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?