Consonance and Dissonance (C/D) in Theory, Practice and Science

1. 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 InterdisciplinaryMusicology, 30 Aug – 3 Sep 2011, Glasgow

2. Scientific approachesto C/D • Helmholtz (1863): roughness • Stumpf (1883): fusion • Cazden (1945): familiarity • Meyer (1965): implication-realisation • Terhardt (1972): virtual pitch • Krumhansl (1990): cognition

3. Humanities approachesto C/D • Tenney (1965): historicalconcepts • Berger (2007), Dreyfus (1996), van der Merwe (2004): parataxis versus hypotaxis

4. Historical C/D conceptsafter James Tenney (1988)

5. Ourapproach • Humanities andsciencesareequally relevant  Considercomplexity but lookforgeneralities 2. C/D isholistic  Ithasmanycomponents but isoneconcept

6. Psychoacousticsof C/D ofsonorities Two components: • Roughness (Helmholtz) • Fusion (Stumpf), “harmony” (Terhardt) Chordrootsdepend on • Root-support intervalsP1, P5, M3, m7 and M2 (Terhardt) • Voicing Of all setsof 3 pcs, onlymajorandminortriadshave: • Low roughness (nosecondintervals) • High fusion (perfectfifthinterval) Of all chromaticintervals, • P4, m6 aretheonlyoneswithroot in uppervoice

7. Implicationandrealisation • Leonard B. Meyer (1965): • originofemotion in musicalstructure? • a dominant chordcanimply a tonic • a risingleapcanimply a fallingsteporseriesofsteps • Chopin example:

8. Pitch commonalityoftwosonoritiesParncutt (1989) • Not physical • Not frequencies in common • Not based on notation • Not notes in common • But experiential • (experienced) pitches in common • includesaudiblepartialsandmissingfundamentals • ignorestuningandenharmonicspelling

9. The non-notatedpitchesof CEG Missingfundamentals: A, F, D • A isfoif E is 3rd harmonicand G is 7th • F isfoifC is 3rd harmonicand G is 9th • D isfoif C is 7th harmonicand E is 9th Prominent partials: B, D • B is 3rd harmonicof E and 5th of G • D is 3rd harmonicof G and 9th of C

10. The non-notatedpitchesof DFA Missingfundamentals: G, Bb • Gisfoif Dis 3rd harmonic, F is 7th, A is 9th • BbisfoifF is 3rd harmonicand D is 5th Prominent partials: C, E • Cis 3rd harmonicof F and 7th of D • Eis 3rd harmonicof A and 9th of D

11. Perceptualsalienceofsharpsandflats In thekeyof C major, • F# isthe 5th harmonicof D  fusion • Bbisfoif D isits 5th harmonic prominence  Tonicizationof flat-sidekeyareasismorenoticeable

12. Verticaland horizontal C/D • Vertical • Roughness • Fusion • Horizontal • Pitch commonality • Pitch proximity

13. C/D in different styles

14. Humanities approachto C/D • Historical change • James Tenney, Karol Berger, Pieter van der Merwe, Lawrence Dreyfus • Holistic nature of C/D • The work as an organism

15. 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)

16. Paratactical form: an assortment of compatible things of equal importance e.g. Baroquefugue 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.

17. 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)

18. 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)

19. 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)

20. Musical organicism • Melody (motive) • Rhythm • Harmony?

21. 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

22. Tonalityas a bundleoffeatures 3 quasi- independentingredients • Consonance • Diatonicism • Centricity Example: middle-period Bartók • Low consonance • Low diatonicism • High centricity

23. Cognitivedissonance ... 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)

24. Ourapproach • Humanities andsciencesareequally relevant  Considercomplexity but lookforgeneralities 2. C/D isholistic  Ithasmanycomponents but isoneconcept

25. C/D in worldmusics?Interestingforscience, problematicforhumanities… 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. Vosand Troost (1989): Most commonmelodicintervalisapprox. M2 Schellenberg & Trehub (1996): (Western) infantsprefer (Western) consonance  Universal basisfor C/D in infantpreferenceforcaringadults?