172A. Cognitive Psychology of Music
(Introduction) |
|
Kendall & Carterette's model of musical communication (reader, page 10
7, Figure 1) links all frames of reference - outlined in the week 1 notes - and suggests that:
172A. Cognitive Psychology of Music (Introduction)
Undergraduate, non-major course
Week 2
Summary of lectures
Kendall & Carterette's model of musical communication (reader, page 10
| Understanding music involves
interpretive translation across frames of reference, with music arising as the result of
interaction (at some level) between composer, performer, and listener. Music is a form of communication that is possible only when the
parties involved share some common explicit (verbalizable) and implicit (non-verbalizable)
knowledge (more about implicit and explicit knowledge later.) This is
what makes the answers we infer, when we observe a behavior, meaningful. Composer: imagination - ideation - structuring  musical score: notational frame of reference (however, not all ideas can be put on paper in the form of notation.)Performer: musical score - interpretation - performance skills - structuring acoustical waves: vibrational/acoustical
frame of reference.Listener: (acoustical waves - physiology of the ear sounds: biological frame of reference)
+ (sounds - imagination - interpretation - structuring music: perceptual/cognitive frame of reference). |
|
Figure 1: A model of musical communication. C: composer, P: performer, L: listener. |
Although a message always implies an
intent, what is communicated can and often is different from that intent, especially in
the case of music with its a-referential (or better self-referential) potential.
Shared knowledge facilitates communication. At the same time, the fact that there is also
un-shared knowledge explains partly why there is no isomorphic relationship between the composer's intended message
and the listener's constructed message. The term 'constructed message' implies that listeners are not
passive observers being effected by music. "Listening music" means
"configuring music". The act of listening involves a configuring operation that
turns a series of abstract incoming sounds into "meaningful" patterns,
relationships, temporal wholes.
I.e.: a) "Rout" (an aria-like vocal piece with lyrics made out of
non-sensical word-like vocal sounds) and b) "A Color Symphony" (with four
movements named after colors), both by Sir Arthur Bliss (20th century British composer;
died in 1975.)
As opposed to the above model Seashore (1938) believes that music is located in the acoustical wave ( :"..everything that a singer or player of music conveys to the listener is conveyed through sound waves." Reader p.93, Seashore p. 13.)
Psychophysics / Music Psychology
Seashore's
approach is an example of Cartesian thought. He focuses on the "objective"
external world and engages in the science of"Psychophysics" (Psycho-:
mind, internal world; -physics: external world).
The term originates in the work of Weber
(1834) who linked the physical and perceptual
frames of reference by mapping physical
magnitudes to perceptual (sensory/psychic) magnitudes.
In this mapping, it was clear from the very
beginning that physical and perceptual worlds are measurable with different degrees of
accuracy. Perception connects to the 'external world' with considerably less precision
than physics do.
The
terms JND (just
noticeable difference) and Difference Threshold both refer to the smallest perceivable change of a physical variable.
The term Absolute Threshold
refers to the limits in the values of a physical variable beyond which the variable looses
its perceptual identity.
Psychology of music, as a discipline, has its origin in psychophysics. It was
delimited in mid 19th century with the works of German physicists, mainly:
a) Fechner ("Elements of Psychophysics", 1860) who codified the
idea of mapping physical and perceptual variables. Fechner's
"Psychophysical Law" states that
perception relates logarithmically to the physical world. That is, multiplication in
physical variables correspond to addition in the relevant perceptual variables.
b)Helmholtz ("On the Sensation of Tone, as a Physiological basis for a
Theory of Music", 1862) who can probably be seen as the last Homo Universalis
(he produced seminal works in diverse areas spanning a large portion of what we call
science.)
These works influenced the American school of Psycho-acousticians such as Carl Seashore
("Psychology of music", 1938) and others.
S. S. Stevens (1940's)
attempted to answer objections against Cartesian claims that everything is measurable
(including feelings) by introducing the idea that measurement is possible on all of the
following categories of variables:
a) Nominal variables, outlining categories without specifying any specific order (i.e. a group of musical instruments.)
b) Ordinal variables, outlining categories organized into a specific hierarchical order (i.e. management hierarchy in a company.)
c) Intervals, describing variables that can be measured on a continuum outlined by arbitrary boundaries / reference points (i.e. 0 degrees in a temperature scale, the origin of some coordinate system, the beginning of a calendar, etc.)
d) Ratios, describing variables that are also measured on a continuum but which are outlined by absolute boundaries and permit multiplication and division (i.e. most mathematical and many physical concepts, economic models, etc.)
