[Smt-talk] Harmonics

Fri Jul 25 05:37:33 PDT 2014

Andrew has located a critical point: The idea is to be alive in one's time. The "more democratic, less hierarchical and more ambiguous" era in which we live calls for flexibility in every department, not least in our ability to listen. All the more reason to make clear that our visual responses are different from our auditory responses and to keep the auditory choices open to the fullest possible extent.

Most of the comments on this thread are posted by advanced scholars: But the skills to which such scholarship applies are open to all beginners in the study of music, and especially music theory, and would seem to call for cultivation of auditory diversity. 

I cannot resist an anecdote: Seated next to a prominent avant-garde pianist, I was subjected to the whacking to bits of a Haydn minuet by a dutifully trained youngster. Incredulous, I asked my colleague: "Can you believe that people are still teaching children to play like that?" Reply: "It's my student."

Nancy Garniez
New York City

http://nancygarniez.blogspot.com
www.tonalrefraction.com
-----Original Message-----
From: Andrew Milne [mailto:andymilne at tonalcentre.org]
Sent: Thursday, July 24, 2014 07:31 PM
To: 'JAY RAHN'
Cc: 'Nicolas Meeùs', smt-talk at lists.societymusictheory.org
Subject: Re: [Smt-talk] Harmonics

There are many aesthetic decision to be made in art. Given the psychoacoustical qualities of a major triad — which include low roughness and a strong virtual pitch (root) — a musical culture can “choose" to privilege such sounds and the qualities of order, clarity and hierarchy (privileged root) that they manifest. Alternatively a musical culture may choose to privilege the more dissonant intervals favoured in the music described by Ambrazevičius. 

Common practice harmony, with its insistence on asserting a strong tonic, establishing hierarchies, moving away from them and then reasserting them is perhaps a reflection of the culture in which this music developed. The revolutionary — and highly rule-based — serial method of imposing different organizational principles onto all twelve chromatic degrees without favouring any of them is perhaps a reflection of its time. And what about recent pop music, which commonly uses triads but connects them in ways that don’t seem to assert such a strong sense of a tonic — it uses modes, ascending fifths progressions, repeating cycles of harmony, and softer IV-I and modal cadences (e.g., bVII-i). This harmony is arguably a reflection of our more democratic, less hierarchical and more ambiguous age.

This is just a long way of saying that acoustical properties matter (and structural properties too — e.g., evenness of scale pitches and pulse). Under the control of an artist or cultural tradition, they can be organized so as to produce a compelling aesthetic form. But there is no single “right” way in which the precise palette of such properties is chosen, and the method by which they are organized. However, if we subscribe to the Russian formalist belief that the purpose of art is to make the familiar unfamiliar, then novelty is hugely important — we can’t just carry on doing the same old thing over and over. The last thing I am attempting to suggest here is that we return to the past.

—

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

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

On 25 Jul 2014, at 12:26 am, JAY RAHN <jayrahn at rogers.com> wrote:

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 ofInterdisciplinary 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
Australia

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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