Psychoacoustics
MODULE 1

READINGS
Plack, 2005: Chapter 1 (skim through)

HOMEWORK


Lecture notes

 

t o p i c s
Psychophysics and Psychoacoustics: definitions and scope of study
Sound, Music, Noise: Essential & operational definitions
Basic physical variables and units- Review

 

  


 

 

Psychoacoustics: definitions and scope of study

 

DEFINITIONS

Psychoacoustics is a multidisciplinary field that deals with the physical (e.g. vibrations, wave theory), physiological (e.g. construction of the ear), and perceptual (e.g. auditory sensations) correlates of sound production, transmission, and reception.  More specifically, it forges a link among the physical, physiological, and perceptual frames of reference, examining ways in which physics and physiology interact to give rise to auditory sensations/perceptions.
[*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]
 
As a field of study, Psychoacoustics has its origin in Psychophysics.  The science of psychophysics [psycho-: internal world (from the Greek psyhi: mind/soul)  & physics: external world (from the Greek physis: nature)] represents a systematic attempt to link the physical world with sensation, whether tactile, visual, aural, gustational (taste), olfactional (smell), or kinesthetic. 

The science of psychophysics concerns itself with

  1. sensation limits (absolute threshold) or absolute lowest/highest magnitudes (levels) of a stimulus that safely and reliably gives rise to a corresponding sensation

  2. relative sensation thresholds or difference thresholds (e.g. minimum amount of change in the magnitude of a stimulus that can be perceived as a predetermined degree of change in corresponding sensation): Just Noticeable Difference or JND

  3. type of relationship between stimulus and sensation changes (e.g. linear versus nonlinear and type of nonlinearity)

  4. changes in 1-3 due to stimulus duration and level (e.g. issues of adaptation, fatigue, etc.)

  5. changes in 1-4 due to stimulus interactions (e.g. due to the simultaneous, past, or future presence of additional stimuli whether in the same modality(ies) as or in different modality(ies) than the original stimulus).

Weber (1834) was the first to map physical magnitudes to perceptual (sensory/psychic) magnitudes, indicating that the physical and perceptual worlds are non-isomorphic and are measurable with different degrees of accuracy and at different levels of nonlinearity.  In general, sense perception connects to the 'external world' with considerably less precision than physics.
Note: Cognitive abilities developed through experience may help us surpass the limits of perceptual and even physical precision, depending on context. Relevant examples will be discussed throughout the semester. For a more in-depth examination of these issues see the "Perception and Cognition of Sound" course.
 
Psychoacoustics and the related discipline of Music Psychology were delimited in the second half of the 19th century through the work of the following physicists:

Fechner ("Elements of Psychophysics," 1860) 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 corresponds to addition in the relevant perceptual variables.  Fechner's "law" applies to several sonic variables, including pitch and loudness. 
 
Helmholtz
("On the Sensation of Tone, as a Physiological Basis for a Theory of Music," 1862) produced seminal works in diverse areas that span a large portion of what we call science.  His works influenced the American school of Psychoacousticians, including Carl Seashore (author of the first "Psychology of music" in 1938) and others.  Helmholtz's understanding of the hearing mechanism, sound wave production and propagation, resonance, and the concepts of consonance/dissonance continue to be very influential.
 
Lord Rayleigh ("The Theory of Sound," 1896) first addressed acoustical concepts that are still fueling cutting edge research in musical-instrument, speech, biological, underwater, and nonlinear acoustics. 
 

Psychoacoustics incorporates some of the many disciplines involved in Cognitive psychology of sound. Cognitive (from the Latin cogitans) psychology of sound addresses implicit and explicit processes involved in the organization of sonic perceptions into meaningful wholes and provides empirical support to the understanding of how we interpret and evaluate sound and sound structures.  It links some or all of the frames of reference outlined below with the perceptual frame of reference (i.e. some sort of observation) in an attempt to answer sound-related questions. 

