[Smt-talk] The Ubiquitous Triad

Nicolas Meeùs nicolas.meeus at scarlet.be
Mon Jul 21 12:35:46 PDT 2014

Le 21/07/2014 00:01, Stephen Soderberg a écrit :
> I want to thank Nicolas for his thoughtful response (copied below).  I 
> have read his comments over several times and must say that there is 
> nothing in them  that I find truly dissonant with points I have made 
> in my blog entry –– which is not to imply a consonance with his 
> conclusion. And so ....
No dissonance, indeed. I probably overstated my argument, as you 
probably did also. Isn't that the fun of the argument?
> I must admit that I hadn't thought about it all starting as a 
> gentlemen's agreement ("Western music or its musicians decided" –– 
> consciously? Maybe "decided" is not the right word, but I know what 
> Nicolas is getting at) that was periodically renewed across the 
> centuries ("'our' choice"? –– Really?? I don't remember being asked 
> and I doubt Nicolas was –– unconscious acceptance - the unexamined 
> life - is one of my primary issues). Nevertheless, I like the audacity 
> of this justification. An argumentum ab auctoritate stretched over 
> 1,000 years is nothing to sneeze at. But neither is it anything to 
> genuflect for.
These gentlemen probably did not foresee the consequences of what they 
agreed upon, but they did agree, certainly, to perform (consonant) 
polyphony – this would hardly have been possible without some agreement. 
They did not agree on consonances as "pleasing", or "suave", or anything 
of the kind. They merely confirmed a choice (that already existed in 
monodic chant, but not to the same extent) of easily identifiable and 
reproducible intervals – for these are the most important 
characteristics of consonances. In order to increase these 
characteristics, they opted for the types of vocal and instrumental 
emissions that produced the most stable pitches. They also chose the 
instruments most suited to the purpose, instruments with a sustained 
supply of energy: winds (including the organ) or bowed strings. And when 
they (re)invented notation, first literal, then diastematic, they made 
sure that it would indicate pitch above all, because pitch became the 
most important category for Western music.
> Re my identification of the culprit as the "tonal triad": I'm trying 
> to critique the "perdurability" (as one anonymous reader put it –– 
> I'll add that to the growing list) and relatively recent near 
> fetishist attachment associated with 
> the usual/traditional/common-practice-period/over-determined/ubiquitous/tonal/consonant/diatonic/3-11/<3,4,5>/(p,sign)/pretty-sounding 
> triad.
Agreed, but your critique may not aim at the real culprit, which is the 
idea that all this results from "laws of nature", and that's what I'm 
fighting against (as you are, probably). All what our forefathers agreed 
upon (or not) eventually led to the discovery of "the overtones" – by 
which, obviously, we should understand "harmonic overtones". Because the 
sounds privileged by our forefathers (see above) had the unexpected 
characteristic of producing harmonic overtones, more recent of our 
forefathers (and many of your contemporaries and, I am sorry to have to 
admit, too many of mines) came to believe and to claim that harmonic 
partials were "universal", too easily concluding that all the categories 
resulting from this initial choice also were universal: consonance, 
pitch, and the like – and eventually the triad... the "tonal triad"... 
tonality itself... universal?
     This all is THE major misconception of musical Eurocentrism. And I 
acknowledge with some surprise that this misconception in increasing. Up 
to the early 20th century, (I'd say, until Schenker and Schoenberg; but 
I wont say it, by fear of the reactions) it was generally believed that 
overtones could not normally be heard. Today, it appears that everybody 
hears overtones anywhere, and that I am of the very few not to hear them 
(or, more probably, not ashamed to say that I don't hear them).
     Let's be clear: I am not a composer, merely a historian of music 
and of music theory. As such, I an very much attached to studying the 
common-practice period of tonal music. As such, also, I am convinced 
that we should view this common-practice period for what it is, not as 
something to which one should have any kind of fetishist attachment. But 
let's leave that for another discussion.
> But for the record: of course I know the triad /itself/is innocent; 
> and as to that triad itself, I'm an admirer. In fact, as will soon be 
> seen, I believe the object in question /may/ have a future role to 
> play /beyond/ its essential backward-facing role in support of "music 
> theory today" whose goals are embedded in analysis. But perhaps its 
> new role will be taken down a notch or two or three. [...]
I have no real opinion on this, and I ain't entitled to have any. But 
beware: the triad as such is linked to so many more important 
characteristics (consonance, harmonicity, pitch, 'note', etc.), that I 
don't think one could easily 'take it down a notch'. But once again, 
this is not my concern...
> One final note re Nicolas' statement, "Musical analysis, that I know, 
> never claimed to state how music should be." Not directly perhaps, but 
> this claim is less convincing now and has become much more difficult 
> to defend in the past century or so. The sheer weight of accumulating 
> analysis and the curriculum to support it and the oversupply of 
> teachers to teach it all clearly favor an approach that strongly 
> urges, without necessarily meaning to say such an impolite thing out 
> loud, that "this music we're teaching is superior" [...].
This, Stephen, is not a situation that I have resented here (in France, 
I mean), on the contrary. Under the heavy shadow of Ircam and others, we 
would rather be under pressure to defend common practice as something 
worth some minimal preservation. I am quite actively involved in the 
preparation of the next European Music Analysis Conference 
(http://www.euromac2014.eu/): I think some of these questions will be 
much discussed there...

Nicolas Meeùs
Professeur émérite, Université Paris-Sorbonne
nicolas.meeus at scarlet.be

PS. @Ildar: I never said, nor thought, that Pythagoras is a joke, merely 
that this medieval legend of hammers and blacksmiths is.
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