[Smt-talk] Harmonics

Andrew Milne andymilne at tonalcentre.org
Wed Jul 23 06:04:14 PDT 2014

It is actually very easy for almost any to human to produce a pitch with a perfectly harmonic spectrum — by singing. And it is, perhaps, in singing with others that the richness and beauty of a well tuned major triad is most apparent.


Dr Andrew Milne
Postdoctoral Research Fellow
Music Cognition & Action Group
MARCS Institute
University of Western Sydney

Email: 			a.milne at uws.edu.au
Web: 			Portfolio • Dynamic Tonality • SoundCloud • Google Scholar

On 23 Jul 2014, at 6:51 pm, Nicolas Meeùs <nicolas.meeus at scarlet.be> wrote:

> 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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