Cognitive psychology of sound embraces:

i) Acoustics: examination of sound in terms of generation, transmission and modification of acoustic waves (vibrational/physical frame of reference)

How is sound produced and how is it influenced by sound source construction and excitation?  How does sound wave transmission through the air etc. modify the sound before it arrives at our ears? 
What are the physical bases of our meaningful and emotional responses to sound?

ii) Physiology: human body reaction to sound vibrations (biological/physiological frame of reference)

How and with what accuracy do our ears process acoustic energy and how do they transform it into sensation? 
What are the physiological bases of our meaningful and emotional responses to sound?

iii) Psychology: perceptual and cognitive responses to sound and sound structures, closely related to context and previous experience (perceptual/cognitive frame of reference)

How does the information obtained by our senses relate to acoustics and physiology and how does it acquire meaning and emotional significance? 
What are the psychoacoustic and cognitive bases of our meaningful and emotional responses to music?
Note: Psychology does not focus on an individual's perceptual and cognitive experiences (psychiatry and psychoanalysis focus on these). Rather, it examines how/what perceptions and interpretations arise on average for all humans (or for a given social, cultural, or demographic sub-group).

iv) Signal processing / Notation: examination of sound waves in terms of their graphic and mathematical representations; in many respects a special case of semiotics (notational/symbolic frame of reference)

How does manipulating symbols relate to manipulating acoustic waves and sound sensations and vice versa? 
What is the formal basis of our meaningful and emotional responses to sound?

v) Sociology/History: examination of sound in terms of its historical, sociological, and cultural context (historical frame of reference)

How does the historical, sociological, and cultural context of a sound relate to its meaning, value, and emotional dimension? 
What are the historical bases of our meaningful and emotional responses to sound?

vi) Philosophy (reflective frame of reference).

Examination of broader questions such as:
_ How do we know what we know?
_ How is understanding of new events guided by and how does it enhance our experience and prior understanding of the world?
_ Can behavior be objectified and studied scientifically?
_ What are the problems and limits of trying to understand a system which we are part of? Can the 'mind' ever fully understand itself without 'escaping' itself so to speak?  Can science bypass such problems?
In essence, all thought on 'reality' is reflective thought and the concept of science is an invention that allows us to model reality. 
What kinds of sound and sound organization (e.g. music) models does science enable the examination of and what methods/approaches are best fit to what questions?

 

 

 


 

Sound, Noise, Music: Essential & operational definitions

 

Essential definition: a definition of a concept that
(a) includes components that are both necessary (i.e. without them the concept would lose its identity) and sufficient (i.e. no other components are needed) to the concept's description and
(b) uniquely identifies it (i.e. no other concept shares exactly the same defining components).
 
Operational definition: an essential definition of a concept that also outlines possible operations (i.e. processes; numerical or otherwise) that assist in the reliable identification and measurement of the concept's occurrences.


Sound
The term "Sound" is often used loosely to refer to more than one phenomenon/observation:
(a) An auditory sensation
(b) The disturbance of a medium that may cause an auditory sensation or
(c) An intended/desired auditory sensation (i.e. as opposed to noise)
In our class, we will adopt the following definition:
Sound is the sensation arising when energy from a vibration, within the ear's perceptual limits, reaches the ear.

Noise
The term "noise" may be defined differently depending on frame of reference (physics vs. communication) and is often approached in opposition to the concepts of "signal" or "sound":
a) auditory sensation arising in response to non-periodic sound waves/signals, with flat and dense spectral distributions
(vibrational/physical frame of reference)
b) auditory sensation that is undesirable/unpleasant/unintended within a given context, interfering with auditory sensations that are desirable/pleasant/intended (i.e. sounds) within the same context
(cognitive/semantic frame of reference, focusing on communication)
We will be moving back and forth between these two definitions, depending on ... context.

Music
Music will provide context for several of our discussions during this course so, defining it is an important task. 
 
For the purposes of this course, we will adopt the following operational definition for music:
Music is temporally organized sound and silence, a-referentially communicative within a context.
 
