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:• 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 literaturePractice 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 Guest professor Caroline Traube (Université de Montréal)

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 21.6 Nature versus nurtureOverview

12 28.6 Written examination (100% of final grade)

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 perceptionWhy 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 physical matter, energy

World 2 experiential sensations, emotions

World 3 abstract 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 spectrum duration• experiential: pitch loudness timbre perc.

duration• 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 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: identify environmental objects (sound sources)• Approach: monitor frequency-time patterns (contours)• Method: 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

Center frequency

bandwidth

f (Hz)

A (dB)

Frequency analysis by a filter bank

signal

1st harmonic

2nd harmonic

3rd harmonic

bank of bandpass filters

Harmonic complex tone

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 ERBBark: 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

LoudnessDepends 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)

SP

L (

dB)

Frequency (Hz)1000 Hz

50 Hz100 Hz

150 Hz

200 HzPhysical bandwidth

Critical band

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)

LiteratureParncutt, 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 fundamentalASA track 37

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Conclusions:

• Pitch does not necessarily correspond to a partial

• Pitch is multiple/ambiguous• VP at missing fundamental• SP at lowest partial

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Sound demo: Masking SP and VP

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Sound demo: Masking SP and VPConclusion

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

Conclusion:VP corresponds to:• best-fit subharmonic (or

approx. fundamental) of all partials

• NOT to difference in frequencies

Demo no.

SP1 (Hz)

SP2 (Hz)

SP3 (Hz)

VP (Hz)

1 800 1000 1200 200

2 850 1050 1250 210

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Sound demo: VP with random harmonicsACA-CD tracks 43 44 45

HCTs of 3 random successive harmonics1. harmonic numbers 2 to 6

(3 possibilities: 234, 345, 456)2. harmonic numbers 5 to 93. 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 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 – 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 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

log frequency (Hz)100 1000 10000

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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 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, 3.5.06Consonance 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

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 tonesPlomp & 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 : 1000 2000 3000 4000 5000 6000 7000

Tone 2 : 1414 2828 4242 5656 7070

Frequency ratios between almost coincident harmonics : 1.06 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 1:1 1:1

m2 C# 1 16:15 256:243

M2 D 2 9:8 9:8

m3 D# 3 6:5 32:27

M3 E 4 5:4 81:64

P4 F 5 4:3 4:3

TT F# 6 45:32 729:512

P5 G 7 3:2 3:2

m6 G# 8 8:5 128:81

M6 A 9 5:3 27:16

m7 A# 10 9:5 16:9

M7 B 11 15:8 243:128

P8 C 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

• 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 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

historical period

possible perceptual account

CDC-1 melodic affinity before polyphony

pitches in common

CDC-2 sonority of isolated dyads

early polyphony

roughness or pitch salience?

CDC-3 clarity of lower voice

14th C. 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

Consonance-dissonance of sonorities in western music

Three perceptual factors:1. roughness

peripheral origin

2. clarity of harmonic functioncentral origin

3. familiaritydepends 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 … 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 perceptionlabel in World 3meaning

Intonationpitch in World 2experience

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 qualityalso 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 easilybecause 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 labelingOnly 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• notationto 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 necessaryamount 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 musicObservation: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 theorybiology (Darwin) music

diversity Each individual is (genetically) unique

variation and improvisation many different melodic fragments

constraint limited resources (e.g. food)

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, 17.5.06Test

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 perceptiona. 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 analysisa. 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. 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.

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. 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?

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 timevan 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 ASASequential (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 aspect3. rhythmic aspect

Musical examples 6. Telemann Sonata in C (from Der getreue Musikmeister)7.-9. East African Xylophone

Competition between principles17. Part crossing (proximity versus good continuation)

Spectral integration (VP)18. Mistuning of a harmonic partial24. 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 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 semitonesafter 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!

ConsonanceCompositional 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 InventionsNon-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 tonesTask: 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 timbreSolid 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, 14.6.06Western 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• 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

0

1

2

3

4

5

6

7

C C# D D# E F F# G G# A A# B

Tone

Ra

tin

gs

fo

r C

Ma

jor

0

1

2

3

4

5

6

7

C C# D D# E F F# G G# A A# B

Tone

Ra

tin

gs

fo

r C

Min

or

Stability of scale degreesin major and minor scales

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)

frequency (Hz)

100 1000 10000

ampl

itude

0

1

2

Octave-complex tones (OCTs)

V

W

X

Z

Y

C

D

E

FG

A

B

CEG CWG

Origin of Krumhansl’s tone profiles

syntax, frequency of occurrence

perception, expectations

compositionalprocedures

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 tonePT (C4)

2. harmonic complex tone HCT (C4)

3. octave complex tone OCT (C)

The harmonic series as a pattern-recognition template

0

1

0 4 8 12

16

20

24

28

32

36

40

interval (semitones)

po

ids

(1

/n)

11

1

2

34

5 6 7 8 109

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

(Parncutt, 1988)

0

24

68

10

0 1 2 3 4 5 6 7 8 9 10 11

interval class (semitones)

we

igh

t

P5

M3

M2m7

P1 The five “root-support intervals”

Circular representation of the harmonic template

0

1

2

3

4

5

6

7

8

9

10

11

M2

M3

P5

m7

P1

Major triad CEG = 047

notes pitches

0

1

2

3

4

5

6

7

8

9

10

11

0

1

2

3

4

5

6

7

8

9

10

11

Minor triad CEbG = 037 notes pitches

0

1

2

3

4

5

6

7

8

9

10

11

0

1

2

3

4

5

6

7

8

9

10

11

Diminished triad CEbGb = 036 notes pitches

0

1

2

3

4

5

6

7

8

9

10

11

0

1

2

3

4

5

6

7

8

9

10

11

Augmented triad CE#G# = 048

notes pitches

0

1

2

3

4

5

6

7

8

9

10

11

0

1

2

3

4

5

6

7

8

9

10

11

Matrix multiplicationnotes x template = saliences

notes 1 0 0 0 1 0 0 1 0 0 0 0

saliences18033

1062

103710

template

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, 21.6.06Nature 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.uni-graz.at/staff/parncutt/• Examples of questions from previous years in the following pages

Prüfungsrichtlinie (1)Am Anfang des Semestersbitte im musikwissenschaftlichen Sekretariat eine Karteikarte ausfüllen

bzw. Ihre Karteikarte aktualisierenZur 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 ZeugnisAb ca. 2 Wochen nach der Prüfungbitte 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 FragenBeantworten Sie alle 8 Fragen.2. Wissenschaftlichesa) 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

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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).

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ReferencesBregman, 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, 35-

50. 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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