Klarinet Archive - Posting 000063.txt from 2002/12

From: alevin@-----. Levin)
Subj: [kl] The concept of error
Date: Wed, 4 Dec 2002 15:30:13 -0500

UNDERSTANDING THE CONCEPT OF ERROR

As the 18th century ended and the concept of prosperity through=20
commerce became accepted, scientists and mathematicians thought to create=20
standardized units of length, time, volume, etc. This movement was=20
particularly strong in France and was encouraged by the monarchy, by the=20
various revolutionary bodies, and by Napoleon. It resulted in creation of=
=20
a decimal system of measurement including length (the meter); volume (the=20
liter), weight (the gram), time (a day of 20 hours of 100 minutes of 100=20
seconds, a 10-day week and a year of 12 3-week months), and a 400-degree=20
circle with 4 100-degree right angles. The key was to settle on standards=
=20
which were sort of familiar but new. It was decided to make the meter=20
precisely equal to 1/10,000,000 of a quarter-circle of longitude (quarter=20
meridian) - a distance assumed through prior experimentation to be a bit=20
over 6200 miles - creating 100 kilometer spacings between degrees of=20
latitude, and a meter length not too different from the yard and other=20
common measurements of the time.
Two prominent geodetic surveyors (Jean Baptiste-Joseph Delambre=20
and Pierre-Francois-Andr=E9 M=E9chain) were appointed to resurvey the known=
=20
meridian line running from Dunkerque to Barcelona using an elaborate system=
=20
of triangulation, by two sets of incredible instruments called Borda=20
repeating circles. (1 set for each surveyor; 2 devices for each - one=20
marked off in 360 degree circles and one in 400 degree circles.)
Despite revolution in France and a war with Spain the measurements=
=20
were completed in seven years. Each surveyor took multiple sightings from=
=20
each location in his own assigned territory; yet M=E9chain found that there=
=20
were serious discrepancies in the measurements made in Spain. He could not=
=20
resolve them so he threw out the inconsistent measurements to enable his=20
survey to meet Delambre=92s survey at the mid-point. Before submitting his=
=20
final data he returned to Spain, took more measurements and found the same=
=20
discrepancies. He died wracked with self-doubt before he could solve the=
=20
problem.

To quote Alder:

=93M=E9chain and his contemporaries did not make a principled=20
distinction between =91precision=92 (the internal consistency of results)=
and=20
=91accuracy=92 (the degree to which those results approached the =91right=20
answer=92). The two are not the same: precise results may appear =91reliabl=
e=92=20
in the sense that they give very nearly the same answer when measured=20
again; yet they may lack =91validity=92 in that they deviate consistently=
from=20
the =91right answer=92. Of course, in practice, distinguishing between the=
two=20
can be extremely difficult because the =91right answer=92 is unknown.=94 K.=
=20
Alder, =93The Measure of All Things,=94 The Free Press, 2002, p.298.

In fact, M=E9chain=92s unfudged measurements were closer to the=
=93right=20
answer=94 than Delambre because he repeated them until internal precision=20
created an accuracy of about 40' or less in absolute reference. He didn=92t=
=20
realize - or could not then have known that

a. Any physical machine changes dimensions with wear;

b. His star tables were not as accurate as they would become in=20
another 30 years;

c. The earth=92s meridians are not of equal length. (If you picture=
=20
a point at the center of the earth with spokes reaching =93sea-level=94 at=
=20
numerous points, those spokes will not all be the same length. The=20
scientists knew that the earth is flattened at the poles but they erred in=
=20
believing it to be completely symmetrical.)

Ironically, the =93theoretical=94 meter calculated for interim=20
use was closer to the =93right answer=94 than the surveyed meter which is=
now=20
standard!

How does all of this apply to our discussions?

We don=92t have agreement as to how to attain precision. We know=
=20
that clarinets mouth pieces and reeds can be measured in millimeters. We=20
have some precision in picking a mouthpiece or a barrel, or a Bb instrument=
=20
versus one in A or C, etc. But:

a. Each person=92s embouchure is different, so the sound produced=
=20
varies in ways we do not now measure. We don=92t even have a common=
standard=20
of reference.

b. Our methods of grading reeds are only relative. Not all No.=20
4's are equivalent.

c. There is no commonly accepted standard that will create an=20
instrument of equal quality every time. Instrument makers always seem to=20
start by taking an existing instrument and attempting to copy it (Mistaking=
=20
accuracy for precision). No one seems to have catalogued all of the=20
variables of length, bore, hole placement and mechanism.

2. For the same reason, we have problems with description of=20
tone. Each of us has a concept of tone quality (e.g. =93dark=94) which fits=
=20
our experience. It would not even be enough to have all of us in one place=
=20
at one time listening to one performer - or even recordings - which=20
interpose more variables (speakers, amplifier curves, reproduction quality).
What we should do is put all of us in one room to listen to a lot=
=20
of performers - several times each . There we must categorize what we hear=
=20
in our own terms. Then we must look for patterns in the terminology as=20
applied to what was heard. Then attempt to compare those patterns to=20
measurements of the actual sounds produced. Then, with some degree of=20
precision, we can accurately define what we hear.

Still, we cannot define what the =91right answer=92 is as to =93goo=
d=94 vs=20
=93bad=94 interpretation. That is a matter of taste and cultural=20
background. We can learn to define - with some degree of precision - what=
=20
is an artistically (and/or historically) accurate performance. We must=20
then decide for ourselves if that is an artistically satisfying performance.
I was a serious, committed student of aesthetics, yet all I really=
=20
learned was that I know what I like - and I can probably tell you why I=20
like it - but I cannot understand or explain why someone else doesn=92t.
If the foregoing seems unduly complex, please remember that=20
precision never reaches the level of perfection. We may get close but we=20
never get there. Moreover, if we did, that would still be just a part of=20
the process. Accuracy (finding the =93right answer=94) evolves from the=
data=20
collected. It can only be assessed in retrospect.

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