[Smt-talk] Harmonics

Ildar Khannanov etudetableau at gmail.com
Wed Jul 23 12:13:44 PDT 2014

Dear Nicolas and the List,

I hear, again, angry Schenkerian tenor and lecturing tone. If the rest of
the SMT participants keep hearing natural overtone series in music it is
worth discussing. All the arguments that Nicolas provided are not new. The
diatribe is directed at harmonic understanding of tonality which has to be
subverted at all costs. I am so amazed at Schenker's project, its energy. I
wish it would be channeled somewhere else and directed at something more
musical and creative.

The arguments that not all partials are exactly harmonic is weak. It relies
on physical qualities of sound and does not consider perception of sound.
In fact, all music is out of tune if one wanted to compare it with perfect
tuning or exact set of frequencies. Perception of pitch is based not upon
detection of points with exact values, but with sensation of thresholds.
The tone A is not a frequency of 440 Hertz, it is not a point on the set of
real numbers. It is a zone.

Zonal nature of sound perception is described in a book by Juan
to the Physics and Psychophysics of Music.  *

Much earlier, in 1920s Nicolas Garbuzov published a treatise Zonal Nature
of Musical Hearing.

The pitch A is not a point A but a neighborhood of a. Pitch is the object
of non-Euclidian geometry, or topology. Stephen Soderberg mentioned
Euclide's Fifth Postulate and Lobachevsky's proof of the straight lines
that cross--this is what we are dealing when listening to pitch.

A third--any third--is a third generically because it refers to the third
contained in the natural overtone series. There is no other way to explain
its ubiquitousness. The thirds that we take vary and deviate from the ideal
pitch of the fourth harmonics--but this has never been a problem.

I am in St. Petersburg, in my summer home. Piano is out of tune here, but
Chopin's mazurkas sound so beautifully nostalgic on this instrument!

Best wishes,

Ildar Khannanov
Peabody Institute
etudetablea at gmail.com

2014-07-23 4:51 GMT-04:00 Nicolas Meeùs <nicolas.meeus at scarlet.be>:

>  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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