Curt A quoted wikipedia as he wrote
>From http://en.wikipedia.org/wiki/Overtone :
"Some musical instruments produce overtones that are slightly sharper
or flatter than true harmonics. The sharpness or flatness of their
overtones is one of the elements that contributes to their unique
sound."
and also:
"... some overtones in some instruments may not be of a close integer
multiplication of the fundamental frequency, thus causing a small
dissonance. "High quality" instruments are usually built in such a
manner that their individual notes do not create disharmonious
overtones. In fact, the flared end of a brass instrument is not to make
the instrument sound louder, but to correct for tube length ?end
effects? that would otherwise make the overtones significantly
different from integer harmonics."
If we presume that some horn overtones tend to be sharp, and the
perceived pitch is thereby sharpened according to some weighted average
of the fundamental plus overtone frequencies, then the preferential
attenuation of these overtones will cause a distant observer to
perceive a lower pitch than the player.
What about this presumption about sharp overtones?
*********
The word harmonic (or overtone) can be used in two senses when applied
to a brass instrument
1. A playing frequency of the instrument. As in "written middle
C is the fourth harmonic of the horn."
2. One of the frequencies present when a note is played. As in
"when I play middle C on the
horn, the second harmonic of the note is an octave higher."
I believe that the Wikipedia article confuses these two meanings. in
this sentence
"In fact, the flared end of a brass instrument is not to make
the instrument sound louder,
but to correct for tube length ?end effects? that would
otherwise make the overtones
significantly different from integer harmonics."
the word "overtone" is being used in the first sense; but the article
is about the second sense of the word.
(By the way, though the article is correct about how the bell changes
the playing frequencies, it is wrong
in asserting that the purpose of the bell is not not make the
instrument louder. The bell does both.)
Let me define two words so that I can discuss this with precision. A
partial is any frequency that
is present in a complex tone. A harmonic is any frequency in a complex
tone that is an integer
multiple of the lowest frequency. The lowest frequency, also called
the fundamental, is the first
harmonic.
If I play the written middle C on my horn, then all the partials
present will be harmonics.
On the piano, however, the partials are "stretched." If you play
middle C on a piano, then the
next highest partial will be very slightly higher than twice the
frequency of middle C. This
effect is due to the stiffness of the string; it depends on the length,
diameter, tension, and
material of the string. It also depends on the mode of vibration, so
that the higher partials of
the string will be stretched more than the lower ones. Therefore, when
a piano tuner tunes
high C, they do so by minimizing beats between the fundamental of high
C and the second
(stretched) partial of middle C. Hence they tune the notes slightly
more than an octave apart.
The stretching is less for a grand piano, and more for an upright. The
result is that the
highest C on a piano is typically a quarter step more than seven
octaves above the lowest C.
However, there is no effect corresponding to this in a brass
instrument. This is because
energy is being fed into the instrument at the fundamental frequency,
so responses at any frequency
which is not a multiple will be damped out. There are inharmonicities
present in the sound of a
brass instrument, but they are much less important than the
inharmoncities in a piano.
Gotta go,
Cabbage
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