Transcript Consonance and Dissonance in Theory, Practice and Science

Consonance and Dissonance (C/D)
in Theory, Practice and Science
Richard Parncutt
Centre for Systematic Musicology, University of Graz, Austria
Graham Hair
Science and Music Research Group, University of Glasgow,
Scotland
Conference on Interdisciplinary Musicology, 30 Aug – 3 Sep 2011, Glasgow
Scientific approaches to C/D
•
•
•
•
•
•
Helmholtz (1863): roughness
Stumpf (1883): fusion
Cazden (1945): familiarity
Meyer (1965): implication-realisation
Terhardt (1972): virtual pitch
Krumhansl (1990): cognition
Humanities approaches to C/D
• Tenney (1965): historical concepts
• Berger (2007), Dreyfus (1996), van der Merwe
(2004): parataxis versus hypotaxis
Historical C/D concepts
after James Tenney (1988)
definition
period
perception
CDC-1
melodic affinity
ancient –
medieval
perceived spectral
pitches in common
CDC-2
sonority of isolated
dyads
12th-13th Century
roughness? fusion?
CDC-3
clarity of lower voice
14th Century
pitch salience of lower
voice
CDC-4
property of individual
tones in chord
18th Century
dependence of overall
roughness on
amplitudes of individual
tones
CDC-5
smoothness or
roughness
19th Century
roughness of whole
sonority
Our approach
1. Humanities and sciences are equally relevant
 Consider complexity but look for generalities
2. C/D is holistic
 It has many components but is one concept
Psychoacoustics of C/D of sonorities
Two components:
• Roughness (Helmholtz)
• Fusion (Stumpf), “harmony” (Terhardt)
Chord roots depend on
• Root-support intervals P1, P5, M3, m7 and M2 (Terhardt)
• Voicing
Of all sets of 3 pcs, only major and minor triads have:
• Low roughness (no second intervals)
• High fusion (perfect fifth interval)
Of all chromatic intervals,
• P4, m6 are the only ones with root in upper voice
Implication and realisation
Leonard B. Meyer (1965):
origin of emotion in musical structure?
• a dominant chord can imply a tonic
• a rising leap can imply a falling step or series of steps
Chopin example:
Pitch commonality of two sonorities
Parncutt (1989)
• Not physical
– Not frequencies in common
• Not based on notation
– Not notes in common
• But experiential
– (experienced) pitches in common
– includes audible partials and missing fundamentals
– ignores tuning and enharmonic spelling
The non-notated pitches of CEG
Missing fundamentals: A, F, D
• A is fo if E is 3rd harmonic and G is 7th
• F is fo if C is 3rd harmonic and G is 9th
• D is fo if C is 7th harmonic and E is 9th
Prominent partials: B, D
• B is 3rd harmonic of E and 5th of G
• D is 3rd harmonic of G and 9th of C
The non-notated pitches of DFA
Missing fundamentals: G, Bb
• G is fo if D is 3rd harmonic, F is 7th, A
is 9th
• Bb is fo if F is 3rd harmonic and D is
5th
Prominent partials: C, E
• C is 3rd harmonic of F and 7th of D
• E is 3rd harmonic of A and 9th of D
Perceptual salience of sharps and flats
In the key of C major,
• F# is the 5th harmonic of D  fusion
• Bb is fo if D is its 5th harmonic  prominence
 Tonicization of flat-side key areas is more
noticeable
Vertical and horizontal C/D
• Vertical
– Roughness
– Fusion
• Horizontal
– Pitch commonality
– Pitch proximity
C/D in different styles
Individual sonorities (vertical)
Pairs/groups (horizontal)
fusion
smoothness
pitch commonality
pitch proximity
Renaissance
polyphony
high
high
high
high
Baroque
counterpoint
medium
medium
medium
medium
Surprising progs in
Gesualdo and Liszt
high
high
low
high
Wagner, Debussy
medium
medium
medium
medium
“atonal” Schoenberg low
low
low
medium
bebop
medium
low
medium
high
Reich
low
medium
medium
high
Humanities approach to C/D
• Historical change
– James Tenney, Karol Berger,
Pieter van der Merwe,
Lawrence Dreyfus
• Holistic nature of C/D
– The work as an organism
By 1825, the understanding of harmony seems
already to have been reduced to its narrow, modern
sense ... the craft of constructing chords and chord
progressions ... [But earlier, in] a somewhat
broader, still musical-technical, sense harmony also
included the counterpoint, the craft of combining
diverse, simultaneous melodic lines. In its broadest
sense the audible harmony produced by musicians
participated in the intelligible harmony of creation.
