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Generating a continuum of consonant to dissonant sounds
This discussion has been a nice illustration of why it is not a good
idea to speak of dissonance without specifying the term more precisely.
I find that is even true in the harmony classroom! Among the features
that are often referred to as "dissonant" are:
3. instability i.e. a sound's predilection to resolve to a different sound
4. distance from the tonic triad or another tonic chord or triad
5. any musical features that don't go together or exhibit tension, e.g.
6. anything difficult to conceptualize in any realm, e.g. "cognitive
The first two ought to involve minimal learning, although learning and
context can make them more or less salient. 3 and 4 have the most to do
with Western musical harmony as it is currently taught. 5 and 6 are
usages that illustrate how metaphorical the word "dissonance" can be,
and how difficult to pin down.
Dissonance is more or less the opposite of consonance, so it's worth
mentioning that in recent music theory the status of the major and minor
triads as the most stable sounds in tonal music is understood to be as
much a consequence of voice leading as of the psychophysical features of
triads. In other words, tonal music uses the triad because if you change
one or two notes of a triad by a step and keep the rest the same, you
usually get another triad. Richard Cohn is a ringleader of this view;
one could look at Cohn (1997) Neo-Riemannian Operations, Parsimonious
Trichords, and Their 'Tonnetz' representations. Journal of Music Theory,
All that aside, I think it might indeed be interesting to see how well a
machine could learn to recognize one or another of the first four
features on the list. So in an attempt to answer Mike Coen's original
question, I would recommend:
For #2: Parncutt, R., & Strasburger, H. (1994 c). Applying
psychoacoustics in composition: "Harmonic" progressions of
"non-harmonic" sonorities. Perspectives of New Music, 32 (2), 1-42.
For #1-#4: I would recommend Huron (2001), Note and Tone, Music
Perception as a starting place.
For #3 and #4: Lerdahl, Fred (2001), Tonal Pitch Space, Oxford
Finally, in response to the debate on Schoenberg that's been going on,
Schoenberg's own views on whether dissonance was natural or learned were
nuanced. James K. Wright has an excellent book covering this, called
Schoenberg, Wittgenstein and the Vienna Circle (Bern: Peter Lang, 2005).
Yes, the same author who worked with Al Bregman on auditory scene
analysis and the control of dissonance in polyphony back in the 1980s.
Hope this helps.
Dept. of Music
Claremont, CA 91711
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