[Smt-talk] Harmonics

JAY RAHN jayrahn at rogers.com
Thu Jul 24 07:26:22 PDT 2014

Andrew Milne and others might attribute 'beauty and richness' to a 'well-tuned major triad.' But singers of, e.g., certain traditional idioms of eastern Europe have actually realized simultaneous intervals of ca. 200 cents throughout individual polyphonic songs. (See, for instance, Ambrazevičius,
R., & Wiśniewska, I. 2009. Tonal hierarchies in Sutartinės. Journal of
Interdisciplinary Music Studies 3/1&2: 45–55.) 

'Richness' does not seem to have been a term that has been widely employed in studies of psychoacoustics or music cognition. And, arguably, beauty is in the ears and brain of the beholder.

Jay Rahn, York University (Toronto)

On Wednesday, July 23, 2014 9:04:14 AM, Andrew Milne <andymilne at tonalcentre.org> wrote:

>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
>– 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
>– 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
>Smt-talk mailing list
>Smt-talk at lists.societymusictheory.org
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