Regarding music, Seashore's main belief was that there is an isomorphic mapping between the physical and perceptual attributes of sound and, consequently, that everything about music can be described in terms of the physical attributes of sound.
Physical attributes of acoustical waves
Vibration: A back and forth motion around a point of rest.
Simple Harmonic Motion: A vibration that can be described graphically by a sine curve (look at figures 1, 2, below). i.e The motion of a pendulum.
Complex vibration/motion: A vibration that is described graphically by a complex curve. All such vibrations can be seen as the result of the combination of more-than-one simple harmonic motions. Therefore, the curves (signals) that describe them are essentially the sum of an appropriate number of sine curves.
Wave: Transfer of a vibration across a medium (air, string, etc.).
Simple/pure Wave: Transfer of a simple harmonic motion across a medium (i.e. air, etc.).
Complex Wave: Transfer of complex vibration/motion across a medium.
(Acoustical) Signal: A 2-dimensional graphic representation of a vibration/wave, plotting displacement (: distance from the point of rest), or a number of other variables such as velocity, pressure, etc. (y axis), over time (x axis). It shows how those variables change with time. Signals are also referred to as waveforms. A signal representing a simple/pure wave is called sine signal. A signal representing a complex wave is called complex signal. (See Figure 4.)
Periodic vibration/wave: A vibration/wave that repeats itself at regular time intervals.
Periodicity/regularity are attributes with specific significance. Regularity encourages prediction.
Period: The time it takes for a single full vibration/wave or cycle (represented on x axis).
Frequency: Number of repetitions per unit time: number of cycles per second. It is measured in Hertz (Hz). So, 1 Hz = 1 cycle per second.
Amplitude: Maximum displacement (velocity, pressure, etc.) from point of rest (represented on y axis).
Intensity: An expression essentially of the amount of energy in a vibrational system. It is related to amplitude and is measured in Watts/m2.
Resonance: Phenomenon occurring when the frequency of vibration of one system matches the natural frequency of a second system. ('natural' meaning the frequency with which a system would vibrate if energy was supplied to it and then it was left on its own.). When resonance occurs, maximum amount of energy will be transferred from the first system to the second.Fourier's mathematical law (early 19th cent.) states that all complex signals can be reduced to the sum of sine signals with appropriate frequencies and amplitudes. Those sine signals are referred to as the Fourier/sine components or partials of a complex signal. The component/partial of a periodic complex signal with the lowest frequency value is known as the fundamental. For periodic complex signals (that have a rather definite pitch) the frequencies of all other components/partials (in this case also called harmonics) are integer multiples of the fundamental frequency; that is if the fundamental has frequency ƒ, then the partials occur at the frequencies 1ƒ, 2ƒ, 3ƒ, 4ƒ,..etc. For non-periodic complex signals, (that have a rather indefinite pitch) the frequencies of all other components/partials are not integer multiples of the lowest frequency.
Spectrum: A graphic representation of a complex signal indicating the frequency and amplitude of its components. This is the only variable in the Seashore model that is multidimensional (it is defined as the combination/interaction of 2 other variables: frequency & intensity.)
The signal in Figure 1, with its regular, sinusoidal peaks and valleys, represents a pure wave -in this case one corresponding in frequency to the note A above middle C on the piano. The peaks of the signal are separated regularly at intervals of 2.27 milliseconds, or 1/440th of a second. So the Period of the signal is 1/440th of a second. This means that the signal (and the wave it represents) repeats itself 440 times per second. We say that this wave has a Frequency, or rate of repetition, of 440 Hertz. The Amplitude of the signal is represented as the distance between the top (or bottom) peak and the central horizontal line (representing the point of rest).
