Psychology of Music

Overview

• Psychoacoustics: from physics to percept

• Pitch

• Timbre

• Harmony

– Consonance / dissonance

Components of Music

• Tone• Loudness• Note value• Timbre

Perceptual Acoustic Musical

• Pitch• Loudness• Duration• Timbre

• Frequency• Amplitude• Timing• Overtones

Loudness

• related to amplitude of sound pressure variation

• measured as dB

• loudness is logarithm of amplitude

• loudness depends on frequency also

Duration

• how long or short tones are

• measured in msec

or

• measured by note values (whole, quarter, half notes)

note value indicates number of beats, measured in beats per

minute (bpm)

example: 60 bpm -> quarter note is 1 second

Pitch

• How “high” or “low” tones are

• Related to frequency

- modulation of air pressure (eg. by a string)

- measured as cycles per second (Hz)

human hearing: 20 - 20,000 Hz

piano: 30 - 4,000 Hz

• Perceived pitch is roughly logarithm of frequency – equal

ratios are equal steps (12-tone scale)

Frequency vs. Pitch• A frequency consists of one sine wave, and is

measured by the number of cycles per second(Hz)

• A musical pitch consists of more than onefrequency. The lowest frequency is thefundamental frequency, and (usually) the pitch

Pure vs. Complex Tones

• A pure tone consists of one frequency (e.g.,a sine wave)

• A complex tone consists of more than onefrequency. It may have a discernable pitch(e.g., a piano sound), or it may not (acymbal crash)

Periodic vs. Aperiodic Sounds

• Periodic sounds are those that have a clearpitch, such as most musical sounds, speech,some animal sounds (e.g., bird calls), andcertain environmental sounds (e.g., carhorns, sirens)

• Aperiodic sounds are complex waves thatdon’t have a clear pitch (e.g., some drumsounds, white noise, engine sounds, fans)

What makes a sound periodic?

• Periodicity refers to the relationshipbetween the partials (the higher frequenciesof a complex wave), and whether thefrequencies are divisible by a commondenominator (the fundamental frequency)

• Aperiodic sounds are made up of soundwaves that do not occur at integer multiplesof the fundamental

Examples• Periodic sound:

– 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, etc.

• Aperiodic sound:– 100 Hz, 160 Hz, 350 Hz, 415 Hz, 570 Hz, etc.

Perceiving Pitch• In order to perceive pitch, a tone burst must be

sufficiently long enough for phase to be computed– Tones that are several tens of cycles long sound like clear,

short musical tones– Tone bursts only 2 to 4 cycles long sound like clicks with

no clear musical pitch• The number of cycles taken in producing a clear

sensation of pitch could be the number of cyclesnecessary to establish a steady pattern of vibrationalong the basilar membrane

PITCH“THAT ATTRIBUTE OF AUDITORY SENSATION IN TERMSOF WHICH SOUNDS MAY BE ORDERED ON A SCALEEXTENDING FROM LOW TO HIGH.” (ANSI)

THE BASIC UNIT IN MOST MUSICAL SCALES IS THEOCTAVE. IN MUSIC THE OCTAVE IS DIVIDED INDIFFERENT WAYS. (IN WESTERN MUSIC IT ISGENERALLY DIVIDED INTO 12 SEMITONES)

PYTHAGORAS DISCOVERS THE OCTAVE (ca. 600 B.C.)

PITCH STANDARDS

•EARLY ORGANS HAD A’s

TUNED FROM 374 TO 567 Hz

•HANDEL’S TUNING FORK

VIBRATED AT 422.5 Hz

•1859: A 435 Hz ADOPTED BY

FRENCH GOVERNMENT

•C 256 (POWERS OF TWO)

WHICH RESULTS IN A 431 Hz

•1939: A 440 Hz INTERNATIONAL

STANDARD ADOPTED

Pitch – Perceptual Phenomena

Octave equivalence – a note doubled in frequency soundssimilar to the original

• cross-cultural (cross-species?)

• perceptual quality is “chroma”

• pitch = “chroma” + “height”

Octave Equivalence• Idea that tones separated by octave are musically identical

– common to all musical cultures

• Might be expected to have unique physiological properties

• However, perception of octave equivalence does not seemto be inherent to pitch perception

• Rats, human infants, and musicians show octaveequivalence, but starlings, and nonmusicians do not

Acoustical and Physiological Basesfor Octave Equivalence

• For two pitches an octave apart, all of the partials of the higherpitch will coincide exactly with the even partials of the lowerpitch, which is a unique quality among musical intervals, andis related to the theory of musical consonance

• Musical consonance is thought to reflect the relatedness of thepartials shared by two tones, which tones sharing more partialsbeing perceived as more consonant. The octave is consideredto be the most consonant musical interval

“SHEPARD’S ILLUSION”

TIMBRE(A MULTIDIMENSIONAL ATTRIBUTE OF SOUND)

DEFINITION (ANSI): “Timbre is that attribute of auditorysensation in terms of which a listener can judge twosounds…having the same loudness and pitch as dissimilar.”

