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Psychoacoustics and Music Perception


available in the internet and updated regularly. only a PART of the course material. ... Frank Sinatra: 'White Christmas' ('pop') Miles Davis 'So what' ('modal jazz' ... – PowerPoint PPT presentation

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Title: Psychoacoustics and Music Perception

Psychoacoustics and Music Perception
  • 509.211 VO, 2st.
  • S06, Mi 1730-1915
  • HS 06.03
  • Richard Parncutt
  • Email ((my last name))
  • 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
  • contents of folder in reading room of department
  • sound examples (including those linked to this
    document but many of these are on the CD in the
  • written in point form but exam answers must be
    complete sentences! (see Schriftliche
  • Questions and suggestions? ((familyname))_at_uni-graz

Lecture 1, 8.3.06
  • Adminstrative details
  • aims
  • dates
  • examination
  • Introduction Musical relevance of
  • 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
  • Consider some psychological issues
  • What do you hear or experience in this music?
  • Chain physics perception structure
  • Direct perception ecological psychology
  • Indirect perception cognitive psychology

Relevance for music analysis
  • Perception of pitch structures
  • harmony, voice-leading, phrasing, tonality,
  • Quality of sound
  • consonance/dissonance, timbre
  • Cognitive organisation
  • foreground, background
  • Emotional character
  • associations
  • Not considered
  • Accents dynamic, grouping, metrical, melodic,
  • Expressive timing and dynamics

Some course aims
  • Overview and understand
  • musically relevant fundamentals of
  • 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

Tentative semester plan (1)
Tentative semester plan (2)
  • 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.
    1730-1915) than to schedule two additional

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 secretarys 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
  • 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 perceptionWhy do we
experience a complex tone as one thing?
Philosophy of reality Karl Poppers three
worlds (1)
  • World 1 physical matter, energy
  • World 2 experiential sensations, emotions
  • World 3 abstract information, knowledge,
  • 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 Poppers 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 spectrum duration
  • experiential pitch loudness timbre perc.
  • abstract note dynamic instrument 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
  • 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
  • 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
  • Darwins theory of evolution
  • individual differences (mutation)
  • environment danger limited resources
  • survival successful reproduction
  • Relevance for hearing and music
  • aim survival by identifying and describing
  • 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 identify environmental objects (sound
  • Approach monitor frequency-time patterns
  • Method frequency analysis (separate

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)
f (Hz)
Center frequency
Frequency analysis by a filter bank
Harmonic complex tone
Critical bandwidth
  • Auditory filters have no sharp cut-off
  • gt 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
  • 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
  • Depends on
  • number of excited hair cells (hence bandwidth of
  • excitation of each cell (energy in each auditory
  • Repeat sound demonstration (ASA Track 7)

Critical band
SPL (dB)
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,
  • 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,
  • 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.
  • 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 fundamentalASA track 37
  • Conclusions
  • Pitch does not necessarily correspond to a
  • Pitch is multiple/ambiguous
  • VP at missing fundamental
  • SP at lowest partial

Sound demo Masking SP and VP
ASA-CD tracks 40
41 42
Sound demo Masking SP and VPConclusion
  • Westminster chimes example demonstrates that
    pitch at missing fundamental is virtual,
  • 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
  • If it were physical it would be audible

Sound demo Shift of VPASA-CD Track 39
  • Conclusion
  • VP corresponds to
  • best-fit subharmonic (or approx. fundamental) of
    all partials
  • NOT to difference in frequencies

Sound demo VP with random harmonicsACA-CD
tracks 43 44 45
  • HCTs of 3 random successive harmonics
  • harmonic numbers 2 to 6
  • (3 possibilities 234, 345, 456)
  • harmonic numbers 5 to 9
  • 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 chimeASA-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
  • 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

Pitch properties of complex tones
  • A CT generally evokes several pitches.
  • If only one is perceived at a time, the pitch is
  • If more than one can be perceived at a time, the
    pitch is multiple.
  • The pitches of a CT vary in salience, i.e.
  • 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)
Terhardts 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

