Psychoacoustics and Music Perception
509.211 VO, 2st.
S06, Mi 17:30-19:15
HS 06.03
Richard Parncutt
Email: ((my last name))@uni-graz.at
Office hours: Thursday 10 am
This file is…
• available in the internet and updated regularly
• only a PART of the course material. Missing:
– verbal explanations in lectures
– figures drawn on board and displayed with OHP
(transparencies)
– contents of folder in reading room of department library
– sound examples (including those linked to this document –
but many of these are on the CD in the folder)
• written in point form – but exam answers must be complete
sentences! (see “Schriftliche Prüfungen”)
Questions and suggestions? ((familyname))@uni-graz.at
Lecture 1, 8.3.06
• Adminstrative details
– aims
– dates
– examination
• Introduction: Musical relevance of psychoacoustics
• Course outline, literature
• Philosophy of perception: the “3 worlds” of Popper & Eccles (1977)
Literature:
• Parncutt, R. (in press). Psychoacoustics and music perception
• Terhardt, E. (1998). Akustische Kommunikation. Berlin: Springer. (1.
Kapitel)
Musical relevance
Consider some everyday musical examples:
•
•
•
•
J. S. Bach: „O Haupt voll Blut und Wunden“ („Baroque choral“)
Frank Sinatra: „White Christmas“ („pop“)
Miles Davis „So what“ („modal jazz“)
Igor Stravinsky: „Sacré du printemps“ („modern orchestral“)
Consider some psychological issues:
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•
•
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What do you hear or experience in this music?
Chain: physics – perception – structure – associations
Direct perception:
ecological psychology
Indirect perception: cognitive psychology
Relevance for music analysis
• Perception of pitch structures
– harmony, voice-leading, phrasing, tonality, modulation
• Quality of sound
– consonance/dissonance, timbre
• Cognitive organisation
– foreground, background
• Emotional character
– associations
Not considered:
• Accents: dynamic, grouping, metrical, melodic, harmonic
• Expressive timing and dynamics
Some course aims
• Overview and understand
– musically relevant fundamentals of psychoacoustics
– perceptual correlates of music-theoretical concepts (cons./diss., root/tonic)
• Understand technical primary literature
– extract relevant information from it
• Show relevance for music theory and analysis
• Contribute to understanding of musical meaning
– perceptual/cognitive processes
– personal/cultural associations
•
Raise awareness of applications
– music theoretical, analytical, and practical
•
Prepare for the SE "Cognition of Musical Structure"
Tentative semester plan (1)
#
Date
Content
Literature (Handapparat)
1
8.3.
Course outline, musical relevance
Philosophy of perception (“3 worlds”)
Parncutt (in press)
Terhardt 1998 Ch. 1
2
15.3.
Intro to psychoacoustics (examples)
Freq. perception: object perception &
survival; freq. analysis, physiol.,
masking, CBW, loudness
ASA CD (Houtsma et al.)
Rasch & Plomp 1999;
Howard & Angus, 1996;
Terhardt 1988
-
break
Read and summarize literature
Practice exam questions
See end of this file
3
26.4.
Pitch perception: Psychoacoustics
and neuroscience of pitch
Parncutt 1989, ch. 2;
Laden, 1994; Zatorre 1988
4
3.5.
Consonance/dissonance & masking:
critical bandwidth, freq. ratios,
roughness, familiarity
Plomp & Levelt 1965;
Tenney, 1988
5
10.5.
Categorical pitch perception: musical
scales, absolute pitch, intonation,
learned intervals
Burns 1999
6
17.5.
Mid-term test (40 minutes, not
graded); sample answers
Tentative semester plan (2)
7
24.5. Timbre perception
8
31.5
Localization & subjective room
acoustics
9
7.6.
Auditory scene analysis and
perception of counterpoint
Bregman 1993, Huron 2001
10 14.6
Harmony, root, tonality
Parncutt 1993, Krumhansl
1990
11
Nature versus nurture
Overview
21.6
12 28.6
Written examination (100% of final
grade)
Guest professor
Caroline Traube
(Université de Montréal)
Answer 5 of 10 questions
Preparation for lectures
Read the literature in advance!
Making up for lost time
Students at the first lecture on 8.3.06
preferred to extend each lecture by 15
minutes (i.e. 17:30-19:15) than to schedule
two additional lectures.
Central literature sources
• Houtsma et al.(1987). Auditory
demonstrations on compact disc.
• Articles in Semester Plan above
Both are in folder „Psychoacoustics“
• Handapparat, reading room, musicology
To copy articles:
• take folder to secretary‘s office
Auxiliary literature sources
•
•
•
•
•
•
•
•
•
•
•
•
•
Bregman (1994). Auditory scene analysis
De la Motte-haber (2005). Musikpsychologie.
Deutsch (Ed., 1999). Psychology of music (2. ed.)
Hall (1997). Musikalische Akustik
Handel (1993). Listening
Harwood & Dowling (1995). Music cognition
Howard & James (1996). Acoustics and psychoacoustics.
McAdams & Bigand (Eds., 1993). Thinking in sound
Pierce (1985). Klang
Roederer (1993). Physikal. und psychoakust. Grundlagen der Musik
Rosen & Howell (1991). Signals & systems for speech & hearing
Terhardt (1998). Akustische Kommunikation
Zwicker (1982). Psychoakustik
The process of sound perception
Why do we experience a complex tone as one thing?
Process
Result
source vibration
sound in air
physical
transmission
vibration at ear drum, middle ear,
oval window
Fourier analysis
(basilar membr.)
auditory spectrum (pitch and salience
of each audible partial)
fusion (brain)
holistic qualities of complex tones
(pitch, loudness, timbre…)
cognition
meaning and identity of sources incl.
music
Philosophy of reality:
Karl Popper‘s „three worlds“ (1)
World 1
World 2
World 3
physical
experiential
abstract
matter, energy
sensations, emotions
information, knowledge, culture
Example: A visit to an art gallery
• physical:
walls, floor, canvas, paint, light waves, retina
• experiential: colors, shapes, emotions (feeling, mood), sound or
silence, smell, taste, touch
• abstract:
program, thoughts, content of conversation, historical
knowledge, digital representations, theory of art
Group exercise: repeat this analysis for a visit to a concert
Philosophy of reality:
Karl Popper‘s „three worlds“ (2)
Aim: clarity of terminology and thinking
Example: A visit to concert
• physical:
walls, floor, violins, human bodies, sound waves,
frequencies, amplitudes, spectra
• experiential: what it sounds like, melodic shape, tension-relaxation,
sense of time, speed, emotion (mood, feeling)
• abstract:
music notation, program, thoughts, historical
knowledge, digital representations
Especially relevant for this course:
• physical:
freq.
amplitude
• experiential: pitch
loudness
• abstract:
note
dynamic
spectrum
timbre
instrument
duration
perc. duration
note value
Lecture 2, 15.3.06
Intro to psychoacoustics
• Sound examples
Frequency perception
• object perception & survival
• freq. analysis, physiol., masking, CBW, loudness
Literature:
• Houtsma, A. J. M. et al. ((1987) Auditory demonstrations. New York:
Acoustical Society of America.
• Howard, D. M., & Angus, J. (1996). Acoustics and psychoacoustics.
Oxford: Focal. Chapter 2 (pp. 65-91): “Introduction to hearing”.
• Rasch, R. A., & Plomp, R. (1999). The perception of musical tones.
In D. Deutsch (Ed.), Psychology of music (2nd ed., pp. 89-111).
• Terhardt, E. (1988). Psychophysikalische Grundlagen der
Beurteilung musikalischer Klänge. In J. Meyer (Hg.),
Qualitätsaspekte bei Musikinstrumenten (S.1-15) Celle: Moeck.
Psychophysics: Worlds 1 and 2
Each experiential parameter depends on each physical parameter!
