172A. Cognitive Psychology of Music (Introduction)
Undergraduate, non-major course


Mid-Term Review

 

All indented text gives information that you are not going to be directly asked for
but which outlines other relevant issues we covered in class.
You should, however, know all these terms.

Definitions

Amplitude
Maximum displacement (velocity, pressure, etc.) relative to a point of rest. (represented on y axis of a signal or spectrum). It's an expression of the energy in a vibration.

Atomism/Reductionism 
A belief that, breaking down a complex system into its elementary units and studying those units tells us everything we need to know about the complex system itself. (The whole is the sum of its parts).

Basilar membrane
A piece of flexible tissue located in the inner ear (cochlea).  It vibrates at different places in response to incoming vibrations/waves of different frequencies, and with different amplitudes in response to incoming vibrations/waves of different intensities. In other words, a widely tuned resonator that performs a frequency analysis on incoming vibrations.

Beating
Loudness fluctuation perceived when the amplitude fluctuation (that results from adding together two sines with similar frequency values: F1 and F2) has a low rate. The rate of this fluctuation is called beating rate and is equal to |F2 - F1|.

Cartesian approach
Science is a topological map of reality. The external world (res extensu) is objective and true, while our perception of it is subjective and, whenever it does not match the external reality, it is an illusion.

Categories
Psychological constructs (according to Brunner) that help us reduce the complexity of incoming information so that it can be processed in short term memory. Large number of data can be enveloped in a single category, which is then understood in terms of the criterial attributes that link these data into a unit. Related to 'schemata' and the idea of data reduction.

Criterial attribute
An attribute whose presence is necessary and sufficient to the existence of a category.

Coherence principle
No distance/interval between any two successive scale notes/degrees should be larger than the addition of any two successive intervals of a scale)

(Acoustic/sensory) Consonance
Absence of beating/roughness. The further apart on the basilar membrane the resonance regions for the components of two notes, the less 'rough' the resulting sound and the more consonant (smooth) the interval.

Critical band
The specific area along the basilar membrane that goes into vibration in response to an incoming simple tone, or component of a complex tone. Its length is determined by the elastic properties of the basilar membrane, and studies indicate an average value of approx. 1.2 mm., representing ~1/3 of an Octave.

Critical bandwidth
The frequency separation in Hz. between two simultaneous sines necessary for beats/roughness to disappear and for the tones to sound clearly apart.

Decibel (dB)
Unit for Sound Intensity Level, related logarithmically to the Intensity of (amount of energy in) a sound wave.
i.e. 10dB increase in Sound Intensity Level means 10 times more energy; 20dB increase in Sound Intensity Level means 100 times more energy etc.

(Acoustic/sensory) Dissonance
Term referring to the perceptual 'roughness' of an interval. It results from the interaction between the components of the notes involved. Such interaction happens when the respective resonance regions along the basilar membrane are less than a critical band apart.

Elemental capacities
Four genetically endowed capacities (tonal, dynamic, qualitative, temporal) representing the accuracy (Just-Noticeable-Difference) by which we can perceptually resolve the four physical variables describing sound (frequency, amplitude/intensity, signal-form/spectrum, time). According to Seashore, those capacities are a measure of musical talent.

Envelope
A graph representing how the amount of energy in a signal changes with time. The portion of an envelope representing how energy is built up is called attack. The portion representing how energy dies out is called decay. The portion representing how energy is sustained is called steady state.

Equal loudness contours
Graphs illustrating the dependence of loudness on frequency. They demonstrate how the loudness of simple tones with the same intensity changes with frequency.

Fechner's psychophysical law
The perceptual magnitude of stimuli relates logarithmically to the physical magnitude of stimuli. (i.e. Hertz / Pitch; Intensity in W/m2 - Intensity in dB)

Fourier's theorem
All complex signals can be reduced to the sum of sine signals with appropriate frequency and amplitude values.

Frame of reference
A collection of concepts and definitions accepted by a particular field or bounded area of discourse. It represents a particular world view.

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. (represented on the x axis of a spectrum). JND: ~1% of the frequency value. For example, if we start from 100Hz we have to increase the frequency to 101Hz before we perceive a change in pitch and if we start from 1000Hz we have to increase the frequency to 1010Hz before we perceive a change in pitch.

Frequency range of human hearing
20Hz to 20.000Hz (20KHz). Frequencies outside that range are inaudible. We are most sensitive to frequencies in the range 1000Hz - 3000Hz (approx.) This may have some evolutionary significance since speech sounds have most of their energy within this range.

Fundamental
The component of a harmonic complex wave with frequency that has the following property: All other components have frequencies that are integer multiples of the fundamental frequency. Usually it is the lowest component present in a complex wave.

Humean approach
No 'objective' / 'subjective' distinction is recognized. Perception defines reality.

Hypothesis
A statement of expected relations between variables, as they have been operationally defined within the context of a specific experimental design. A hypothesis is usually linked to a theory, representing one of the theory's predictions. 