Terhardts 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
  • 2. recognition of harmonic pitch patterns ? VPs
    and saliences
  • Salience depends on
  • fit between harmonic template and spectrum
  • number and accuracy of matches
  • salience of matching SPs
  • 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
  • experiential spectrum contains both
  • relative weighting depends on analyic/holistic

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
Spectral dominanceTerhardt 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

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, 3.5.06Consonance 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 exampleTerhardt CD track 8
  • harmonic interval of two pure tones

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 lt fb lt 300 Hz
  • e.g. semitone at 300 Hz, 300320 ? 20 Hz
  • e.g. semitone at 600 Hz, 600640 ? 40 Hz
  • Two HCTs many contributions to roughness
  • fb lt 20 Hz individually audible beats
  • e.g. mistuned piano strings
  • most prominent near 4 Hz (cf. speech)
  • fb gt 300 Hz no roughess
  • Isolated HCTs above 300 Hz no roughness

Roughness of a harmonic interval of pure tones
Source Campbell Greated (1987). The musicians
guide to acoustics (p.58). New York Schirmer.
Roughness depends on overlap between excitation
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 11.414) Tone 1
1000 2000 3000
4000 5000 6000 7000 Tone 2
1414 2828
4242 5656
7070 Frequency ratios between almost coincident
harmonics 1.06
1.01 (1.06 corresponds to one semitone)
Roughness of a harmonic interval of HCTs
  • Predictions according to Plomp Levelt

Frequency ratios of intervalsWhich one is the
right one?
interval note chr. pure ratio
Pythagorean P1 C 0
11 11 m2 C 1 1615
256243 M2 D 2 98
98 m3 D 3 65
3227 M3 E 4 54
8164 P4 F 5 43
43 TT F 6 4532
729512 P5 G 7 32
32 m6 G 8 85
12881 M6 A 9
53 2716 m7 A 10
95 169 M7 B
11 158 243128 P8 C
12 21 21
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
  • audible difference between P8 M7/m9, P5
    TT/m6, P4 TT/M3
  • Limitations on accuracy of intonation in vocal
  • 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
  • F C G D A ? F C G D A E B
  • These P5/P4s are not very exact! ( 20-50 cents?)
  • Chromatic scale
  • add m2, M3 or P4 to diatonic tones, e.g. F/Gb
  • 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).

  • 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

Tenneys Consonance-Dissonance Concepts
Consonance-dissonance of sonorities in western
  • 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, 10.5.06Categorical 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
  • nurture formant frequencies of /a/ are learned
    from speech (? culture-specific)

Categorical perception and the three worlds of
  • 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 Mus
icians Question Which of 24 categories
(quarter tones)?
Results(Burns Campbell, 1994)
  • All intervals on a continuous scale are
  • Familiar categories are
  • broader
  • more often selected
  • Category centres
  • familiar tuning (equal temperament)
  • Category width
  • distance between familiar categories

Another psychological definition of categorical
  • Heightened discrimination near category boundary
  • Just noticeable difference (JND) is smaller at
  • E.g. frequency JND of successive pure tones,
    central range 110 cents
  • This definition
  • Does not necessarily hold for musical categories
  • Is not assumed here

Categorical pitch perception versus intonation
  • Hard to distinguish empirically. Whats 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
  • 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
  • ? 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
  • 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
  • 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
  • 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,
  • AP involves both long-term memory and labeling
  • Only musicians can apply musical pitch labels
  • AP is acquired in a critical period (like
  • provided there is sound-label relation and
  • 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
  • defined by chromatic scale, accuracy 50-100
  • Properties
  • weak correlation with other musical or perceptual
  • many have it to some extent (also non-musicians)

Musical rhythm as categorical perception
  • Examples
  • swing ratio 21 vs dotted rhythm 31
  • triplet 111 vs 112
  • Each category has
  • a range of possible realisations (rubato)
  • that depends on context
  • triple meter makes 111 more likely
  • duple meter makes 112 more likely

Pitch-rhythm analogy
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

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
  • 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
  • Duple and triple rhythms, or time ratios of 12
    and 13
  • 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
  • rhythm 21 and 31 ratios (pulse)
  • Leads to
  • simple scales (pentatonic or diatonic) and

Evolutionary theory
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, 17.5.06Test
  • 5 questions _at_ 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 dont 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.

