Transcript Pitch Salience in Tonal Contexts and Asymmetry of

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
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
Aim: facilitate reading by reducing the number of symbols
Relative to scale steps:
rule
melodic
sharps
M2 below
flats
M2 above
harmonic
M3 above
M3 below
 A sharp is like mi in the tetrachord ut-re-mi-fa
 A flat is like fa in the tetrachord mi-fa-sol-la
Terhardt’s theory of pitch perception
Harmonic
template 
poids (1/n)
Cognitive
template matching
1
1
2
3
4
5
P8
P5
P4
M3
0
40
36
interval (semitones)
32
28
24
20
16
12
8
4
0
Real-time
spectrum
(bell) 
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?
Predictions
Flats are more noticeable than sharps
Flats happen less often than sharps
Perceived distance is greater to flatside key than to sharp-side key
Deutscher Liederschatz (1859-1872)
Collected by Ludwig Erk - Band 1: 200 songs
196 songs in major keys
Relative to key signatures: 1016 sharps, 459 flats
Distribution when all transposed to C major:
14000
12000
10000
8000
natural
sharp
flat
6000
4000
2000
0
c
d
e
f
g
a
b
Deutscher Liederschatz (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 transposed to A minor:
300
250
200
natural
150
sharp
100
flat
50
0
a
b
c
d
e
f
g
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 chorales excluded from counts
Accidental 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 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”
Major versus minor keys
In minor:
• progs sound
more
“unusual”
• musicians not
more likely to
hear
accidentals
9
8
7
6
5
4
3
2
1
major
minor
mus-acc mus-unu non-unu
n.s.
p<.001
p<.001
Major versus minor keys
Altered progressions only
In minor:
• sound more
unusual
• musicians more
likely to report
accidentals
9
8
7
6
5
4
3
2
1
0
major
minor
mus-acc mus-unu non-unu
p<.001 p<.001 p<.001
Original versus altered progressions
• Musicians
could identify
accidentals
• Progs with
accidentals
sounded
more unusual
9
8
7
6
5
4
3
2
1
diatonic
one accidental
mus-acc
mus-unu
non-unu
Sharps versus flats
• Musicians
noticed flats
and sharps
equally often
• Flats (or minor
triads) sounded
more unusual
for all listeners
9
8
7
6
5
4
3
2
1
sharp
flat
mus-acc
mus-unu
non-unu
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)
(a) C major
(b) C minor
K&K82
7
Pmo88
pc-weight/3 (Pmo88)
average rating (K&K82)
7
5
5
3
3
1
1
C
D
E F
G
A
B
-1
C
D
E F
G
A
B
12
chroma
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 implications
for 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