(Musical) Interval
Distance between two notes. It represents frequency ratios and not frequency differences.

Isomorphism
A term describing a one-to-one relationship between variables.

Intensity
An expression of the amount of energy in a vibrational system. It is related to amplitude and is measured in Watts/m2 or, more commonly, in decibels.

Intensity range of human hearing
0dB (= 10-12 watts/m2) to 120dB (1 watt/m2). Sounds below the lower limit are inaudible. Sounds above the upper limit are potentially harmful. The upper limit (120dB = 1 Watt/m2) is therefore also called the 'threshold of pain'. JND: ~ 1dB.

JND
Just Noticeable Difference. Term referring to the smallest change in a physical variable that can be perceived.

Loudness
Perceptual attribute of sound related mainly to intensity (but also to frequency and spectrum). Large intensity values result in 'loud' sounds while low intensity values result in 'soft' sounds.

Measurement
Assignment of a value to a variable based on explicit rules .

Miller's 7±2 rule
A maximum of only 7±2 unrelated / unpatterned / random events can be stored in short-term memory.

Missing fundamental
Term describing the following phenomenon: If the fundamental frequency (or even the first few harmonics) is (are) removed from the spectrum of a periodic sound wave, the perceived pitch remains unchanged and matches the pitch of a pure tone with frequency equal to that of the 'missing fundamental'.

Music
Temporally organized sound and silence, a-referentially communicative within a context.

Normal illusions
Term used by Seashore, referring to instances where his isomorphic mapping between physical and perceptual variables breaks down. This term reflects Seashore's Cartesian approach that the physical world is objective and the perceptual subjective.

Ohm's law
Based on Fourier's theorem, it states that the ear acts as a frequency analyzer, breaking down complex tones to its sine components. For periodic (harmonic) complex waves the perceived complex tone has a pitch that matches in frequency the lowest component (fundamental.)

Period
The time it takes for a single full vibration/wave or cycle (represented on the x axis of a signal).

Octave
Interval between two pitches that have a frequency ratio: 2/1. Pitches separated by octave intervals are characterized (universally) by a high degree of sameness / smoothness.

Operational definitions
Definitions of variables based on explicit rules within the context of a specific study, series of studies, or frame of reference. Such definitions are not fixed and do not have any claim to absolute truth.
They represent interpretive decisions made by an experimenter, that allow him to control the independent variables and measure the dependent variables within a study. These decisions are very important, however, since they are partly responsible for the levels of reliability and validity of a study.

Pitch
Perceptual attribute of sound related mainly to frequency (but also to intensity and spectrum). Large frequency values result in 'high' pitch while low frequency values result in 'low' pitch.

Pitch chroma
The distinctive quality of a specific tone, separating it from the rest of the tones within an octave.
It describes perceptual 'differences'/'distances' of pitches within an octave and the perceptual sameness of pitches separated by one or more full octaves.

Pitch height
Term describing the perceptual 'highness' or 'lowness' of a pitch; it is related to frequency.

Pitch spiral
A graph that combines the linearity of pitch height changes and the circularity of pitch chroma changes. A hypothesized cognitive schema that outlines the relationship between pitch height and pitch chroma.

Psychology
Science of observable behavior.

Reliability
The degree of an experiment's replicability, self-consistency, and predictive power.

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.

Scale
A subset of 7±2 (usually) functional pitches within an octave, with prescribed interval relationships.

(Major) scale
A scale with 7 notes separating the octave into 7 intervals (five whole-steps, and two half-steps) with the following distribution in terms of semitones:
2, 2, 1, 2, 2, 2, 1.

(Natural Minor) scale
A scale with 7 notes separating the octave into 7 intervals (five whole-steps, and two half-steps) with the following distribution in terms of semitones:
2, 1, 2, 2, 1, 2, 2.

Schemata
Knowledge structures in memory that are largely based on implicit rules and become part of implicit knowledge. It is such rules that make possible the abstraction of criterial attributes from an information input. Related to 'categories' and the idea of data reduction.

Semitone
A minor second. The smallest musical interval (the modular interval unit) in the Western musical system. The Octave is divided in 12 such intervals.
An interval of a semitone between 2 notes represents a fixed ratio (=21/12 = twelfth root of 2 = 1.059) between 2 frequencies.

Signal
A 2-dimensional graphic representation of a vibration, plotting displacement [that is: distance from the point of rest, or the equilibrium of a number of other variables such as velocity, pressure, etc.] (y axis), over time (x axis).

(Sine) Signal
A signal representing the most simple type of vibration called simple harmonic motion. It has the shape of a sine.

Simple/Pure tone
The sound sensation that results from a simple harmonic motion (simple/pure wave.) It is represented by a sine signal. i.e. sound of a tuning fork.

(Complex) Signal
A signal representing a complex vibration with a shape other than a sine. Each complex signal can be analyzed into a sum of sine signals.

(Complex) tone
The sound sensation 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.

