[Smt-talk] Harmonics

Thu Jul 24 05:53:43 PDT 2014

Dear List:
Whatever the history or the mathematics of overtones, the reality in terms of making music in the here and now, is that sometimes major thirds are in tune and sometimes not. I have been experimenting with vocal intonation for years, as I am equally fascinated with the chaotic overtones of the equally-tempered piano (my instrument of choice) as with the purity of a cappella singing, also a life-long activity. I have better luck getting amateurs to sing in tune than professionally trained musicians. 

I had regular informal a cappella get-togethers with a group of Music Theory grad students. As they did not truly sing in tune, though they always sang correct pitch classes, I had them do an exercise I devised to loosen the ear and enable good participatory tuning. Though they responded well and with pleasure to the exercise, as soon as a printed page appeared they reverted, helpless, to equal temperament.

This is a serious problem, and one that should concern Music Theorists as it affects the transition from inside theory class to the real world of making music.

Nancy Garniez
New York City

http://nancygarniez.blogspot.com
www.tonalrefraction.com
-----Original Message-----
From: Ildar Khannanov [mailto:etudetableau at gmail.com]
Sent: Wednesday, July 23, 2014 03:13 PM
To: 'Nicolas Meeùs'
Cc: smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Harmonics

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 Roederer,Introduction to the Physics and Psychophysics ofMusic. 

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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