[Smt-talk] The Ubiquitous Triad

Nicolas Meeùs nicolas.meeus at scarlet.be
Sun Jul 20 11:46:06 PDT 2014

It is not true that "a vibrating string produces overtones in the lower 
partials of a major triad, then a dominant 7th". Supposing that the 
string is of constant diameter and density along its length (which 
requires quite a lot of technicity in its making), the partials produced 
are: 8ve; 12th; 15th; 17th; 19th; then a note about a quarter tone lower 
that what we would describe as the 21th (or a quarter tone higher than 
the 20th), etc. This may be considered to correspond to the major triad 
and, in approximation, to the dominant 7th, but this correspondence is 
far from obvious. (Many of you may have had to count on their fingers 
what a 19th could be.)

It is troubling, in addition, that the realization of the existence of 
the overtones came roughly a century later than the date Victor Grauer 
mentioned in a previous message for the apparition of triads... The 
story of Pythagoras and the blacksmith shop is a myth – and a joke – as 
is the medieval idea that the pitch of bells is dependent on their 
weight. Even in the late 19th century, it was considered (e.g. by 
Helmholtz and his translator Ellis) that the overtones could not 
normally be heard.

If there is a physical law behind all this, it is that of consonance. It 
produced: the major triad, but also the minor one; harmony; to some 
extent tonality. But the conditions of the law of consonance are so 
strict (mainly, pitch stability) that they require a technicity that has 
been developed only in the Western world – precisely because that is 
where the question of consonance has been considered of paramount 

Hindemith's and other 20th-century composers' phantasms concerning the 
overtones have proved quite fruitful, but that doesn't turn them into 
physical laws. The diatonic scale can be described, with some 
approximation, as formed of two intertwined dominant 7ths; it could also 
be described (with roughly the same approximation) as corresponding the 
16th first partials of a fundamental which may or may not be the 'tonic' 
of the scale (Momigny, unless I am mistaken, considered that the major 
scale corresponded to the overtones of its dominant).

Tonal music does to some extent rely on triads (not necessarily major, 
nor triads exclusively); it involves many other aspects, for instance in 
its syntax. But "traditional music" is something else: music can be made 
in an endless variety of combinations, not necessarily including 
consonance, nor the diatonic scale, as important categories.

Nicolas Meeùs
Professeur émérite
Université Paris-Sorbonne

Le 19/07/2014 00:16, CARSON FARLEY a écrit :
> Considering the fact that a vibrating string produces overtones in the 
> lower partials of a major triad and then a dominant 7th chord it would 
> seem that the ubiquitous triad is present in nature as a law of 
> physics and heard consciously or unconsciously throughout human 
> history as overtones produced in some manner by taught strings, 
> overblown wind/brass instrument partials, or in Pythagoras' case the 
> differing notes of a struck anvil/metallurgy as he passed the 
> blacksmith shop.   How to overcome the "ubiquitous" triad?  As a 
> composer I believe that the harmonic partials of a single tone are the 
> electrons to any fundamental pitch/atom.  For example, a scale can be 
> created by extracting a dominant 7th chord (either tempered or non 
> tempered) from the lower 8 partials of a single tone and then doing 
> the same for another interval pitch and combining the results - C and 
> B for example resulting in the following pitches: B,C,D#,E,F#,G,A,and 
> Bb (or the normal form of A,Bb,B,C,D#,E,F#,G).  Hindemith explores the 
> importance and gravity of partials and overtones as compositional 
> material and so do other 20th century theorists like Mathieu in 
> "Harmonic Experience."  The way to get away from/avoid the 
> "ubiquitous" triad is to approach any individual tone as it's own 
> microcosm of overtone/partial electrons and avoid using triads as the 
> essential building blocks so long taken for granted as the starting 
> place for harmony.  Just as physics moved in modernity into the realm 
> of microcosm, so must music.  A triad is in many ways a relic of the 
> past no longer relevant to contemporary science/practice unless of 
> course the desired result is traditional sound/music.
> Carson Farley
> Composer/cellist/theorist
> University of Washington Alumnus
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