[Smt-talk] The Ubiquitous Triad

[Stephen Soderberg]

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 ....

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.

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. I had to pick one and stick with it. So please pardon me –– to avoid a confusion not unlike that of trying to keep Tolstoy's characters straight through the first five chapters, a scholar's accuracy was not as important to me here. In particular, I consciously avoided using "consonant" for several  reasons, among which are those hinted at by Nicolas.

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. As a preview of thoughts I don't know that anyone has even had yet, we might consider yet another modifier to describe a future role: the Janus-faced triad –– but not a Janus like the one we have today where one face is looking into the past and the other face is looking into a nostalgic mirror of the past. This will not be easy & maybe not even possible for a very long time.

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" –– and I'm not only referring to ethnologically different musics "of other traditions" as Nicolas seemed to be suggesting as the only other options (we've managed to infiltrate a lot of them at any rate), but also to musics that have emerged over the past century from the larger liberal Western intellectual tradition, whether as evolutionary developing variations on that tradition or reactions and experiments going in radically new paths.

Re Isaac Malitz' comments on, shall we say, the folly of getting all feverish over the notes: I agree, but I'll be taking it in a different direction that, again, doesn't involve considering the note to be a "relic." A minor triad, for example, is both three individual notes in a certain relationship (however they got there) and a gestalt one doesn't have to analyze into parts  to recognize immediately. But another time on that.

Stephen Soderberg
Keswick, VA


On Jul 18, 2014, at 05:29 PM, Nicolas Meeùs <nicolas.meeus at scarlet.be> wrote:

It seems to me too easy and futile to render "the tonal triad" responsible of so many confusions.

Western (or Occidental, or European, as you like) music or its musicians decided, about a thousand years ago, to base the musical game on an opposition between consonance and dissonance. Many other musics made other choices, e.g. oppositions of rhythms, or of timbres, etc. But consonance/dissonance was 'our' choice (you may belong to another tradition, but I don't think Stephen does).

Now, basing the musical game on consonance/dissonance entails defining these terms. This took time, several categorizations have been tried, and several justifications; these would deserve a discussion here, but as this isn't the question raised by Stephen, I'll refrain entering it now. Our forefathers came to a general agreement on the intervals that could be considered consonances and those considered dissonances. Once again, I won't discuss now their conscious or unconscious reasons. We all know the result: unison, third, fourth, fifth, sixth and octave are consonances, seconds and sevenths dissonances, and augmented fourths/diminished fifths somehow between the two.

The logical consequences are simple, even if not immediately evident:
– The maximum number of pitch classes all 'consonant' between themselves is three.
– Granting the principle of inversion, they all and exclusively form "triads" (properly speaking, those that Stephen calls "tonal triads").
– All other combinations of intervals include 'dissonances' and therefore do not form "triads" properly speaking. (One argument for saying this is that in most definitions of "chords", dissonant combinations of three notes imply some other, absent note. This boils down to the theory of piled up thirds, but again this is not the question raised by Stephen: he should perhaps begin realize that his question is not the good one...).
– "Tonality" by no means is implied in this, so that the notion of "tonal" triad is irrelevant.

Neo-Riemannian Tonnetze (which describe triads) invite us to consider other possible combinations. I think to remember that Rick Cohn shew that the richest Tonnetz is that of which the coordinates are arranged in fifths and thirds. 

All this evidences specific properties of triads, and explains why they have played such a prominent role in our music for the last thousand years. Triads by no means are a norm for ANY music. They certainly were a norm for our music for these last centuries, especially (but not exclusively) in its tonal period, and I see no problem in acknowledging that. Musical analysis, that I know, never claimed to state how music should be. It does try to show how the music analyzed has been: our Western (etc.) music has been triadic for many centuries, and I see no problem in this.

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