Pitch Salience in Tonal Contexts and Asymmetry of Perceived

Key Movement Richard Parncutt

Centre for Systematic Musicology, University of Graz, Austria

Craig SappCCARH, Department of Music, Stanford University

Society for Music Perception and CognitionEastman School of Music, Rochester NY

11-14 August 2011

SysMus Graz

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 (Deutscher Liederschatz, 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.

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 (add one flat)• C to Bb (add two flats)

…than to sharp-side keys• C to G (add one sharp)• C to D (add two sharps)

2. That is true in chord progressions but not individual voices

“Ecological” hypotheses

1. The asymmetries are due to the perception of the altered notes themselves - not the cognitive representation of the cycle of fifths

2. The effect depends directly on the interaction between tones in chords (that‘s why it‘s absent in melodic presentations)

The difference between sharps and flats:

Rules of enharmonic spelling

rule sharps flatsmelodic M2 below M2 aboveharmonic M3 above M3 below

Relative to scale steps:

Aim: facilitate reading by reducing the number of symbols

A sharp is like mi in the tetrachord ut-re-mi-fa A flat is like fa in the tetrachord mi-fa-sol-la

0

1

0 4 8 12 16 20 24 28 32 36 40Terhardt’s theory of pitch perception

Cognitive template matching

Harmonictemplate

Real-time spectrum(bell)

P8 M3P4P5

1

2

34

5

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.

Accidentals and pitch salience

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

Makes the flat more salient

Origin of asymmetry?

PredictionsFlats are more noticeable than sharpsFlats happen less often than sharpsPerceived distance is greater to flat-

side key than to sharp-side key

Deutscher Liederschatz (1859-1872)Collected by Ludwig Erk - Band 1: 200 songs

196 songs in major keysRelative to key signatures: 1016 sharps, 459 flats

Distribution when all transposed to C major:

c d e f g a b0

2000

4000

6000

8000

10000

12000

14000

naturalsharpflat

Deutscher Liederschatz (1859-1872)Collected by Ludwig Erk - Band 1: 200 songs

4 songs in minor keysRelative to key signature: 115 sharps, 0 flatsDistribution when all transposed to A minor:

a b c d e f g0

50

100

150

200

250

300

naturalsharpflat

Bach chorales185 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 chorales excluded from countsAccidental counts are relative to key signature

Our experimental approach• How noticeable are accidentals?

– Directly noticed?– Making music sound strange?

• Progressions of only major/minor triads low variation of consonance/dissonance

• Eliminate other possible confounds– chords of octave-spaced (Shepard) tones– all possible progs within given constraints– different random order for each listener

• Systematically add sharps and flats flat changes major triad to minor sharp changes minor triad to major

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

Independent variables

1. Mode (major or minor key)2. Alteration (accidental or not)3. Accidental (sharp or flat)

Dependent variables1. How unusual does the progression sound?

1 = very usual … 9 = very unusual20 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 = definitely20 musicians “mus-acc”

Major versus minor keys

In minor:

• progs sound more “unusual”

• musicians not more likely to hear accidentals mus-acc mus-unu non-unu

123456789

majorminor

n.s. p<.001 p<.001

Major versus minor keysAltered progressions only

In minor:

• sound more unusual

• musicians more likely to report accidentals

mus-acc mus-unu non-unu0123456789

majorminor

p<.001 p<.001 p<.001

Original versus altered progressions

• Musicians could identify accidentals

• Progs with accidentals sounded more unusual

mus-acc mus-unu non-unu1

2

3

4

5

6

7

8

9diatonic

one accidental

Sharps versus flats

• Musicians noticed flats and sharps equally often

• Flats (or minor triads) sounded more unusual for all listeners

mus-acc mus-unu non-unu123456789

sharpflat

n.s. p<.001 p<.001

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)

Open triangles: Key profiles1

Full squares: pc salience profile of tonic triad2

Source: Parncutt (Music Perception, 2011)

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(a) C major

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C D E F G A B

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(b) C minor

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C D E F G A B

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's psychoacoustical model of the root(s) of a musical chord. Music Perception

Broader implicationsfor music psychology and music theory

The score is not a perceptual representation!• Tones vary in salience

– masking– harmonic pattern recognition

• Some tone sensations are not notated– missing fundamentals– prominent partials

Acknowledgments

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