Figure 2: Signal of the first 2 periods of a vibration with frequency: 440Hz and amplitude: 1
The signal in Figure 2,below, represents a pure wave -corresponding in frequency to the note A below middle C on the piano. This signal repeats more slowly than the previous one; its frequency is 220 Hz, or 220 cycles per second. Although the vibration it represents would travel to our ear about as quickly as the one represented in Figure 1, it would cause the air to vibrate at a rate half as fast.
Figure 3: Signal of the first period of a vibration with frequency: 220Hz and amplitude: 1. (perceived as a pure tone -look below for definition- with "lower" pitch than the one in Figure 1)
Figure 4: Example of synthesis of a complex signal out of two sine components with frequencies f1 = 250Hz and f2 = 500Hz.(first graph). The pitch of the complex signal (second graph) matches in frequency the fundamental component (250Hz).
The last graph is the spectrum of the complex signal.
(These graphs are for illustration purposes. You will not have to make any calculations)
Perceptual attributes of sound
Sound: The aural sensation stimulated when energy from a vibrational system travels in the form of a wave and reaches the ear.
Simple/Pure tone: The sound that results from a simple harmonic motion (simple/pure wave) and is represented by a sine signal. i.e. sound of a tuning fork.
Complex tone: The sound that results from a complex motion (complex wave: wave made up from the combination of more than one simple/pure waves) and is represented by a complex signal. i.e. sound of a violin.
Ohm's law uses Fourier's theorem and states that the ear acts as a frequency analyzer, breaking down complex tones to its sine components. For periodic (harmonic) complex signals the perceived complex tone has a pitch that matches in frequency the fundamental.
Pitch: Perceptual attribute of sound related mainly to frequency. Large frequency values result in 'high' pitch while low frequency values result in 'low' pitch. The frequency range of hearing extends from 20Hz to 20.000Hz (20KHz). Frequencies below 20Hz sound as individual pulses with no definite pitch. Frequencies above 20KHz are inaudible by humans.
JND for Pitch: approx. 1% of frequency.(for pure tones and middle frequencies). According to the American Standards definition of pitch, pitch A corresponds to frequency of 440Hz.
For simple/pure tones, the pitch relates to the frequency of the simple/pure/sine waves.
For periodic complex tones, (resulting from periodic complex waves: waves made up from the combination of more than one simple/pure/sine waves) the pitch relates (in general) to the frequency of the sine component with the lowest frequency value. All other components have frequencies that are integer multiples of this value.
Loudness: Perceptual attribute of sound related mainly to intensity. Large intensity values result in 'loud' sounds while low intensity values result in 'soft' sounds.
The perception of intensity is related logarithmically to the physical magnitude of intensity. The logarithmic unit is 1 decibel.
If intensity is I in w/m2 then it is 10*log10 I/10-12 in dB.
The intensity range of (functional and safe) hearing extends from 10-12w/m2 or 0dB to 1w/m2 or 120dB. Sounds with Intensity levels below 0dB are inaudible while sounds with intensity levels above 120dB are damaging to the ear.
JND for loudness: approx. 1dB (for pure tones, middle frequencies and 'regular' background noise)
Notice that 10dB increase in sound intensity level represents 10 times increase in energy, 20dB represents 100 times increase in energy and so on.
The loudness unit is called Phon. We do not use dBs because intensity and loudness do not map isomorphically. Loudness depends also on frequency as well as intensity.
Timbre: Perceptual attribute of sound related mainly to the spectral composition (relative amplitude of the individual frequency components) of a complex wave.
Two sounds of the same pitch and loudness may have recognizably different qualities: for instance the sounds of string instruments vs.\ reed instruments in the orchestra. These distinguishing qualities of sound are called timbre.
Further reading on the relationship between physical and perceptual attributes of sound
Campbell, M. and Greated, C. (1987). The Musician's Guide to Acoustics. New York: Shirmer Books.
Deutsch, D. ed. (1999). The Psychology of Music. San Diego: Academic Press.
Moore, B. C. J. (ed.) (1995). Hearing. In the series "Handbook of Perception and Cognition. 2nd Edition." E. Carterette & M. Friedman editors. London: Academic Press.
Plomp, (1976). Aspects of Tone Sensation. A Psychophysical Study. London: Academic Press.
Ethnomusicology Department - UCLAİ
