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- From: "Tom Potter" <tdp1001@xxxxxxxxx>
- Date: Sat, 9 Dec 2006 21:22:05 +0800
OG wrote:
"Tom Potter" <tdp1001@xxxxxxxxx> wrote in message
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"OG" <owen@xxxxxxxxxxxxxxxxxxx> 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.
It seems that you're not aware that there is no inherent 'standard' to the
frequencies used for particular notes.
Here is an extract from the Wikipedia article on Pitch (music)
http://en.wikipedia.org/wiki/Pitch_(music)
===============
Quote
"Until the 19th century there was no concerted effort to standardize
musical
pitch, and the levels across Europe varied widely. Pitches did not just
vary
from place to place, or over time-pitch levels could vary even within the
same city. The pitch used for an English cathedral organ in the 17th
century
for example, could be as much as five semitones lower than that used for a
domestic keyboard instrument in the same city.
Even within one church, the pitch used could vary over time because of the
way organs were tuned. Generally, the end of an organ pipe would be
hammered
inwards to a cone, or flared outwards, to raise or lower the pitch. When
the
pipe ends became frayed by this constant process they were all trimmed
down,
thus raising the overall pitch of the organ.
Some idea of the variance in pitches can be gained by examining old
pitchpipes, organ pipes and other sources. For example, an English
pitchpipe
from 1720 plays the A above middle C at 380 Hz, while the organs played by
Johann Sebastian Bach in Hamburg, Leipzig and Weimar were pitched at A =
480
Hz a difference of around four semitones. In other words, the A produced
by
the 1720 pitchpipe would have been at the same frequency as the F on one
of
Bach's organs.
From the early 18th century, pitch could be also controlled with the use
of
tuning forks (invented in 1711), although again there was variation. For
example, a tuning fork associated with Handel, dating from 1740, is
pitched
at A = 422.5 Hz, while a later one from 1780 is pitched at A = 409 Hz,
almost a semitone lower. Nonetheless, there was a tendency towards the end
of the 18th century for the frequency of the A above middle C to be in the
range of 400 to 450 Hz.
The frequencies quoted here are based on modern measurements and would not
have been precisely known to musicians of the day. Although Mersenne had
made a rough determination of sound frequencies as early as the 1600s,
such
measurements did not become scientifically accurate until the 19th
century,
beginning with the work of German physicist Johann Scheibler in the 1830s.
"
end quote
As a practical example, how could you know what actual pitch Pythagoras
used
as his 'standard'?
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.
As we've seen there is no reference unit that is inherent in the idea of
'pitch' itself. Yes, you could define a 'standard' pitch in some measure
such as 'the pitch that is the same as that that produced by a 1 metre
long
steel wire of density X kg per metre^3 and strung to a tension of Y
Newtons", but these are at very best no more 'fundamental' than the
definition of the second.
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.
But there is no stability to the Pythagorean instrument.
Hopefully "OG" will explain what "ACTUAL frequency"
really is.
It is the number of cycles per unit time.
"It seems like OG is not aware" that a measurement
consists of two parts, a reference unit, and the number of
the reference units in something to be measured.
One's "reference unit" can be anything that works,
and some of the frequency reference units are
days, months, years, a pendulum, the "middle C"
associated with some particular instrument or device,
a spring-mass system, a capacitance-inductance system,
a crystal controlled oscillator, an atomic clock, etc.
(Note that by the "middle C", I mean any frequency
that you use as your reference.)
Apparently OG is also not aware that the "second"
is a convenient pseudo-standard reference that has to be
referenced to some real frequency one the standard end,
and to the thing to be measured at the other end,
thus introducing error at both ends.
As I suggested in my previous post,
I am anxious to hear what OG considers to be
an "ACTUAL frequency".
--
Tom Potter
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--
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