Re: Measurement of pitch


OG wrote:
"John Bailey" <john_bailey@xxxxxxxxxxxxxxxx> wrote in message
news:08ran2labqmc71frg5mat6v05k66o0i3v8@xxxxxxxxxx
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.

Mersenne had to consider two systems,
the vibrating wire and his clock,

and the clock he used had to be scaled to
other clocks which were eventually scaled
to a second defined in terms of an Earth year,
and every scaling introduced errors.

It is more precise to zero beat unknowns
directly with one's standard clock
(Oscillating system), or some harmonic
or subharmonic of one's clock,
to determine what harmonic range it is in,

and then to count any steady state difference
from the zero beat, or perhaps as the Pythagoreans did,
listen to the difference, to determine the "note" offset.

And of course,
no one can ever
"define <the> pitch into an exact number of vibrations per second",

as the "second" is an artificial "middle C",
that has to be defined in terms of a more stable "Middle C",
such as an atomic clock.

In other words, it is best to
"define" a frequency by comparing it directly
to one's standard clock, or it's harmonics,

than to introduce a man made standard such as the second,
which introduces, real numbers, scaling errors, and plus and minus
count errors
at every step of the way from one's "local second"
to the second of one's standard clock,
which in term is scaled to an Earth year.

Rather than go from the "middle C" to the second,
and then compare the harmonic of some pitch to the second,
it is better to compare the harmonic directly to one's
"middle C" standard, and if you don't get a
zero beat, then count the deviations from the beat.

unknown ~ "my standard pitch"

unknown ~ (second ~ my clock ~ transfer clock + variations enroute ~
standard clock ~ Earth year)

Which is more precise?

What is the difference between using the second as one's time unit,
or using the period of some "Middle C" (such as one's standard)
as one's time unit?

The second, like all units is politics, not science,

and it introduces real numbers,
where real numbers may not be appropriate,

and scaling and comparison errors,
when they are not necessary

--
Tom Potter
http://home.earthlink.net/~tdp/
http://tdp1001.googlepages.com/home
http://no-turtles.com
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http://tom-potter.blogspot.com

.

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