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Klarinet Archive - Posting 000437.txt from 1995/03

From: Jonathan Cohler <cohler@-----.NET>
Subj: Tone quality; Tone color
Date: Wed, 15 Mar 1995 12:50:07 -0500

A few comments on the entire discussion of dark vs. bright and tone quality
in general.

First, there has been much discussion to the effect that sound quality or
tone quality is "intangible". This is simply not true. Intangible means
"Incapable of being perceived by the senses" or "Incapable of being
realized or defined".

Clearly, tone quality can be perceived by the senses. Therefore, it is not
intangible. Many experiments have been done that show that people can
readily distinguish, for example, the sound of a trumpet from the sound of
a flute, when properly controlled for dynamic, pitch and the like.

Furthermore, it CAN be defined with a great degree of accuracy. The
problem with the entire discussion to date is that everyone has been
speaking of defining tone color in ONE dimension, i.e. a linear scale from
dark to bright.

It has long been known that it requires somewhere in the range of three to
five dimensions (sorry to those that have forgotten their linear algebra
classes) to accurately describe tone color. A simple analogy to illustrate
the discussion that has been occurring would be the following:

Question: What is the volume of this solid object?
Answer: Three feet tall.

Volume is expressed in cubic feet (three dimensions) not feet. And you
cannot describe a three dimensional object in one dimension, period. (You
can project it into one dimension. See below.)

The reason that tone color of musical instruments is multidimensional
should be fairly obvious. Musical instruments have multiple overtones, and
it is the relative amplitude of these overtones that largely (although not
entirely) determines the perceived "tone color". The next question might
be that since there are an infinite number of overtones, then "tone color"
should have infinite dimension. To be exact, that is true, but because the
amplitude of harmonics drops off rather rapidly up high, you can express
tone color quite accurately with three to five dimensions.

Perceived tone color is of course a function of the ear also. By dividing
the hearable spectrum of the ear (0 to 20Khz) into bands and then measuring
sound level in each band one can create a multi-dimensional representation
of tone color. Experiments have been done that map this calculated number
against the results of listener experiments. The results show that the
listener results agree with great accuracy to the vectors in "spectral

So, all that is to say, that tone color CAN be described very accurately by
people. But, it CANNOT be described by single words such as dark and
light. Not only is there no consensus of meaning on those terms (as Dan
and others pointed out)--- which makes them meaningless -- they are
insufficient in describing tone color, because tone color is inherently a
three- to five- dimensional thing.

On the other hand, were we to create a mathematical definition of
"darkness" based on spectrum (which is certainly possible), then it would
be possible to make @-----.
Just as one can say, "this file cabinet is taller than that one". We
aren't saying anything about the volume of the file cabinet, but since we
have defined "height" (a one dimensional characteristic) as the linear
dimension in a certain direction, we can make relative statements about
height between three dimensional objects.

This would be unambiguous and would mean the same to all people.

Now we come to the real problem.

* We know that tone color is tangible and can be accurately
perceived by people. (Obviously, training helps.)

* We know that tone color space is somewhere between three-
dimensional and five-dimensional.

How do we chose the three to five basis vectors for this linear space so
that the basis vectors themselves are all easily recognizable
characteristics? (If you remember your linear algebra classes, an
n-dimensional vector space can be defined by n orthogonal basis vectors.)

This is the stumbling block (which may have been solved or partially solved
by someone). It's easy to create a mathematical definition of a vector
entity based on the mathematical spectrum of a sound. But if that
mathematical formula creates a vector entity that in and of itself cannot
be easily distinguished by people, it is not very useful in describing the

I would be interested to hear from anyone that has come up with some easily
interpretable dimensions for "tone color" space. That's the real rub.


Jonathan Cohler

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