PROPOSED TIMBRE SCALES

Dull______|______BrilliantCold______|______WarmPure______|______Rich

(Pratt and Doak, 1976)

Dull______|______Sharp Compact______|______Scattered Full______|______Empty Colorful______|______Colorless

(von Bismark, 1974)

Spectra

• The spectrum of a sound is a graphicalrepresentation of the frequencies that comprise asound and their respective amplitudes

• Fourier analysis is one way of computing aspectrum

• The spectrum of a sound is the primarydeterminant of a sound’s timbre

Trumpet Tone

FOURIERSYNTHESIS

SPECTRAL(FOURIER)ANALYSIS

Timbre

• what differentiates a note of the same pitch andloudness played on two different instruments

• “color”, “depth”, “sound quality”

example: saxophone sounds different than a trumpet

• related to purity vs. complexity of tones fundamental & overtones (harmonics, partials)

• fundamental frequency is perceived pitch, even if fundamental is missing!

Missing fundamental illusion

Timbre: ASDR Envelope

Harmonic Fusing and Common Fate

• The brain is able to assimilate various frequencycomponents into one perception of a pitched tone

• The Gestalt law of common fate offers areasonable explanation for this perceptualgrouping– The harmonics are all present at the same time, and

begin, shift, and end at the same time

Computing Pitch through Periodicity

• The brain makes use of the harmonic partialseries of periodic tones to compute pitch

• The harmonics above the fundamentalfrequency are crucial for computing pitch, andare more important than the fundamental

• The fundamental doesn’t even need to bepresent in a periodic sound for the brain tocalculate the pitch

The Missing Fundamental• Since the brain calculates the lowest

common denominator between a group ofpartials, the fundamental frequency doesn’teven need to be present for the brain toperceive this frequency– 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz will

sound the same as a sound consisting of 200Hz, 300 Hz, 400 Hz, 500 Hz, because thebrain fills in the missing fundamental

Virtual pitch in animals• The phenomenon of the missing fundamental is also known as

“virtual pitch” and “periodicity pitch”, and has beendemonstrated in animals as well as humans

• Cats were trained on a shock avoidance task with 2 stimulimissing their fundamentals

• When tested with the fundamental, the cats showed a highdegree of transfer to the fundamental

Pitch relationships in music

Harmonythe pitch relationships between tones played at the same time• harmonic interval (2 notes)• chord (3 or more notes)• triad (3 notes separated by a specific interval)

Melodythe relationship between tones played one after the other

Consonance & dissonancescale - a set of tones that fit into an octave

example: modern 12-tone scaleexample: 9-tone scale

interval - distances between pairs of tones in a scaleexample: 3rd, 5th, etc.

Consonance and Dissonance

• The simultaneous sounding of several tones may bepleasant or euphonious to various degrees. The pleasantsound is called consonant; the unpleasant or rough onedissonant

• Sensory consonance and dissonance are distinguishablefrom musical consonance/ dissonance (though musicalconsonance does have its root in perceptual consonance)

Perceptual Consonance

• The perceptual consonance of two simple tones dependsdirectly on the frequency difference between the tones, noton the frequency ratio (or musical interval)

• If the frequency separation is very small (less than asemitone) or larger than critical bandwidth, the two tonestogether sound consonant. In the first case, the tones fuseto a single one, in the second case, the tones do notinterfere with each other

Perceptual Dissonance• Dissonance occurs if the frequency separation is less than a

critical bandwidth• The most dissonant interval arises with a separation of about ¼

critical bandwidth (in higher frequencies, this is a little lessthan a semitone)

• Usually a separation of a minor 3rd will sound consonant,unless the frequencies are very low, since the criticalbandwidth for low frequencies may be greater than a minor3rd

Musical Dissonance• The concept of musical dissonance is based on

perceptual dissonance, but also incorporatesrelationships between the harmonic partialseries of two notes

• For instance, intervals under a minor 3rd aredissonant, as are their musical inverses (minorand major 7th)

• Additionally, the diminshed 5th is highlydissonant

What determines consonance-dissonance?(consonant pitch interval)(dissonant pitch interval)

Pythagorean theory - integer ratios of frequency• simpler ratios are more consonantbut,• small deviations from ratios don’t matter• different intervals considered consonant at different times in history

Helmholtz theory - consonant if tones share harmonics• doesn’t explain how pure tones can be consonant or dissonant (no harmonics)

Musical conventions & aesthetics