Sound examples: ASA-CD
• Pitch depends on spectrum (missing fundamental) (Track 37)
• Timbre depends on temporal envelope: backward piano (Track 56)
• Loudness does not double when intensity doubles (Track 9)
More examples:
• Pitch depends on intensity (Tracks 27-28)
• Pitch salience depends on tone duration (Track 29)
• Loudness depends on frequency (Tracks 17-18)
• Loudness depends on spectrum (Track 7)
Frequency perception: Intro
…as opposed to pitch perception
– object perception and survival
– frequency analysis
– physiology
– masking
– critical band
– loudness
Survival value of frequency perception
• Darwin‘s theory of evolution
– individual differences (mutation)
– environment: danger; limited resources
– survival = successful reproduction
• Relevance for hearing and music
–
–
–
–
–
aim: survival by identifying and describing objects
input to ear: superposition of direct and reflected sound
unaffected: frequency
randomized: phase
frequency is reliable
phase is unreliable
sensitivity to frequency insensitivity to phase
Musical implications
• Timbre (identifies sound sources)
– strongly dependent on spectrum (esp. frequencies)
– not directly dependent on waveform (phase)
• Music notation and theory
– primary: pitch, time
– secondary: loudness, timbre
– irrelevant: phase
Aural frequency analysis
• Aim:
• Approach:
• Method:
identify environmental objects (sound sources)
monitor frequency-time patterns (contours)
frequency analysis (separate frequencies)
Physiology of frequency analysis
Basilar membrane changes along length
– heavy, floppy end:
sensitive to low frequencies
– light, tight end:
sensitive to high
frequencies
Each hair cell on basilar membrane:
• responds to limited range of frequencies
• is an „auditory filter“
• filter bandwidth = critical bandwidth
Cut-off frequency of a filter
Arbitrary cut-off point:
3 dB down from maximum
Bandpass filter
A (dB)
bandwidth
f (Hz)
Center
frequency
Frequency analysis by a filter bank
1st harmonic
2nd harmonic
signal
Harmonic complex tone
3rd harmonic
bank of bandpass filters
Critical bandwidth
Auditory filters have no sharp cut-off
=> exact value of critical bandwidth is arbitrary
depending on experimental method…
• above about 500 Hz:
2...3 semitones
• below about 500 Hz:
60...100 Hz (e.g. 80-160 Hz = 1 oct.!)
Implications for tonal music
If aim is…
Separately audible voices in harmony and counterpoint
Then need… Separately audible partials in sonorities
Physiology:
Excite different hair cells with different partials
Result:
Closer spacing of higher tones in chords
Critical bandwidth: Bark vs ERB
Bark: Eberhard Zwicker et al. (München); ERB: Brian Moore et al. (Cambridge)
Auditory masking
•
•
•
•
•
„drowning out“
everyday example: piano accompanist
simple example: two pure tones
masked threshold of a pure tone (Mithörschwelle)
number of audible partials of a complex tone
Auditory threshold
Masked threshold of a complex tone
Loudness
Depends on:
• number of excited hair cells (hence bandwidth of sound)
• excitation of each cell (energy in each auditory filter)
Repeat sound demonstration (ASA Track 7)
SPL (dB)
Critical band
50 Hz
100 Hz
150 Hz
200 Hz
Physical bandwidth
Frequency (Hz)
1000 Hz
Loudess of a steady-state
complex sound
after Stevens and Zwicker
• within critical bands:
– add energy (physical)
• across critical bands:
– add loudness (experiential)
Revision until Easter
• Read the literature
• Reread the lecture notes
• Ask questions (e.g. email)
Lecture 3, 26.4.06
Pitch of complex tones
• psychoacoustics (explained in lecture)
• neuroscience (read Laden and Zatorre)
Literature
Parncutt, R. (1989). Harmony: A psychoacoustical approach. Berlin:
Springer. (Chapter 2, Psychoacoustics).
Laden, B. (1994). A parallel learning model of musical pitch perception.
Journal of New Music Research, 23, 133-144.
Zatorre, R. J. (1988). Pitch perception of complex tones and human
temporal-lobe function. Journal of the Acoustical Society of America,
84, 566-572
Handout:
Parncutt, R. (2005). Perception of musical patterns: Ambiguity, emotion,
culture. Nova Acta Leopoldina NF 92 (341), 33-47
Pitch: Introduction
• Abbreviations
– PT: pure tone
CT: complex tone
HCT: harmonic CT
– SP: spectral pitch
VP: virtual pitch
• Pitch perception according to Terhardt
– SP: (analytic) pitch of an audible partial
– VP: (holistic) pitch of a complex tone
• Examples
– most consciously noticed pitches are VPs
– pitch at missing fundamental of HCT is a VP (e.g. telephone)
– pitch of a heard-out harmonic is a SP
– strike tone of church bell is VP; as sound dies, hear SPs
Harmonic series
To typical western ears, harmonics no. 7 and 11
sound noticeably out of tune:
• 7 is 1/3 semitone flatter than a m7 above 4
• 11 is about midway between P4 and TT above 8
The harmonics are:
• equally spaced on a linear frequency scale (e.g in Hz)
• unequally spaced on a log frequency scale (e.g. in semitones)
Pitch at the missing fundamental
ASA track 37
1
amplitude
2
Conclusions:
1
• Pitch does not necessarily
correspond to a partial
0
0,2
0,4
0,6
0,8
1
1,4
1,2
1,6
2
1,8
frequency (kHz)
2
amplitude
2
• Pitch is multiple/ambiguous
• VP at missing fundamental
• SP at lowest partial
1
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
frequency (kHz)
2
1
0
0,2
0,4
0,6
0,8
1
1,2
1,4
frequency (kHz)
1,6
1,8
2
2
amplitude
amplitude
amplitude
2
3
5
4
1
1
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
frequency (kHz)
1,6
1,8
2
0,2
0,4
0,6
0,8
1
1,2
1,4
frequency (kHz)
1,6
1,8
2
1,2
1,2
1
1
0,8
0,8
amplitude
ASA-CD tracks
40
amplitude
Sound demo: Masking SP and VP
0,6
0,4
0,2
0,6
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
0,2
0,4
0,6
0,8
frequency (kHz)
amplitude
41
0,8
0,6
0,4
1,6
1,8
2
1,4
1,6
1,8
2
1,4
1,6
1,8
2
0,8
0,6
0,4
0,2
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
0,2
2
0,4
0,6
0,8
1
1,2
frequency (kHz)
frequency (kHz)
1,2
1,2
1
1
0,8
0,8
amplitude
42
1,4
1
1
amplitude
1,2
1,2
1,2
amplitude
1
frequency (kHz)
0,6
0,4
0,6
0,4
0,2
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
frequency (kHz)
1,4
1,6
1,8
2
0,2
0,4
0,6
0,8
1
1,2
frequency (kHz)
Sound demo: Masking SP and VP
Conclusion
Westminster chimes example demonstrates that
pitch at missing fundamental is „virtual“, because:
– when PT masked by low-pass noise,
• missing fundamentals is audible inside the noise
• If it were physical it would be masked!
– when HCT masked by high-pass noise,
• missing fundamental is inaudible outside the noise
• If it were physical it would be audible
Sound demo: „Shift of VP“
ASA-CD Track 39
2
amplitude
amplitude
2
1
1
0
0
0,2
0,4
0,6
0,8
1
1,2
1,4
1,6
1,8
2
0,45
0,65
0,85
1,05
1,25
1,45
1,65
1,85
2,05
frequency (kHz)
frequency (kHz)
SP3
(Hz)
0,25
Demo SP1
no.
(Hz)
SP2
(Hz)
VP
(Hz)
1
800
1000 1200 200
2
850
1050 1250 210
Conclusion:
VP corresponds to:
• best-fit subharmonic (or
approx. fundamental) of
all partials
• NOT to difference in
frequencies
Sound demo: VP with random harmonics
ACA-CD tracks 43
44
45
HCTs of 3 random successive harmonics
1. harmonic numbers 2 to 6
(3 possibilities: 234, 345, 456)
2. harmonic numbers 5 to 9
3. harmonic numbers 8 to 12
Conclusion:
•
salience of VP depends on effective harmonic
number of SPs above it
–
lower harmonic numbers  more salient VP
Sound demo: Strike note of a chime
ASA-CD Track 46
47
1. hearing out partials
– pure reference tone, then complex test tone
– Can you hear the PT inside the CT?
– Procedure encourages analytic listening
2. matching a virtual pitch
– reverse order: first complex test tone, then pure reference tone
– Do the two tones have the same pitch?
