena? Would he have had any clue how
many vibrations corresponded to one of his heartbeats, for instance?

As you may know,
the Pythagoreans thought that all things were integers,
and they no doubt tried to "zero beat" their frequency references
to as many things as they could, and the Pythagorean Theorem
made them very happy as it provided them with a triangle
that had integer relationships (3,4,5), and they probably used
these ratios and the ratios of string lengths in musical
instruments in their experiments.

Regarding your comment that
"strings and pendulums in question could be made physically perfect enough
for super-precision time measurements.",
the definition of "super-precision time measurements"
depends upon technology and time.

Even the rotation of the Earth
is not "perfect enough for <Some> super-precision time measurements."

Before the development of temperature controlled
crystal "oscillators" the best frequency standard was probably
the year, and now man has constructed atomic clocks
that keep better time than the earth, moon and the sun.

No doubt, better oscillators will continue to be discovered,
and the second will be referenced to the best of them.

Of course, the LGM's who have heartbeats
60 times slower than man,
will reference the minute to their standard oscillators.

--
Tom Potter
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