pitch salience in tonal contexts and asymmetry of perceived key movement richard parncutt centre for...
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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)
1
3
5
7
chroma
(a) C major
Pmo88
K&K82
C D E F G A B
1
3
5
7
-1 12
(b) C minor
ave
rag
e r
ati
ng
(K
&K
82)
pc-
weig
ht/
3 (
Pm
o8
8)
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