Consonance and Dissonance (C/D) in Theory, Practice and Science Richard Parncutt Centre for...
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Transcript of Consonance and Dissonance (C/D) in Theory, Practice and Science Richard Parncutt Centre for...
Consonance and Dissonance (C/D) in Theory, Practice and Science
Richard ParncuttCentre for Systematic Musicology, University of Graz, Austria
Graham HairScience 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 conceptsafter 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 sonoritiesTwo 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 sonoritiesParncutt (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 importancee.g. Baroque fugue
Hypotactical form: focus on the build-up and release of harmonic tension, and on a heightened sense of drive towards cadence-pointse.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-the-other (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?