(Harmonic) Signal
A complex signal with sine components whose frequencies are integer multiples of a single frequency called the fundamental (usually the frequency of the lowest component).

Spectrum
A graphic representation of a wave indicating the frequency (x axis) and amplitude (y axis)of its sine components.

Theory
A set of ordered, non-contradictory statements of relationships among variables, directed towards explanation.
A theory is not a guess. It is strongly connected to the idea of a model and its power is reflected in the number of testable predictions it makes.

Timbre
Multidimensional perceptual attribute of sound related mainly to the spectral composition (relative amplitude of the individual frequency components) of a complex wave. It is also related to envelope.
It represents different qualities between sounds with the same pitch and loudness.  

Validity 
The degree of an experiment's relation and applicability to a "real world" situation: one that we are likely to encounter and find important.

Variables 
Constructs or concepts, invented by us, that can take different values and allow the breaking down of a question into measurable, related parameters.

(Independent) Variables
Variables manipulated by the experimenter. In musical studies these are usually musical or acoustical concepts.

(Dependent) Variables 
Variables that represent the responses of subjects (and 'measure' behavior). They are presumed to change as a result of the manipulation of the independent variables.

 

Short Answers

 

1) Outline briefly the process of empirical investigation in music.

2) Outline the problem described by the phrase 'reification of concepts/theory'. Does this problem mean that theories are not useful? 

3) Outline the basic premises of Cartesian thought. 

4) Outline the basic premises of Humean thought. 

5) What do we mean by 'reliability' and 'validity' in the context of empirical investigation and how do they relate? 

6) State and briefly discuss the definition for 'music' given in the class.

7) Outline Kendall & Carterette's model of musical communication.

8) What can you tell about a sound wave from its signal? What can you tell about a sound wave from its spectrum?
What is an important piece of acoustical information they both leave out?

Signal:
From its shape we can conclude if it represents a pure wave or a complex wave.

A shape of a sine represents a pure wave. For such a wave the signal includes all necessary acoustical information:
        a) Amplitude: y axis (and how it may change with time: envelope).
        b) Period (and therefore Frequency): x axis.

A shape other than a sine represents a complex wave. For such a wave the signal includes the following acoustical information:
        a) Total energy in the complex wave (and how it may change with time: overall envelope).
        b) Overall repetition rate, which usually (but not always) matches the frequency of the lowest component in the complex wave and is responsible for the pitch of the resulting complex tone. 
    It does not tell us anything about the individual components that make up the complex wave.

Spectrum:
It shows how many sine components are in a wave and what is their individual amplitude (y axis) and frequency (x axis) values.
It does not tell us anything about the overall envelope of the complex wave or the envelopes of its individual components. In other words it provides us with no time-variance information.

For complex signals, neither signal nor spectrum let us know if and how the amplitude and frequency of individual components changes with time.

9) What do we mean by the terms 'explicit knowledge' and 'implicit knowledge? What is their role in perception/cognition?

10) Discuss Seashore's approach to musical talent.

11) Compare and contrast Davis' and Seashore's approaches to the science of music.

12) Give examples of why Seashore's isomorphic relationship between physical and perceptual attributes of sound does not hold.

13) Discuss the idea of 'scale' as a psychological construct.

It is possible to argue that musical scales (subsets of 7±2 pitches within an octave) in general, and those of the Western musical system (major/minor) in particular, are not arbitrary but are based on a set of cognitive rules.
    There is a limit to the amount of information that can be processed in short term memory. Miller's rule: short term memory can only deal with 7±2 unrelated/random pieces of information at a time. This means that the practically infinite pitch possibilities (in terms of JNDs) must undergo a data reduction in order to be workable by short-term memory. The term data reduction refers not only to actual elimination of data but to a reduction in their complexity; to their organization into categories (perceptual constructs).
    The Octave is one such category. Division of the pitch continuum into octaves reflects the perceptual similarity between pitches with 2/1 frequency ratios. This similarity groups together a large number of frequencies under a single category (i.e. reflecting the 'ci-ness' of all C notes ..  etc.) and divides pitch into large repeating interval units, the octaves.
    Within the octave, scales define subsets of only up to 7±2 functional pitches that describe different pitch chromas and different pitch heights, and complete the desirable data reduction.
    The specific subset-configurations involved in western scales (division of the octave into 12 modular intervals, the 12 semitones, and selection of seven successive pitches outlining 5 two-semitone intervals and 2 one-semitone intervals) allow for maximum intervalic variety.
    The octave also outlines a 'cognitive geometry' of pitch known as the 'pitch spiral'. It reflects the circularity of pitch in terms of pitch chroma (perceptual distances of pitches within an octave) and the progression of pitch in terms of pitch height (increasing/decreasing frequencies).

The entire Western tuning system (equal temperament: octave divided in 12 equal log units) and Western scale system (major / minor) is therefore based on this optimal combination of cognitive limits (short term memory/Miller's rule), data reduction/pitch circularity (octave), and maximum variety (major/minor scales).

 

Ethnomusicology Department - UCLA©