Philosophy of perceptiona. Apply Poppers
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.
  • 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

2. Spectral analysisa. Why does the ear separate
high frequencies from low frequencies?b. The
separation is imperfect and has limits. Why?
  • 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
  • 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

3. Pitcha. 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.
  • 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. Consonancea. 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?
  • 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?
  • 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
  • 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, 8164, is bigger than
    the pure or just major third, 54).
  • 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 (54). 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 lt 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
  • 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

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

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 timevan Noorden, 1975
the perceptual origin of the step-leap
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
  • 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 generalizationThe auditory scene
  • Graph of frequency (SP) against time (3rd dim.
  • 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
  • 7.-9. East African Xylophone
  • Competition between principles
  • 17. Part crossing (proximity versus good
  • 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 speech, music
  • natural environment animal sounds
  • artificial environment 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 tonecalculated after Terhardt et al.
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 lt 1 second
  • Perceptual explanation
  • Duration of echoic memory
  • Coherence of melodic stream
  • Implication
  • Importance of legato for singing and instrument

Critical bandwidth in semitonesafter Moore
Glasberg 1983
PT-chord-spacing that minimizes masking and
roughnessafter 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

  • Compositional rule
  • Dont 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!
  • Compositional rules
  • Prefer consonances to dissonances
  • But also avoid P1s and P8s (also P5s)
  • Regardless of temporal context
  • Perceptual explanation
  • harmonicity
  • ? more consonance usually desirable in western
  • ? more fusion not desirable in deliberately
    polyphonic music
  • Implication
  • Consonant sonorities are more prevalent (also
    triads, tetrads)
  • Triads and sevenths should contain all pitch

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

Similar motion
  • Compositional rule
  • Prefer contrary to similar motion
  • Perceptual explanation
  • Avoid fusion
  • Implication
  • Two-part counterpoint favours thirds and sixths

  • 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

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
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
  • 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

Textural density
  • Compositional rule
  • Write in 3 to 6? parts
  • Perceptual explanation compromise between
  • Optimal roughness
  • Optimal tonalness
  • Maximum number of active voices

  • Many rules have a perceptual basis
  • Not necessarily universal
  • Culture-specific
  • Complexity and polyphony (notation)
  • Independence of voices

Lecture 10, 14.6.06Western 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
  • 0C, 1C, 2D
  • Pitch-class sets
  • CEG 047
  • CEbG 037
  • CEbGb 036
  • CEG 048

Background in music psychology Krumhansls tone
Stability of scale degrees in major and minor
Krumhansls tone profilesExperimental method
  • Musical context a well-defined major or minor
  • 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 generalizationoctave-complex tone (OCT,
Shepard tone)
Octave-complex tones (OCTs)
Origin of Krumhansls tone profiles
Background in psychoacoustics
  • Pitch of a complex tone according to Terhardt
  • Pitch Poppers world 2 (experiential, not
  • 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 Terhardts 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
tonePT (C4)2. harmonic complex tone HCT
(C4)3. octave complex tone OCT (C)
The harmonic series as a pattern-recognition
Terhardts virtual pitch algorithm
  • Spectral analysis
  • ? frequencies and amplitudes of pure tones
  • Masking
  • ? audibility of pure tones
  • Spectral dominance region
  • around 700 Hz (between the first two formants of
  • ? salience of spectral pitches SPs
  • Recognition of harmonic pitch patterns
  • ? Virtual pitches VPs

Octave generalisation of the harmonic
template(Parncutt, 1988)
The five root-support intervals
Circular representation of the harmonic template
Major triad CEG 047 notes
Minor triad CEbG 037 notes
Diminished triad CEbGb 036 notes
Augmented triad CEG 048notes
Matrix multiplicationnotes x template saliences
notes 1 0 0 0 1 0 0
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
Tonal stability and pitch salience in the tonic
Tonal stability and pitch salience in the tonic
  • 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