Pitch Salience in Tonal Contexts and Asymmetry of Perceived Key Movement

1. Pitch Salience in Tonal Contexts and Asymmetry of Perceived Key Movement Richard Parncutt Centre for Systematic Musicology, University of Graz, Austria Craig Sapp CCARH, Department of Music, Stanford University Society for Music Perception and Cognition Eastman School of Music, Rochester NY 11-14 August 2011 SysMus Graz

2. Thompson and Cuddy (1989) found that perceived key distance is greater for modulations to flat-side keys (in chord progressions but not individual voices). Cuddy and Thompson (1992) explained the asymmetry with probe-tone profiles. Flats relative to a key signature may be more salient simply because they lie at perfect fifth and/or major third intervals below scale steps (Terhardt). That could explain why, relative to key signatures, sharps are more common than flats. In 200 songs with piano accompaniment (DeutscherLiederschatz, 1859-1872, Vol. 1, Ludwig Erk), in 196 songs in major keys, 1016 notes are sharpened and 459 flatted relative to the starting key; in 4 minor songs, 115 notes are sharpened and none are flatted. In 370 Bach four-part chorales, 185 are major with 1534 sharps and 465 flats; 139 are minor with 2628 sharps and 208 flats; 37 are Dorian (classified by Burns, 1995) with 656 sharps and 608 flats; and 9 are Mixolydian with 110 sharps and 18 flats. To test directly whether flats are more perceptually salient than sharps, we presented diatonic progressions of five chords to musicians and non-musicians. All chords were major or minor triads of octave-complex tones. The first was the tonic; the others were ii, IV, V and vi in major keys and ii, IV, v and VI in minor. The last four chords were presented in all 24 different orders. In half of all trials, the penultimate chord was changed from major to minor or vice-versa. All listeners heard all trials in a unique random order and rated each progression's unusualness. Musicians were separately asked whether the last chord contained an accidental. We predict that a chord with a flat will sound more unusual and that accidentals will be identified more often if they are flats.

3. Thompson and Cuddy (1989)Empirical work on perception of Bach chorales 1. Perceived key distance is greater for modulations to flat-side keys… • C to F (addone flat) • C toBb (addtwoflats) …thanto sharp-sidekeys • C to G (addone sharp) • C to D (addtwosharps) 2. That is true in chord progressions but not individual voices

4. “Ecological” hypotheses • The asymmetriesare due totheperceptionofthealterednotesthemselves - not thecognitiverepresentationofthecycleoffifths • The effectdependsdirectly on theinteractionbetweentones in chords (that‘swhyit‘s absent in melodicpresentations)

5. The differencebetweensharpsandflats:Rules ofenharmonicspelling Aim: facilitatereadingbyreducingthenumberofsymbols Relative toscalesteps:  A sharp islikemi in thetetrachordut-re-mi-fa  A flat islikefa in thetetrachordmi-fa-sol-la

6. Terhardt’s theory of pitch perception Cognitive template matching 1 Harmonic template 2 3 4 5 P8 P5 P4 M3 Real-time spectrum (bell) 

7. And by the way: That “pitch template” can be either • represented in the time or the frequency domain • acquired in ontogeny or phylogeny That’s interesting…but for the present purpose the consequence is the same.

8. Accidentalsandpitchsalience A harmonic sharp corresponds to the 5th harmonic (2*P8 + M3) of a diatonic pitch Makes the diatonic pitch more salient A harmonic flat makes a diatonic pitch the 5th harmonic of itself • Makesthe flat moresalient  Origin ofasymmetry?

9. Predictions Flats aremorenoticeablethansharps • Flats happen lessoftenthansharps • Perceiveddistanceisgreaterto flat-sidekeythanto sharp-sidekey

10. DeutscherLiederschatz (1859-1872)Collected by Ludwig Erk- Band 1: 200 songs 196 songs in major keys Relative to key signatures: 1016sharps, 459 flats Distribution when all transposedto C major:

11. DeutscherLiederschatz (1859-1872)Collected by Ludwig Erk- Band 1: 200 songs 4 songs in minor keys Relative to key signature: 115 sharps, 0 flats Distribution when all transposedto A minor:

12. Bach chorales 185 in major keys • 42571 notes • 1534 sharps • 465 flats 139 in minor keys • 30847 notes • 2628 sharps • 208 flats Total 370 chorales (4-voice) Modal choralesexcludedfromcounts Accidentalcountsare relative tokeysignature

13. Ourexperimental approach • Hownoticeableareaccidentals? • Directlynoticed? • Making musicsoundstrange? • Progressionsofonlymajor/minortriads  lowvariationofconsonance/dissonance • Eliminateotherpossibleconfounds • chordsofoctave-spaced (Shepard) tones • all possibleprogswithingivenconstraints • different randomorderforeachlistener • Systematicallyaddsharpsandflats  flat changesmajortriadtominor  sharp changesminortriadtomajor

14. Stimuli • In each trial, listener hears five chords • first is tonic triad (major or minor) • major: rest are ii, IV, V, iv (all 24 orders) • minor: rest are III, iv, v, VI (v is minor!) • In altered conditions, second-last chord is changed from maj to min or min to maj • Total 24 x 2 x 2 = 96 trials

15. Independent variables • Mode (majororminorkey) • Alteration (accidentalor not) • Accidental (sharp or flat)

16. Dependent variables 1. How unusual does the progression sound? 1 = very usual … 9 = very unusual 20 musicians “mus-unu” and 20 nonmusicians“non-unu” Separate run of same trials: 2. Is there an accidental? (in minor keys, leading tone is an accidental) 1 = definitely not, 9 = definitely 20 musicians “mus-acc”

17. Major versus minor keys In minor: • progssound more “unusual” • musicians not more likely to hear accidentals n.s. p<.001 p<.001

18. Major versus minorkeysAlteredprogressionsonly In minor: • soundmoreunusual • musiciansmorelikelytoreportaccidentals p<.001 p<.001 p<.001

19. Original versus alteredprogressions • Musicianscouldidentifyaccidentals • Progswithaccidentalssoundedmoreunusual

20. Sharps versus flats • Musiciansnoticedflatsandsharpsequallyoften • Flats (orminortriads) soundedmoreunusualfor all listeners n.s. p<.001 p<.001

21. Caveats • Did flats sound more prominent or did minor triads sound more unusual? • These could be separated in an experiment with real music - but more confounds. • Further confound: Third of minor triad (which is often a flat) is more salient than third of major triad (often a sharp) (Krumhansl & Kessler, 1982; Parncutt, 1988)

22. Open triangles: Key profiles1Full squares: pc salience profile of tonic triad2Source: Parncutt (Music Perception, 2011) 1 Krumhansl, C. L., & Kessler, E. J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review 2 Parncutt, R. (1988). Revision of Terhardt'spsychoacoustical model of the root(s) of a musical chord. Music Perception

23. Broaderimplicationsformusicpsychologyandmusictheory The score is not a perceptualrepresentation! • Tones vary in salience • masking • harmonicpatternrecognition • Some tone sensationsare not notated • missingfundamentals • prominent partials

24. Acknowledgments Students of “Empirical Music Psychology” in “Musikologie Graz” • Raimund Groinig • Herbert Laidlayr • Daniel Revers • Horst Schnattler • Michael Urbanz