Consonance and Dissonance - The Main Theories
Ohio State University
School of Music
Consonance and Dissonance - The Main Theories
A number of hypotheses and theories have been proposed regarding
the origin of consonance and dissonance.
These theories can be broadly distinguished into four groups:
Here are the principal theories.
These theories are based on physical properties of
the acoustical signal, such as frequency ratios.
These theories are based on psychophysiological
aspects of the auditory system, such as the influence
of the basilar membrane.
These theories are based on higher level cognitive
phenomena, such as the categorical perception of
musical intervals due to learning.
These theories are based on social, cultural or stylistic
norms that are internalized by listeners.
This hypothesis proposes that consonance is evoked by simple frequency ratios.
Plomp & Levelt (1965)
quote a charming characterization of this hypothesis
"Agreeable consonances are pairs of tones which strike the ear with a
this regularity consists in the fact that the pulses delivered by
the two tones, in the same interval of time, shall be commensurable in
number, so as not to keep the ear drum in perpetual torment."
Plomp & Levelt note that supporters of this hypothesis have included
Leibniz, Euler, Lipps and Polak.
The component of dissonance that arises due to rapid beating or
proposed the notion that dissonance arises due
to beating between adjacent harmonics of complex tones.
Helmholtz proposed that maximum dissonance would arise between
two pure tones when the beat rate is roughly 35 cycles per second.
Synchrony of Neural Firings.
Boomsliter and Creel (1961) proposed the theory that
consonance arises when neural firings in the auditory system
Irvine (1946) proposed that consonance and dissonance
are related to the length of the periodicity of a cycle.
For example, when tones are related by simple frequency
ratios, the cycle of repetition for the combined signal
is relatively short.
When tones are not related by simple frequency ratios,
the cycle of repetition for the combined signal is long.
Another possibility is that dissonance arises when tones
produce strong audible difference tones.
This hypothesis is most commonly associated with
although there are historical precedents prior to Stumpf.
Stumpf argued that tonal fusion is the basis for consonance.
By "fusion" is meant the propensity for two or more tones
to fuse perceptually and sound as one complex tone.
The tonal fusion hypothesis argues that the most consonant
sonorities are those where the components tend most to sound
like a single tone.
Plomp and Levelt
point out that Stumpf later abandoned the
tonal fusion hypothesis as unsatisfactory.
Plomp and Levelt themselves portray their work as supporting
Helmholtz's idea that dissonance arises from beating harmonics.
Plomp and Levelt (1965)
experiment links dissonance
to the critical band.
Specifically, this hypothesis proposes that dissonance is
eliminated when pure tone components are separated by a distance
greater than the critical band.
The component of dissonance that arises when pure tones are
separated by roughly 40% of a critical band.
Plomp & Levelt, 1965;
Kameoka & Kuriyagawa, 1969a, 1969b).
Virtual Pitch Dissonance.
The component of dissonance that arises from competing (unclear)
Pitch Resolution Dissonance.
Depending on the signal, it has been observed that
listeners may require more or less time to
resolve the pitch of a signal.
In the case of harmonic tones, the resolution
is relatively fast.
Resnick (1981) has proposed that dissonance arises
when the time taken to resolve the pitches of a complex signal
is relatively long.
The component of dissonance that arises due to the thwarting
or delaying of a (learned) expectation.
According to this view, "even a single tone may engender that
urgent expectation of resolution that is the essence of dissonance."
(Cazden, 1980; p.157)
Cazden argued that there are three levels of expectation-related
where a nonharmonic or non-chordal tone has a tendency to resolve
within the framework of an underlying chord or harmony,
Dissonant Chord Moment
where a chord may be dissonant to the extent that it arouses the
expectation of resolving to another chord within a harmonic progression,
Tonal Center Dissonance
where a passage may retain a tonic or dominant tonal center,
and dissonance arises is resolved when the dominant tonal area
ultimately moves to the original tonic area.
Interval Category Dissonance.
The component of dissonance that arises when a two pitches
form an interval that is categorically ambiguous for a listener.
That is, where the interval lies near a learned categorical boundary.
Absolute Pitch Category Dissonance.
The component of dissonance that arises when a pitch
is categorically ambiguous for a listener posessing absolute pitch.
That is, where the pitch lies close to a learned categorical boundary.
Stream Incoherence Dissonance.
The component of dissonance that arises due to confusion
(Wright & Bregman, 1987).
Two additional hypotheses can be identified that are independent of
the above theories.
One hypothesis relates to the contextual or relative perception
The second hypothesis relates to how the density of parts
may influence perceptions of consonance.
The component of dissonance that arises from the context
of dissonant successions.
A sonority might sound relatively consonant when it is preceded by
by other sonorities that are highly dissonant.
Huron has proposed a further factor influencing consonance
-- in addition to the effect of the critical band.
Specifically, Huron has suggested that consonance is positively correlated with
That is, as the number of apparent sound sources is increased,
the overall perceived dissonance is reduced.
* These five historical theories are described in
Plomp and Levelt (1965).