[Smt-talk] The Ubiquitous Triad

[Nicolas Meeùs]

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.

Nicolas Meeùs
Professeur émérite
Université Paris-Sorbonne




Le 18/07/2014 18:56, Stephen Soderberg a écrit :
> Just posted some thoughts on justifications for the tonal triad meant 
> to lead into the final post in the thread "Desperately Seeking 
> Relevance: Music Theory Today"
>
> "The Ubiquitous Triad" 
> <http://essaysandendnotes.blogspot.com/2014/07/desperately-seeking-relevance-music_18.html>
>
> Stephen Soderberg
> Keswick, VA
>

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