– Procedure encourages holistic listening
Conclusions
– partials are audible (as SPs)
– „the pitch“ (VP) is ambiguous
Experimental determination of pitch
Question:
• Pitch is an experience. How can it be measured?
Answer:
• Compare pitch of two successive sounds
• Assume pitch of one sound is known
• If two sounds have same pitch, pitch of second sound is known
The pitch of a pure tone is assumed:
• to be unambiguous
• to correspond to its frequency (provided SPL constant)
Standard experimental method:
• Test sound, pause, reference tone (each about 200-400 ms)
• Listener adjusts frequency of reference until same pitch
• A pitch „exists“ when intra- and inter-listener agreement
Pitch properties of complex tones
A CT generally evokes several pitches.
• If only one is perceived at a time, the pitch is ambiguous.
• If more than one can be perceived at a time, the pitch is multiple.
The pitches of a CT vary in salience, i.e. either:
• the probability of noticing the pitch, or
• the subjective importance of the pitch
Perception of complex tones
Stage 1: Auditory spectral analysis (Ohm, 1843; Helmholtz, 1863)
E.g. A HCT in speech or music typically has 10 + 5 audible harmonics.
Stage 2: Holistic perception of CTs (Stumpf, 1883; Terhardt, 1976)
A HCT is normally experienced as one thing:
a complex tone sensation with pitch (VP), timbre, and loudness.
But when partials are heard out, the CT is experienced as many things:
pure tone sensations, each with pitch (SP), timbre, and salience.
Examples of
physical spectra
(“YL”) and
experiential spectra
(“salience”)
1. pure tone (PT on C4)
2. harmonic complex tone
(HCT on C4)
3. octave-complex tone
(OCT on C)
“Pitch category”: 48 = C4, 60 = C5 etc.
(Parncutt, 1989)
Terhardt‘s model of pitch perception:
Input-output
• Input:
physical spectrum of a steady-state sound
(frequency and amplitude of each partial)
• Output:
„experiential spectrum“
(pitch and salience of each tone sensation)
• Aim:
predict experiential spectrum from physical
spectrum
Terhardt‘s model of pitch perception:
Detail
1. masking  SPs and their saliences
–
–
Nearby partials mask each other more strongly
Inner partials are masked more than outer partials
2. recognition of harmonic pitch patterns  VPs and saliences
–
Salience depends on
•
fit between harmonic template and spectrum
–
•
salience of matching SPs
–
•
number and accuracy of matches
more salient SPs  more salient VP
harmonic number of matching SPs
–
lower harmonic nos.  higher VP-salience
3. combination of SPs and VPs  all pitches and saliences
–
–
experiential spectrum contains both
relative weighting depends on analyic/holistic perception
Hearing out harmonics (1)
Terhardt CD track 17
• HCT, 200 Hz, 10 harmonics
• harmonic numbers 4,3,4,5,6: + 3 dB
Conclusion:
SPs exist independently of VP
Further sound examples
See CD in back of Terhardt (1998)
Hearing out harmonics (2)
Terhardt CD track 18
• HCT, 200 Hz, 10 harmonics
• Pure tone 600 Hz
• Harmonic not heard out
• Same HCT twice, once with missing harmonic
• Attention attracted to „replaced“ harmonic
Conclusions
• Attention is attracted to changes and differences
• Again: SPs exist independently of VP
Virtual pitch (2)
Terhardt CD track 21
• HCT, 200 Hz, harmonics 6-12 („residue tone“ RT)
• Pure tone 200 Hz
Conclusions:
• SPs can be heard out if tone is long and constant
• It is possible to attend directly to VP
Der Dominanzbereich der
spektralen Tonhöhe nach Terhardt
1,5
weight
1,0
0,5
0,0
100
1000
log frequency (Hz)
10000
Spectral dominance
Terhardt CD track 23
• HCT, 200 Hz, 20 harmonics
• Non-harmonic CT:
– lower harmonics shifted down
– upper harmonics shifted up
• Different boundary frequencies:
– 500 Hz: VP determined by upper SPs
– 1900 Hz: VP determined by lower SPs
– 700 Hz: ambiguous
Melody of residue tones (1)
Terhardt CD track 24
• harmonics 2-4 or 3-5 or 4-6
• harmonics 5-7 or 6-8 or 7-9
• harmonics 8-10 or 9-11 or 10-12
Melody of residue tones (2)
Terhardt CD track 25
• three randomly selected harmonics from harmonics 2-9
Melody of residue tones (3)
• Chords in equal temperament
– pure tones
– HCTs: VP becomes root of major triad
„Acoustic bass“
of a church organ
Terhardt CD track 27
• A1 + E2 = A0?
Lecture 4, 3.5.06
Consonance and dissonance of sonorities in western music
• Roughness of harmonic intervals
– critical bandwidth
– pure versus complex tones
– frequency ratios
• Clarity of harmonic function
– fusion
– pitch salience
– cognition of pitch structures
• Familiarity
– historical development of tonal-harmonic syntax
Sound example
Terhardt CD track 8
harmonic interval of two pure tones
No.
f1 (Hz) f2 (Hz) fb (Hz) comment
1
500
504
4
audible
beats
2
500
540
40
rough
3
500
700
200
smooth
A harmonic tritone of two tones in the middle or
high register is quite smooth!
Superposition of two pure tones
same amplitude, similar frequency
f1 = 1/t1
f2 = 1/t2
beat freq.:
fb = |f2 – f1|
carrier freq.:
fc = (f2 + f1)/2
Roughness of a harmonic interval
of pure tones
• 20 Hz < fb < 300 Hz
– e.g. semitone at 300 Hz, 300:320  20 Hz
– e.g. semitone at 600 Hz, 600:640  40 Hz
– Two HCTs: many contributions to roughness
• fb < 20 Hz: individually audible beats
– e.g. mistuned piano strings
– most prominent near 4 Hz (cf. speech)
• fb > 300 Hz: no roughess
– Isolated HCTs above 300 Hz: no roughness
Roughness of a harmonic interval
of pure tones
Source:
Campbell & Greated (1987).
The musician’s guide to
acoustics (p.58).
New York: Schirmer.
Roughness depends on overlap between excitation functions
Roughness of a harmonic interval
of pure tones
Plomp & Levelt (1965)
Critical bandwidth
Roughness of a harmonic interval
of HCTs
Sum roughness contributions from different critical bands
E.g. : tritone (frequency ratio 1:1.414)
Tone 1 :
Tone 2 :
1000
1414
2000
3000
2828
4000
5000
4242
Frequency ratios between almost coincident harmonics :
1.06
1.06
(1.06 corresponds to one semitone)
6000
5656
7000
7070
1.01
Roughness of a harmonic interval
of HCTs
Predictions according to Plomp & Levelt
Frequency ratios of intervals
Which one is the “right” one?
interval
P1
m2
M2
m3
M3
P4
TT
P5
m6
M6
m7
M7
P8
note
C
C#
D
D#
E
F
F#
G
G#
A
A#
B
C
chr. “pure” ratio Pythagorean
0
1:1
1:1
1
16:15
256:243
2
9:8
9:8
3
6:5
32:27
4
5:4
81:64
5
4:3
4:3
6
45:32
729:512
7
3:2
3:2
8
8:5
128:81
9
5:3
27:16
10
9:5
16:9
11
15:8
243:128
12
2:1
2:1
Frequency ratios of intervals
Calculating intervals:
e.g. m7 = P5 + m3 = 3/2 x 6/5 = 9/5
Pure tuning:
• combinations of P8, P5, M3
Pythagorean tuning:
• combinations of P8, P5
• frequency ratio always in the form 2n/3m or 3m/2n
Interval (cents) = log2 (f1/f2) x 1200
Origins of musical scales
• Ancient western music: assumptions
– vocal melody, oral tradition
– tuning of successive intervals by ear
• Role of successive P8, P5, P4 intervals
– theory of tonal affinity:
• coinciding harmonics (Helmholtz)
• coinciding pitches (Terhardt)
– singers approach consonant intervals by trial and error:
• audible difference between P8 & M7/m9, P5 & TT/m6, P4 & TT/M3
• Limitations on accuracy of intonation in vocal performance
– vocal limitations, e.g. jitter (even when no vibrato at all)
– perceptual limitations, e.g. (lack of) sensitivity to slow beats
Evolution of standard western
scales
• Standard pentatonic/heptatonic
– a series of P5/P4s
• FCGDAFCGDAEB
– These P5/P4s are not very exact! (+ 20-50 cents?)
