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It seems to me too easy and futile to render "the tonal triad"
responsible of so many confusions.<br>
<br>
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).<br>
<br>
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.<br>
<br>
The logical consequences are simple, even if not immediately
evident:<br>
– The maximum number of pitch classes all 'consonant' between
themselves is three.<br>
– Granting the principle of inversion, they all and exclusively form
"triads" (properly speaking, those that Stephen calls "tonal
triads").<br>
– 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...).<br>
– "Tonality" by no means is implied in this, so that the notion of
"tonal" triad is irrelevant.<br>
<br>
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. <br>
<br>
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.<br>
<br>
Nicolas Meeùs<br>
Professeur émérite<br>
Université Paris-Sorbonne<br>
<br>
<br>
<br>
<br>
<div class="moz-cite-prefix">Le 18/07/2014 18:56, Stephen Soderberg
a écrit :<br>
</div>
<blockquote cite="mid:06b3721c-6fa0-4676-a5a5-3d3f19dc53e0@me.com"
type="cite">
<div>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"</div>
<div><br>
</div>
<div><a moz-do-not-send="true"
data-mce-href="http://essaysandendnotes.blogspot.com/2014/07/desperately-seeking-relevance-music_18.html"
href="http://essaysandendnotes.blogspot.com/2014/07/desperately-seeking-relevance-music_18.html">"The
Ubiquitous Triad"</a></div>
<div><br>
</div>
<div>Stephen Soderberg</div>
<div>Keswick, VA</div>
<br>
</blockquote>
<br>
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