[Smt-talk] Harmonics
Nicolas Meeùs
nicolas.meeus at scarlet.be
Wed Jul 23 01:51:48 PDT 2014
It is disappointing to see that the same misunderstandings come back and
again. In such conditions, the whole discussion is pointless. Let me try
for the last time:
1. The question of enharmonic notes produced on a string or overblowing
a wind instrument and that of harmonic overtones are only remotely
related. Consider the following facts:
– Brass winds usually are built today to play in ET. This is obtained by
complex adjustments of the bore, with the result that the different
notes obtained by overblowing correspond to those in ET and not to just
intonation. Yet, these instruments still can produce harmonic overtones
for each of their notes, the harmonicity of overtones in this case being
more dependent on the conditions of blowing than on conditions of the bore.
– Clarinets are known not to overblow their even harmonics, because
their reed acts as a closed pipe (i.e. closes when the wave returns);
yet their sounds of course can include all harmonic overtones.
– Natural pipes (conchs, tusks, horns and the like) are very unlikely to
overblow to harmonic notes, even if they might be blowed to produce more
or less harmonic overtones.
– The production of harmonic notes on a string is dependent on the kink
in the string moving at the same velocity on both sides of the dividing
finger. Velocity is directly dependent on linear density and section.
Making strings with a constant density and section along their length is
a complex technology; strings so made are called "harmonic strings".
Natural strings (e.g. vines, braided or not) are unlikely to be harmonic.
– If the pipes or strings are not "harmonic" in this sense, they may
still produce different notes in the same conditions as for harmonic
notes, but the intervals between them will not correspond to those in
the harmonic series, and each of them may or may not include harmonic
overtones.
2. The conditions for producing harmonic overtones are described by
Fourier's theorem. They reduce to one, periodicity. A truly periodic
vibration produces a stable pitch, and a stable pitch produces harmonic
overtones. Reducing the stability reduces the harmonicity of the
overtones, until the concepts of pitch and of overtones loose pertinence.
– Vibrato, for instance, by disturbing the stability of pitch, reduces
the harmonicity of the overtones (which allows more easily playing 'in
tune', as the fusion of the overtones becomes somewhat blurred).
– Slightly non-harmonic strings may appear to produce stable pitches,
but yet become difficult to tune (this was the case with early nylon
harp strings, because it was difficult to maintain a constant diameter
on such lengths).
– Pipes or strings that are significantly non harmonic in the definition
under 1 above cannot be forced to produce stable pitches and therefore
do not produce harmonic overtones.
– Stability of pitch requires a sustained supply of energy, as is the
case with winds and bowed strings. It can be approximated by a high
initial supply of energy and a slow dissipation, as in pianos and some
plucked string instruments. Percussion instruments do not normally
produce harmonic overtones (see for instance
http://soundmath.blogspot.be/2010/08/percussion-instruments.html).
3. About Pythagoras and the smithy, Calvin Bower writes in the Cambridge
History of Wester Music Theory that "The roots of this myth so
fundamental to the history of Western musical thought are buried within
ancient values and archetypes that can never be fully fathomed. The
empirical data offered in the myth is wholly specious, for hammers of
comparable weights would not sound the musical intervals presented in
the story. However, the myths and dreams of a civilization are judged
not by their empirical truth or falsity, but by the expression of
intellectual and spiritual complexes they reveal within a culture."
...The myths and dreams of some SMT-Talk participants similarly
must be judged by their expression of intellectual and spiritual
complexes...
Nicolas Meeùs
Professeur émérite
Université Paris-Sorbonne
nicolas.meeus at scarlet.be
Le 22/07/2014 23:03, CARSON FARLEY a écrit :
> If I pick up my guitar or bass I can produce strong harmonics
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