(Berger, 2007, pp. 121–122)
Paratactical form:
an assortment of compatible things of equal
importance
e.g. Baroque fugue
Hypotactical form:
focus on the build-up and release of harmonic
tension, and on a heightened sense of drive
towards cadence-points
e.g. classical sonata form.
A reader of Bach’s two sets of preludes and fugues The
Well-Tempered Keyboard (WTC) will be struck by the
emphatic gestures by which the composer often
announces the approaching end of the fugue ... For the
greater part of its duration it is impossible to predict
when or how soon the fugue will come to an end. Then
quite suddenly ... it becomes apparent that Bach is
wrapping things up ... Because the nature of the genre is
essentially atemporal, because one never knows in
advance how many demonstrations there will be or in
which order they will be introduced, the end is in danger
of seeming arbitrary and abrupt. Hence the need for
emphatic gestures to announce that the end is imminent
(Berger, 2007, pp. 89–91)
One of my central claims ... is that at some point
between the early and late eighteenth century,
between Bach and Mozart, musical form became
primarily temporal ... earlier phases must not only
precede but also cause the appearance of later ones ...
one-after-another must become one-because-of-theother (Berger, 2007, pp. 179-180)
One of the fundamental changes in nineteenth-century
music is that climax gradually replaced antithesis as the
chief organising principle. I must immediately add here
that the word “climax” is here used in its original
[dictionary] sense of “a figure in which a number of
propositions or ideas ... [are] ... set forth so as to form a
series in which each rises above the preceding in force
or effectiveness of expression ...” the stock example
being Caesar’s “I came; I saw; I conquered”
(Van der Merwe, 2004, pp. 311–312)
Musical organicism
• Melody (motive)
• Rhythm
• Harmony?
C/D dichotomies
•
•
•
•
•
•
•
•
•
•
•
•
•
tense/relaxed
primary/subordinate
centric/acentric
diatonic/chromatic
stable/unstable
close/distant
similar/different
rough/smooth
fused/segregated
related/unrelated
familiar/unfamiliar
implied/realized
tonal/atonal
Tonality as a bundle of features
3 quasi- independent ingredients
• Consonance
• Diatonicism
• Centricity
Example: middle-period Bartók
• Low consonance
• Low diatonicism
• High centricity
Cognitive dissonance
... an uncomfortable feeling caused by holding
conflicting ideas simultaneously. The theory of
cognitive dissonance proposes that people have a
motivational drive to reduce dissonance. They do this
by changing their attitudes, beliefs, and actions.
Dissonance is also reduced by justifying, blaming, and
denying
(Wikipedia)
Our approach
1. Humanities and sciences are equally relevant
 Consider complexity but look for generalities
2. C/D is holistic
 It has many components but is one concept
C/D in world musics?
Interesting for science, problematic for humanities…
Culture-specific:
• C/D itself?
• theoretic discourse on C/D?
Attempt at a cross-cultural definition:
• How any musical elements in any style “sound together”?
E.g. Vos and Troost (1989):
Most common melodic interval is approx. M2
Schellenberg & Trehub (1996):
(Western) infants prefer (Western) consonance
 Universal basis for C/D in infant preference for caring adults?