• Chromatic scale
– add m2, M3 or P4 to diatonic tones, e.g. F#/Gb is:
• F + m2, G - m2 (midway between F and G)
• D + M3
• B – P4
• Underlying assumption:
– consonance is important and is preferred
– culture-specific concept and role of consonance
Clarity of harmonic function
Theory of harmonic function:
Riemann (S D T usw.)
Major and minor triads:
high clarity  more common?
Diminished and augmented triads:
low clarity  less common?
Clarity of harmonic function
= fusion (Stumpf)
= salience of virtual pitch at root (Terhardt)
Cognitive theory:
Pitch structures are easier to understand ( more
consonant) if they have clear reference pitches
(roots and tonics).
Familiarity
Historical development of tonal-harmonic syntax
• Historical listeners are familiar with the syntax of their period
Example: “dominant seventh chord” (e.g. GBDF)
In musical practice:
•
•
•
•
•
in 1500: prepared or accidental
in 1600: unprepared in Monteverdi
in 1700: often unprepared but still dissonant
in 1800: increasingly consonant
in 1900: as if consonant
In music theory:
• before 1700: non-existent
• after 1800: universally recognized
Tenney’s
“Consonance-Dissonance Concepts”
CDC
concept
Tenney’s
definition
CDC-1
melodic affinity before
polyphony
pitches in common
CDC-2
sonority of
early
isolated dyads polyphony
roughness or pitch
salience?
CDC-3
clarity of lower 14th C.
voice
pitch salience of (lower)
melody
CDC-4
property of
individual
tones in chord
18th C.
dependence of
roughness on amplitude
of individual tone
CDC-5
Smoothness
or roughness
19th C.
roughness of whole
sonority
historical
period
possible
perceptual account
Consonance-dissonance of
sonorities in western music
Three perceptual factors:
1. roughness
peripheral origin
2. clarity of harmonic function
central origin
3. familiarity
depends on musical syntax
Are they independent?
•
•
1 is perceptually independent of 2
but 3 depends on 1 and 2
Lecture 5, 10.5.06
Categorical perception
Perception and cognition of music
•
•
•
•
CP and the three worlds of Popper
CP of relative pitch (versus intonation)
CP of absolute pitch
CP of rhythm (versus rubato)
Evolutionary music psychology
• Why does music have pitch and time
categories?
• Implications for origins and prehistory of music
Non-musical categorical perception
• Color
– red = range of light wavelengths
– nature: depends mainly on rods and cones
– nurture: also depends on culture/learning
• Speech sounds
– The vowel /a/ has specific formant frequencies
– nature: all formants are near 500, 1500, 2500 … Hz
– nurture: formant frequencies of /a/ are learned from
speech ( culture-specific)
Categorical perception and the
three worlds of Popper
Psychophysics:
• relationships between Worlds 1 & 2
• E.g. SPL of just audible pure tone
Categorical perception:
• conceptually: between worlds 2 & 3
• empirically: between worlds 1 & 3
Examples
• range of frequency ratios of M3 interval
• scale step, duration, instrument, dynamic…
• range of any continuous parameter corresponding to any label
Experiment on categorical
perception of musical intervals
(Burns & Campbell, 1994)
Stimuli:
Melodic intervals
of complex tones;
all ¼ tones up to
one octave.
Participants:
Musicians
Question:
Which of 24
categories
(quarter tones)?
Results
(Burns & Campbell, 1994)
• All intervals on a continuous scale are categorized
• Familiar categories are
– broader
– more often selected
• Category centres
~ familiar tuning (equal temperament)
• Category width
~ distance between familiar categories
Another psychological definition of
“categorical perception”
Heightened discrimination near category boundary
– Just noticeable difference (JND) is smaller at
boundary
– E.g. frequency JND of successive pure tones, central
range = 1…10 cents
This definition:
– Does not necessarily hold for musical categories
– Is not assumed here
Categorical pitch perception
versus intonation
Hard to distinguish empirically.
What’s the conceptual difference?
Categorical perception
label in World 3
meaning
Intonation
pitch in World 2
experience
What influences intonation?
Real-time frequency adjustment in music performance
depends directly on many factors!
• octave stretch
• beating of coinciding partials
• context, implication (leading tone)
• whether soloist (sharp) or accompaniment (flat)
• emotion (e.g. tension-release)
• timbre (deep = low)
• clarity: preference for equal spacing in chromatic or diatonic scale
• separation of major and minor modes
• pitch salience: less stable tones are more variable
 Hard to investigate scientifically – hard to isolate one factor
Intonation and enharmonic spelling
E.g. F# is usually sharper than Gb, but
– there are many different kinds of F# and kinds of Gb
– enharmonic spelling is often ambiguous (and there is
no clear rule)
– F# can be lower than Gb if intonation approaches
“just” (slow tempo, constant tones)
 Intonation does not depend directly on
enharmonic spelling
When is a tone “in tune”?
Two different ranges:
• Category width corresponding to scale step:
say, + 50-100 cents
• In-tune range (=good timbre?):
say, + 10-30 cents
Role of context:
• Both category width and in-tune range are smaller when
–
–
–
–
–
–
slower music (longer tones)
less vibrato
more familiar tuning
more exact tuning
higher pitch salience
central pitch range
Absolute pitch
“Absolute perception” is normal
 e.g. colour, vowel quality
 also across senses: synaesthesia, chromasthesia
AP is actually “absolute chroma”
“AP possessors” are no better at naming register
AP can apply either to individual tones or
whole pieces
E.g. ask listener if well-known piece is in the right key
AP is learned
Pianists label white keys more easily
because played more often or clearer label
Everyone has some AP
non-musicians tend to sing in right key (Levitin, 1994)
AP involves both long-term memory and labeling
Only musicians can apply musical pitch labels
AP is acquired in a “critical period” (like language?)
provided there is sound-label relation and repetition
Limits of AP also support learning
semitone errors (from pitch shifts?)
octave errors (from pitch ambiguity?)
Absolute versus relative
pitch perception
Both are
• examples of categorical perception (pitch or interval)
• defined by chromatic scale, accuracy + 50-100 cents
Properties
• weak correlation with other musical or perceptual skills
• many have it to some extent (also non-musicians)
Musical rhythm
as categorical perception
Examples
• swing ratio: 2:1 vs dotted rhythm: 3:1
• triplet 1:1:1 vs 1:1:2
Each category has:
• a range of possible realisations (rubato)
• that depends on context
– triple meter makes 1:1:1 more likely
– duple meter makes 1:1:2 more likely
Pitch-rhythm analogy
Category
(World 3)
Center
(World 2)
rhythm
note values,
meter
rubato
pitch
note names,
scale
intonation
Why does music have
pitch & time categories?
“Music” must be stored and reproduced either as
• oral tradition or
• notation
to acquire meaning in a cultural context
Music can be stored in:
• World 3 (memory in oral tradition)
• World 3 (notation) or
• World 1 (sound recording)
categories are necessary
amount of information is limited by cognitive capacity
Speech versus song
• Speech: categories are phonemes, words
• Song: categories are pitch, rhythm
In both cases:
• Categories have meaning
• Categories are part of culture
Origins of music
What motivates/d people to create
pitch/rhythm categories?
•
•
•
•
Practice for cognitive system
Emotional communication  social cohesion
Babies: prelinguistic communication
Fetus: perception of maternal state
Prehistory of music
Observation:
Songs in different oral traditions
• include P8, P5 and P4 intervals between scale steps
• Duple and triple rhythms, or time ratios of 1:2 and 1:3
How did this happen? A theory…
Arbitrary starting point:
• Songs with arbitrary pitch and rhythm categories
Process:
• singers vary performance randomly or deliberately, by trial and error
• clearer structures are easier to remember
– pitch: P8 or P5 between scale steps (pitch commonality)
– rhythm: 2:1 and 3:1 ratios (pulse)
Leads to:
• “simple” scales (pentatonic or diatonic) and meters
Evolutionary theory
biology (Darwin)
music
diversity
Each individual is
(genetically)
unique
constraint
limited resources
(e.g. food)
variation and
improvisation  many
different melodic
fragments
limited memory
(cognitive resources)
survival
The “fittest” or
best adapted is
most likely to
survive and
reproduce
More coherent or
structured patterns are
easier to remember, so
more likely to contribute
to oral tradition
Musical diversity
The described evolutionary process does
not produce simplicity or monotony, but
rather a wide range of musical styles.
