[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 

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 

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 

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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