Possible explanation:
• music has a wide range of social and cultural meanings
and functions
• complexity can be preferred for representational or
aesthetic reasons
Lecture 6, 17.5.06
Test
5 questions @ 10 minutes = 50 minutes
Your options
• I will grade your paper if you want and give it back to you in my
Sprechstunde.
• The grade for the test will not have any effect on your final grade.
Tips on how to answer the questions:
• Read the question carefully and ask yourself why exactly those words
were chosen.
• Answer only the stated question; don’t talk around it.
• Think about your answer before you begin. Quality is more important
than quantity.
• Structure your answer clearly, following the structure of the question
(a, b…).
• Write clearly and legibly. Begin each answer on a new page.
• If appropriate, incorporate diagrams and refer to them in the text.
1. Philosophy of perception
a. Apply Popper’s concept of the three worlds to the art of cooking;
b. to the description of a group of people eating a meal in a restaurant;
c. to the description of an experiment to investigate the perception of
i. the flavour of a piece of food or
ii. of an entire dish.
POSSIBLE ANSWER:
•
Cooking involves ingredients (world 1), flavours (world 2) and recipes
(world 3).
•
The people sitting together at the table put the food in their mouths
(world 1), experience the flavours, the feeling of being hungry or full,
the company, etc. (2), and exchange information about the food and
other topics (3).
•
i. Participants are blindfolded and given different pieces of food whose
texture is identical. They are asked to describe the taste in words
(qualitative approach) or rate the similarity of two tastes on a 7-point
scale (quantitative approach).
ii. Gourmets rate the food in a restaurant qualitatively and/or
quantitatively. Their ratings depend on the individual flavours, the
combination, the visual impression, the ambience etc.
2. Spectral analysis
a. Why does the ear separate high frequencies from low frequencies?
b. The separation is imperfect and has limits. Why?
POSSIBLE ANSWER:
•
The main function of hearing is to identify and describe sound
sources in everday environments. The sound reaching the ear is
mostly a superposition of directed and reflected sound. In this
process, phase information is completely lost and amplitude
information distorted. But provided the source and perceiver are
moving much slower than the speed of sound, the ear can always
rely on frequency information. Therefore the ear has evolved to be
sensitive to frequency and to analyse a sound into its component
frequencies.
•
According to the uncertainty principle in physics, it is impossible to
simultaneously extract both spectral and the temporal structure of a
signal with perfect accuracy. If the effective window duration is
long, the frequency information is more exact and the temporal
information is less exact. The temporal envelope of the ear has
evolved to allow both the important spectral and the important
temporal aspects of environmental sounds that are important for
humans, especially speech, to be perceived.
3. Pitch
a. Describe the perception of the pitches of a church bell using the
terminology spectral pitch and virtual pitch.
b. Explain why the bell is perceived in this way.
POSSIBLE ANSWER:
•
The spectrum of a bell sound is inharmonic, but typically some of the
partials correspond to an incomplete harmonic series. The pitch that
we tend to hear at the start of a bell sound (the strike tone)
corresponds to the fundamental of the clearest, most complete
harmonic series within the spectrum and is therefore a virtual pitch.
As we listen to the sound decay, we can sometimes hear individual
partials, whose pitches are spectral pitches.
•
The main function of hearing is to identify and describe sound
sources. In general it helps if this happens as quickly as possible.
Therefore pitch perception is geared toward holistic perception
(corresponding to the sound source) of the onset of a sound (so that
a quick decision can be made). The pitch at the start of a bell sound
is this kind of pitch. Only once the bell has been identified and
described can the listener hear the bell in a different (analytic, slow)
way that is less closely related to evolution and survival.
4. Consonance
a. Why and in what sense is a harmonic tritone of pure tones in the
middle or upper register consonant?
B. Why and in what sense is a harmonic tritone of harmonic complex
tones in the middle or upper register dissonant?
POSSIBLE ANSWER:
•
A harmonic tritone of pure tones in the middle or high register typically
spans an interval greater than a critical band (which is 2-3 semitones in
high registers). In general, such a dyad sounds completely smooth,
because there is no interference between the two tones on the basilar
membrane. The dyad is consonant in the sense that it has no roughness,
but in a musical context it may be perceived as dissonant because of
associations with musical syntax or because the harmonic function of the
interval is ambiguous.
•
The upper partials of a harmonic tritone of harmonic complex tones form
several intervals of a semitone. For example, the third harmonic of the
lower tone is one semitone away from the second harmonic of the higher
tone. These semitone intervals are perceived as rough, especially if the
amplitudes of the pure tones are similar. Therefore, the whole dyad is
perceived as rough. The dyad is dissonant in this sense. But if it is
presented in isolation it is not necessarily dissonant in the sense of
harmonic clarity or unfamiliarity.
5. Intonation
a. Give three possible reasons why the tone F# might be performed
sharp relative to Gb.
b. To what extent and in what sense does intonation depend on
enharmonic spelling?
POSSIBLE ANSWER:
•
i. F# might be performed sharp relative to Gb because the performer
wishes to communicate the expectation that it will rise to G (leading tone
effect),
ii because the performer wishes to make clear that the interval above D is
a major and not a minor third, or
iii because F# is a perfect fifth above B, which in turn is a perfect fifth
above E (summing fifths results in Pythagorean tuning and the
corresponding major third, 81:64, is bigger than the pure or just major
third, 5:4).
b. Intonation may depend on harmonic spelling if a performer is (sight-) reading
believes that sharps are sharper than enharmonically equivalent flats. If
not, the connection is indirect. Intonation is primarily determined by the
sound and not by the notation. In some cases this can lead to the above
effect, but it can sometimes lead to the reverse. For example if the tones
are long and constant, beating between upper partials may be reduced if
major thirds are tuned to just intonation (5:4). In this case, F# is 5/4 times
the frequency of D and Gb is 4/5 of the frequency of Bb. Since (5/4)3 =
125/64 < 2, three just major thirds add to less than an octave, and F#
would be flatter than Gb in this case.
Lecture 9, 7.6.06
Auditory scene analysis
Perception of counterpoint
Auditory scene analysis
How does the ear recognize and monitor sound sources?
Thought experiment (Bregman, pers. comm.)
• Lake with two boat ramps (inlets)
• Leaf floating on water in each
• Task: from his motion, identify and describe
– people and fish swimming
– boats and water skiers going past
– a stone or a feather hitting the water
• Impossible? Exactly analogous to auditory perception!
Gestalt principles in vision
• Proximity:
– grouping of nearby dots
• Similarity:
– grouping of similar dots
• Closure:
– recognition of incomplete patterns
• Good continuation:
– e.g. 2 lines crossing
Gestalt principles in music
Perceptual coherence of melody
• Proximity: small intervals in pitch and time
• Similarity: constant timbre
• Closure: hearing missing or inaudible
tones
• Good continuation: rising pattern
continues to rise
Pitch proximity in melody
After Huron
Temporal proximity
Distribution of note durations in 52 instrumental and vocal works (Huron)
Dotted line: upper and lower voices of J.S. Bach's two-part Inventions
Dashed line: 38 songs (vocal lines) by Stephen Foster.
Solid line: mean
Bin size: 100 msec. Assumed tempi: typical recordings.
Proximity in pitch and time
van Noorden, 1975
…the perceptual origin of the step-leap distinction
Competition between
Gestalt principles
• Proximity:
– small intervals in pitch and time
• Good continuation:
– rising pattern continues to rise
• Example of conflict between principles:
– elements of rising pattern not „proximate“
• reversal of direction after leap
– crossing parts
• See next slide
Part crossing
“Good continuation”
dominates
“Pitch proximity”
dominates
Foreground and background
• foreground = perceived object
– attention  foreground
• Prerequisite for perception of object:
– separation of foreground elements from
background elements
• group elements within foreground
– perhaps also within background
• separate foreground from background
Perception of melody versus
accompaniment
• grouping of foreground:
– proximity, similarity
• separation of foreground from background:
– common fate (assume non-parallel motion)
Explanation and generalization:
The auditory scene
Graph of frequency (SP) against time (3rd dim.: SPL?)
showing patterns of
• audible partials (pure-tone components)
• noise
Auditory scene analysis (ASA; Bregman)
separation of signal (= source) from noise (background) by:
• integrating (grouping) signal (grouping events)
• segregating (separating) signal from background
Grouping principles in ASA
Sequential (temporal, melodic) integration
• proximity (pitch, time, location)
• similarity (timbre, loudness)
• lack of sudden changes
Simultaneous (spectral, harmonic) integration
• simultaneity of onsets
• coherence of changes
– frequency, SPL, spectral envelope
• harmonicity
Examples (Bregman CD)
see Traube lecture
Sequential integration (melody)
Streaming and implied polyphony
1. melodic aspect
3. rhythmic aspect
Musical examples
6. Telemann Sonata in C (from Der getreue Musikmeister)
7.-9. East African Xylophone
Competition between principles
17. Part crossing (proximity versus good continuation)
Spectral integration (VP)
18. Mistuning of a harmonic partial
24. Coherent modulation of frequency
Origins of ASA principles
Interaction with physical and acoustical world
„Nature“:
phylogenesis
„Nurture“:
ontogenesis
Domains
• human communication:
• natural environment:
• artificial environment:
speech, music
animal sounds
machines
Perception of Counterpoint
• Compositional rules and conventions
– History of music theory and pedagogical
systems
– Modern “normative” harmony texts
• Dependence on perception versus style
– nature versus nurture
– universal versus culture-specific
Perception of Counterpoint
Goals (what composers want to achieve)
„True“ counterpoint requires separately perceptible melodies
•
clear voice-leading; auditory streaming
Means (compositional techniques)
• salient pitches
– harmonic complex tones, central range, legato
– within-voice coherence
– integration, fusion
• between-voice independence
– fission, segregation
“Rules” (compositional conventions)
• sometimes explicit, sometimes not
• remarkably unchanged since medieval polyphony
Perception of Counterpoint
Main source
Huron, D. (2001). Tone and voice: A derivation of the rules of
voice-leading from perceptual principles. Music
Perception, 19, 1-64.
Tone type
Compositional rule
• Prefer harmonic complex tones
Perceptual explanation
• High pitch salience
Origin
• Human voice and speech communication
Implication
• One of many culture-specific aspects
Salience of the strongest VP of a
harmonic complex tone
calculated after Terhardt et al. (1982)
Registral compass
Compositional rule
• Registral compass: F2 to G5
Perceptual explanation
• Virtual pitch salience of HCTs is maximum near 300 Hz
Origin
• Pitch range of human voice
Implication
• „middle C“ is the middle of something!
Temporal continuity
Compositional rule
• Prefer sustained, legato tones
• Gaps between staccato tones < 1 second
Perceptual explanation
• Duration of echoic memory
• Coherence of melodic stream
Implication
• Importance of legato for singing and instrument
construction
Critical bandwidth in semitones
after Moore & Glasberg 1983
PT-chord-spacing that minimizes
masking and roughness
after Huron
Chord spacing
Compositional rule
• More space between tenor and bass
Perceptual explanation
• Minimum masking  pitch salience
• Minimum roughness
• Both determined by critical bandwidth
Implication
• „active“ bass line is possible and ok
Doubling
Compositional rule
• Don’t double leading or chromatic tones
Perceptual explanations
• Avoid parallel octaves (common fate)
• Clarify tonality by reinforcing tonally stable pitches (see
later lecture on tonality)
Consonance and prevalence
of harmonic intervals
Line: sensory consonance of dyads of complex tones (Kaestner, 1909)
Bars: interval prevalence (Huron 1991) in the upper two voices
of J.S. Bach's three-part Sinfonias (BWV 787-801)
Note discrepance at P1 and P8!
Consonance
Compositional rules
• Prefer consonances to dissonances
• But also: avoid P1s and P8s (also P5s) – contradition!
– Regardless of temporal context
Perceptual explanation
• harmonicity
 more consonance: usually desirable in western music
 more fusion: not desirable in deliberately polyphonic music
Implication
• Consonant sonorities are more prevalent (also triads, tetrads…)
• Triads and sevenths should contain all pitch classes
Stepwise motion
Compositional rule
• Prefer steps to leaps
• Fewer leaps at faster tempos
• Increase duration of tones forming leaps
– Both in composition and performance
Perceptual explanation
• Proximity in pitch and time (cf. Noorden)
• „Trill threshold“ corresponds to critical bandwidth?
Similar motion
Compositional rule
• Prefer contrary to similar motion
Perceptual explanation
• Avoid fusion
Implication
• Two-part counterpoint favours thirds and sixths
Parallels
Compositional rule
• Avoid parallel octaves and fifths
Perceptual explanation
• Octaves/fifths AND parallel motion promote fusion
Part crossing
Compositional rule
• Avoid part crossing
Perceptual explanation
• Pitch proximity is stronger principle than good
continuation
Outer voices
Compositional rule
• Apply rules more strictly to outer voices
Perceptual explanation
• Pitch salience: masking from one side only
Leap resolution
Compositional rule
• Follow leap by step in opposite direction
Perceptual explanation
• Pitch proximity between non-successive tones
Onset asynchrony
Onset synchrony for 10 of Bach's 15 two-part keyboard Inventions
Non-zero phase means that one voice is shifted relative to the other
Onset synchrony
Compositional rule
• Avoid onset synchrony
Perceptual explanation
• Cue to fusion
Evidence
• Bach avoids onset synchrony in counterpoint: When
voices shifted relative to each other, onset synchrony is
a minimum at zero shift
Perception of simultaneous tones
Stimuli: sonorities of octave-comlex tones
Task: how many tones?
Source: Parncutt (1993)
Number of active voices
Voice-tracking errors while listening to polyphonic music (Huron)
Listeners: musicians; Task: How many voices do you hear?
Music: polyphonic textures with homogenous timbre
Solid columns: mean errors expert musician subjects
Shaded columns: unrecognized single-voice entries
Number of active voices
Task: how many voices do you hear?  “mean auditory streams”
Textural density
Compositional rule
• No more than three voices can be active
Perceptual explanation
• Listeners cannot count more than three simultaneous
tones or voices
Timbral differentiation
Compositional or performance rules
• A different timbre for each voice
• Vibrato only in the solo voice
• Instruments or loudspeakers at different locations
Perceptual explanation
• Stream segregation
Combinations of rules
Compositional rule
• If voice-leading weakened by violating one rule,
compensate by obeying other rules more strictly
E.g.
• Oblique or step motion to perfect consonances
• In similar motion, prefer steps to leaps
• When approaching a perfect consonance, avoid
synchrony
Textural density
Compositional rule
• Write in 3 to 6? parts
Perceptual explanation: compromise between
• Optimal roughness
• Optimal tonalness
• Maximum number of active voices
Conclusion
• Many rules have a perceptual basis
• Not necessarily universal
• Culture-specific:
– Complexity and polyphony (notation)
– Independence of voices
Lecture 10, 14.6.06
Western harmony and tonality
An analogy between:
1. Perception of harmonic complex tones
– salience and ambiguity of virtual pitches
2. Perception of musical chords
– salience and ambiguity of root
3. Perception of major-minor tonality
– salience and ambiguity of tonic
Background in music theory
• The root of a chord
– No general theory!
• desirable:
– predict the root of any chord
• a problem that theorists never solved:
– root of the minor triad
• Major-minor tonality
– Why two modes - not one or three?
– Why these scales - not others?
Musical pitch terminology
– Pitch classes or “pcs”
• Pitch in chromatic scale without specifying octave
register
• 0=C, 1=C#, 2=D…
– Pitch-class sets
•
•
•
•
CEG = 047
CEbG = 037
CEbGb = 036
CE#G# = 048
Background in music psychology:
Krumhansl’s tone profiles
6
5
4
3
2
1
0
C
C#
D
D#
E
F
F#
G G#
A
A#
B
G G#
A A#
B
Tone
7
Ratings for C Minor
Stability of
scale degrees
in major and
minor scales
Ratings for C Major
7
6
5
4
3
2
1
0
C
C# D
D#
E
F
F#
Krumhansl’s tone profiles:
Experimental method
Musical context: a well-defined major or minor key
– E.g. SDT cadence
• Probe tone
– Every degree of the chromatic scale
• How well does the tone go with the context?
– 1 = very poorly … 7 = very well
• Mean results
 the relative stability of the 12 pcs
Octave generalization:
octave-complex tone (OCT, Shepard tone)
amplitude
2
1
0
100
1000
frequency (Hz)
10000
Octave-complex tones (OCTs)
C
V
B
Z
CEG
D
A
W
E
Y
F
G
X
CWG
Origin of Krumhansl’s tone profiles
compositional
procedures
syntax,
frequency of
occurrence
perception,
expectations
Background in psychoacoustics
• Pitch of a complex tone according to Terhardt
– Pitch = Popper’s world 2 (experiential, not physical!)
– Spectral pitch SP
• Pitch of a pure tone
– Virtual pitch VP
• Pitch of a complex tone
– salience
• Perceptual importance of a pitch
• Probability of perceiving a pitch spontaneously
Pitch perception:
Terhardt’s experimental method
• a complex test tone alternates with a pure
reference tone
– The listener adjusts the frequency of the pure
tone until the two tones have the same pitch
• The salience of a pitch = the probability of
matching it
Physical and
experiential
spectra
1. pure tone
PT (C4)
2. harmonic complex
tone HCT (C4)
3. octave complex tone
OCT (C)
The harmonic series as a patternrecognition template
1
1
1
poids (1/n)
1
2
3
4
7 8
9 10
40
6
36
5
0
32
28
24
20
16
12
8
4
0
interval (semitones)
Terhardt’s virtual pitch algorithm
• Spectral analysis
 frequencies and amplitudes of pure tones (partials)
• Masking
 audibility of pure tones
• Spectral dominance region
– around 700 Hz (between the first two formants of vowels)
 salience of spectral pitches SPs
• Recognition of harmonic pitch patterns
 Virtual pitches VPs
Octave generalisation
of the harmonic template
weight
(Parncutt, 1988)
10
8
6
4
2
0
The five “root-support intervals”
P1
P5
M3
m7
M2
0
1
2
3
4
5
6
7
8
interval class (semitones)
9
10 11
Circular representation of the
harmonic template
0
11
1
P1
10
m7
2
M2
9
3
M3
8
4
P5
7
5
6
Major triad CEG = 047
notes
pitches
0
0
11
10
9
3
4
7
5
6
2
10
2
8
1
11
1
3
9
4
8
5
7
6
Minor triad CEbG = 037
notes
pitches
0
11
0
11
1
10
10
2
9
3
8
4
7
5
6
1
2
9
3
8
4
7
5
6
Diminished triad CEbGb = 036
notes
pitches
0
11
0
1
10
11
2
9
10
3
8
4
7
5
6
1
2
9
3
8
4
7
5
6
Augmented triad CE#G# = 048
notes
pitches
0
0
11
1
11
2
10
10
3
9
4
8
1
2
9
3
8
4
5
7
7
5
6
6
Matrix multiplication
notes x template = saliences
1
0
0
0
1
notes
0
0
template
1
0
0
0
0
saliences
18
0
3
3
10
6
2
10
3
7
1
0
Experimental data
(Parncutt, 1993)
Diamonds:
Mean ratings
Squares :
Theoretical
predictions
Tonal stability and pitch salience
in the tonic triad
Tonal stability and pitch salience
in the tonic triad
At the end of a phrase of tonal music:
Closure produced by last tone
= salience of that pitch within the tonic triad
Tonic of major/minor tonality is a chord
Tones of major/minor scales
= salient tones within tonic triad
(exception: leading tone)
Origins of major-minor tonality
1. Tonality in general (prehistory)
preference for:
•
clear structures
–
•
easy to remember (oral transmission)
pitch hierarchies
–
•
some pitches clearly more prevalent
clear phrases
–
more important pitches at start and end
Origins of major-minor tonality
2. The role of consonance (since 12th century)
• Tolerance for the dissonance of harmonic dyads
– later, of triads
• Preference for sonorities with
– P5/P4
clear root, clear harmonic function
– no M2/m2
less roughness
 Central role of major and minor triads
• By far the most consonant triads
– enumerate all possibilities using theory of pitch-class sets
Origins of major-minor tonality
3. Major and minor triads as tonal
references
• General preference for (tonal) homogeneity and
equilibrium:
– Conclusion of a phrase sums it up, makes it stable
– Prevalence of a scale step corresponds to its salience
within tonic triad
Lecture 11, 21.6.06
Nature versus nurture
• Nature: phylogeny, evolution
• Nurture: ontogeny, learning
• Generally difficult to separate
• In evolutionary theory inseparable
• Intermediate: universal learning
“Nature”
Physical (physiological) limitations
• Pitch range of voice ( pitch salience)
• Duration of a breath ( phrase)
• Memory capacity for pitch-time patterns
– long-term versus short-term
„Nature“
Assumption: if it promotes survival, it is probably innate
Survival value of music
• Survival of babies: bonding
• Acquisition of general cognitive skills through „play“:
– imitation, social behavior
• Social glue: shared emotions and identity
• Mateship rituals (Darwin)
Survival value of auditory frequency analysis
•
•
•
•
•
•
Identification and description of sound sources
„Reliable“ physical parameters in real environments
Auditory physiology: physics of basilar membrane etc.
Sensitivity to frequency and rhythm (best JNDs)
Critical bandwidth, roughness and masking
Dominance regions (SP near 700 Hz, VP near 300 Hz)
„Intermediate“
Universal learning:
a mixture of „nature“ & „nurture“
Intercultural behaviors and sound patterns
•
•
Timbre-object associations
Harmonic series in speech sounds
– Because periodic sounds always harmonic
– Affects process of pitch perception
•
Gesture, emotional communication
– Infant-directed speech
– Melody, melodic contour
– Musical pulse; heart and feet
•
•
Gestalt and grouping (ASA) principles
M2 intervals between successive musical tones
– Emerges from interaction between gestalt principles and singing?
•
P8 and P5 intervals between simultaneous and successive musical tones
– Due to universals of roughness and pitch commonality
 P8 and P5 between scale degrees
 intercultural emergence of pentatonicism
•
Number of simultaneously audible voices (maximum is 3)
– Presumably intercultural - but no clear psychoacoustic theory
„Nurture“
culture-specific
Physical environment
•
•
Weather, landscape, plants and animals
Technology: food, buildings, light & heat
Cultural environment
•
•
•
•
Social structures, careers…
Socially acceptable behaviors and emotions
Political structures
History of ideas; cultural status of complexity, analysis, originality, individuality, works of art
Social functions of music
•
•
•
Power: aristocracy, military, religion
Psychosocial: folk, pop, CDs, radio, religion
Concept of „music“ überhaupt
Related cultural specificities of western music
•
•
•
•
•
•
Role of consonance/dissonance
Major-minor tonality
Clarity of harmonic function of chords
Dissonance of chords in different periods
Compositional goals and rules
Specific musical styles
Example:
harmonic tritone of pure tones
• Nature:
– physical beating
– critical bandwidth
– degree of roughness
• Nurture:
– appraisal of roughness
– association with tritone of HCTs
– association with musical contexts
Example: consonance in general
• Nature:
– Degree of roughness
– Clarity of pitches
• Nurture (or interculturally learned)
– Appraisal of roughness
– Appraisal of pitch salience
– Familiarity with specific culture
Example: intonation
• Nature:
– Beating of coinciding partials (perhaps
irrelevant!)
• Nurture
– Context, musical function
– Structural-emotional clichés
Example: “absolute” perception
• Nature or interculturally learned:
– Color (depends primarily on rods and cones)
• Nurture:
– Pitch in specific scale (AP)
Example: rhythm
• Interculturally learned
– Feeling of pulse in given range
• Nurture
– Categorical perception of rhythmic patterns
Example: key profiles
Theories of origins
• Nurture:
– learned from frequency of occurrence of scale
steps in music
• Mixture of nature and nurture:
– learned from pitch salience in triads (root)
Written examination
28.6.06 at 5:30 pm, HS 06.03
•
•
•
•
Duration: 90 minutes
Questions in English, answers in German or English
Answer any 5 of 10 questions
Guideline: see „Schriftliche Prüfungen“ at http://www-gewi.unigraz.at/staff/parncutt/
• Examples of questions from previous years in the following pages
Prüfungsrichtlinie (1)
Am Anfang des Semesters
bitte im musikwissenschaftlichen Sekretariat eine Karteikarte ausfüllen
bzw. Ihre Karteikarte aktualisieren
Zur Prüfung selbst bitte folgendes mitbringen:
 mindestens 6 Blätter A4
 einen guten Kugelschreiber oder Füller (keinen Bleistift)
 einen Bildausweis (für Studierende, deren erste Studienrichtung nicht
Musikwissenschaft an der Uni Graz ist)
 ein ausgefülltes Zeugnis
Ab ca. 2 Wochen nach der Prüfung
bitte unaufgefordert zur Sprechstunde kommen und
 die Prüfungsfragen und Ihre Antworten besprechen (das
Rückgabegespräch ist eine Chance, Zusätzliches zum Thema der
LV zu lernen)
 Ihr benotetes Zeugnis dem Sekretariat weitergeben und später wieder
abholen
Prüfungsrichtlinie (2)
Die Fragen
Beantworten Sie alle 8 Fragen.
2. Wissenschaftliches
a) Lesen Sie sorgfältig die Fragen und beantworten Sie nur diese.
b) Beziehen Sie sich nicht auf Erfahrung, sondern auf wissenschaftliche Erkenntnisse.
c) Beziehen Sie sich nicht nur auf den Inhalt der Vorlesung, sondern auch auf die darin
zitierte Literatur.
d) Bewerten Sie die zitierte Literatur kritisch. Wenn nötig, bringen Sie Ihren begründeten
Zweifel zum Ausdruck.
e) Verwenden Sie Bilder und Grafiken, soweit sie direkt relevant sind.
f) Beweisen Sie Ihr Begriffsvermögen durch die Klarheit und Vollständigkeit Ihrer
Erklärungen.
3. Präsentation
a) Schreiben Sie leserlich mit Kugelschreiber (nicht Bleistift)
b) Beginnen Sie jede Frage auf einer neuen Seite.
c) Trennen und markieren Sie die Teilfragen (a), (b), (c) usw.
d) Schreiben Sie auf Englisch, Deutsch, Französisch oder Italienisch.
e) Verwenden Sie grammatikalisch vollständige Sätze und logisch gegliederte
Absätze.
Previous exam questions (1)
1. (a) What is the main function of human hearing?
(b) How is this function related to survival and evolution?
(c) How might these functions explain differences in the ear's sensitivity to frequency,
amplitude and phase relationships within complex tones?
2. In what ways might the Gestalt principle of proximity have affected the syntax of tonal,
metrical western music? Consider both (a) pitch and (b) time. In each case consider a
variety of music-syntactic and music-theoretic phenomena.
3. (a) Explain the term "just noticeable difference in frequency". How is it determined
experimentally?
(b) Explain the term "categorical perception of musical pitch". How is it investigated
experimentally?
(c) What is the relationship between (a) and (b)?
Previous exam questions (2)
4. How is critical bandwidth (a) defined and (b) measured? In each case, answer the
question both (i) physiologically and (ii) perceptually.
5. (a) What is perceptual fusion?
(b) What specific roles does perceptual fusion play in the harmonic vocabulary, voicing
and voice-leading of J. S. Bach?
(c) Explain the corresponding compositional goals.
6. The pitch of a harmonic complex tone is determined by either periodicity or harmonicity
– regardless of whether the fundamental is physically present.
(a) Explain how (i) periodicity and (ii) harmonicity might explain the pitch.
(b) Why is it so difficult to determine which of periodicity and harmonicity determines
the pitch?
7. (a) What is a neural network?
(b) How does it work?
(c) Name two different, specific music-perceptual phenomena that can be explained
in terms of neural networks, and briefly explain how the network functions in each
case (i, ii).
Previous exam questions (3)
8. A major or minor key may be characterized by a specific pattern of stability and
instability among the tones of the chromatic scale.
(a) Sketch a graph of this pattern.
(b) Explain its origin in two contrasting ways (i, ii).
9. (a) What is meant by "perceptual dimensions of timbre"?
(b) Describe the design of an experiment to find out the most important perceptual
dimensions of the timbre of typical musical tones.
(c) What are the typical results of such an experiment?
10. (a) Formulate three distinct definitions or aspects of consonance and dissonance (i, ii,
iii).
(b) Describe the corresponding psychological models (i, ii, iii).
Empfohlene Freifächer
Diese angaben sind nicht aktuell!
Psychologie
Soziologie
Einführung
04W: 602.001 Einf. in die
Fächer der Psychologie;
VO, 1st.
- Früh im Semester
- sich für Prüfung
anmelden!
- Infos im Internet
04W: 319.102 Kuzmics:
Grundbegriffe u.
Sichtweisen der
Soziologie; VO, 2st.
04S: 319.104
Angermann-Mozetic:
Geschichte d. Soziologie
I; VO, 2st.
Methoden
04W: 602.861 PichlerZalaudek:
Forschungsmethoden d.
Psychologie; VU, 2st.
04W: 319.107 Höllinger:
Einf. in die empirische
Sozialforschung I; VO 2st.
References
Bregman, A. S. (1993). Auditory scene analysis: Hearing in complex environments. In S. McAdams & E.
Bigand (Eds.), Thinking in sound: The cognitive psychology of human audition (pp. 10-36).
Burns, E. M., & Campbell, S. L. (1994). Frequency and frequency-ratio resolution by possessors of absolute
and relative pitch: Examples of categorical perception? Journal of the Acoustical Society of America, 96
(5), 2704-2719.
Houtsma, A. J. M., Rossing, T. D., & Wagenaars, W. M. (1987). Auditory Demonstrations on Compact Disc.
New York: Acoustical Society of America.
Howard, D. M., & Angus, J. (1996). Acoustics and psychoacoustics. Oxford: Focal.
Huron, D. (2001). Tone and voice: A derivation of the rules of voice-leading from perceptual principles. Music
Perception, 19, 1-64.
Krumhansl, C. L. (1990). Cognitive foundations of musical pitch. Oxford University Press.
Laden, B. (1994). A parallel learning model of musical pitch perception. Journal of New Music Research, 23,
133-144.
Levitin, D. J. (1994). Absolute memory for musical pitch: Evidence from the production of learned melodies.
Perception & Psychophysics, 56, 414-423.
Parncutt, R. (1989). Harmony: A psychoacoustical approach. Berlin: Springer.
Parncutt, R. (1993). Pitch properties of chords of octave-spaced tones. Contemporary Music Review, 9, 3550.
Parncutt, R. (in press). Psychoacoustics and music perception. In H. Bruhn, R. Kopiez, A. C. Lehmann, & R.
Oerter (Eds.), Musikpsychologie — das neue Handbuch. Reinbek, Germany: Rowohlt.
Plomp, R., & Levelt, W. J. M. (1965). Tonal consonance and critical bandwidth. Journal of the Acoustical
Society of America, 38, 548-560.
Popper, K.R., & Eccles, J.C. (1977). The self and its brain. Berlin: Springer.
Rasch, R. A., & Plomp, R. (1999). The perception of musical tones. In D. Deutsch (Ed.), Psychology of
music (2nd ed., pp. 89-111). New York: Academic.
Tenney, J. (1988). A History of 'Consonance' and 'Dissonance'. Excelsior, New York.
Terhardt, E. (1998). Akustische Kommunikation. Berlin: Springer.
Zatorre, R. J. (1988). Pitch perception of complex tones and human temporal-lobe function. Journal of the
Acoustical Society of America, 84, 566-572.
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