Emphasis is placed on the temporal and communicative aspects of music.  Music is an essentially temporal art, fact that may point to its significance [music as virtual time (Langer) - music as articulating our emotional dimension (Reimer)]. 
In listening to music, there is always some sort of response, some kind of behavioral change, indicating that we "received" and/or participated in the creation of something.  What is received is an intention communicated in terms of patterning/configuring/organizing (akin to the prosodic aspect of language - prosody: the rhythmic and intonational aspects of language). 
The importance of context is a direct consequence of music as communication.  All communication involves shared and unshared knowing, and this is what we will broadly refer to as context.
The potentially a-referential/self-referential nature of music (i.e. music may but does not have to refer/point outside itself in the same way as language) is what distinguishes it from other forms of communication.  Music may be seen as a "noun-less" language, made just from verbs (potential, motion, action, narrative:  time.)

Music and communication
Understanding music involves interpretive translation across frames of reference, with music arising as the result of interaction (at some level) among  composer(s), performer(s) , and listener(s), all broadly defined. 
Music, as a form of communication, is possible only when the parties involved share some common explicit and implicit knowledge (more on implicit and explicit knowledge later on in the course).  This sharing helps make the messages we infer, as we observe a musical behavior, relatively consistent and meaningful. 
Although a message always implies an intent, communicated messages can be and often are different from intended messages, especially in the case of music with its a-referential (or better self-referential) potential.
In addition, although some degree of shared knowledge is necessary for efficient communication, each communication event will always involve some degree of un-shared knowledge, explaining partly why there is no isomorphic relationship between a composer's intended message and a listener's constructed message. The term 'constructed message' implies that listeners are not passive observers being effected by music.
"Listening to music" means "configuring music." The act of listening involves a configuring operation that turns a series of incoming sounds into "meaningful" patterns, relationships, temporal wholes. Listeners will always strive for pattern recognition and may identify patterns that were not intended during composition, even in the extreme case when no patterns were intended at all (e.g. aleatoric pieces of music, environmental sounds, etc.).  It is this endless potential for new organizations and meanings to be discovered, by means of listening, that permits sonic works to outlive their composers, era, style, intensions, and cultural context during creation. 
Sounds alone do not constitute music or sound art. The listener is the agent through whom sounds and sound combinations are elevated into music/art; the composer of a work can be considered its first listener and, in some respects, this may be where his/her privileged status ends.

 


 

Basic physical variables and units - Review

  

All physics (and acoustics) is based on the following three fundamental concepts/measures (and units):
    i) Mass (kg)
   ii) Distance (m)
  iii) Time (sec)
All other concepts/measures (and units) derive from these three.

Velocity:  v = ds/dt (change in distance per unit time). 
                   Unit
: m/s (meters per second).  
Velocity of 1 m/s represents an increase in distance (away from a reference point) by 1 meter, each second.

Acceleration:  a = dv/dt (change in velocity per unit time). 
                            Unit: m/s2 (meters per second-squared).
Acceleration of 1 m/s2 represents an increase in velocity by 1 m/s, each second.

Force:  F = m*a (mass times acceleration).  In terms of gravity, a = g = 9.81 m/s2 and F = m*g
               Unit
: 1 Newton (N). 1 N = 1 Kg* m/s2.
Force of 1 N represents the force that must be applied to a mass of 1 Kg in order to accelerate it by 1 m/s2.

Newton’s Laws of motion: a) If F = 0, v is constant  b) F = m*a  c) Action – Reaction

Pressure:  P = F/A (force per unit area). 
                     Unit
: 1 Pascal (Pa). 1 Pa = 1 N/m2. = 1 Kg/(m*s2). 
Pressure of 1 N/m2 represents a force of 1 Newton applied over 1 square meter of area.

Atmospheric pressure (at sea level): Patm = 105 N/m2
Smallest pressure fluctuation that can be perceived as sound (limit threshold for pressure fluctuation) : Pref = 2*10-5 N/m2.

Work/Energy:  E = F*ds (work done by a force F when it moves a mass m over a distance ds). 
                            Unit: 1 Joule (J).  1 J  = 1 N*m. 
If the mass is lifted at a height h, its potential energy (manifested as load) is: Ep = F*h = m*g*h
If the mass is in motion with speed v, its kinetic energy (manifested as motion) is Ek = (1/2)m*v2
1 J is the energy needed to move a mass of 1 Kg for 1 meter. 
Types of energy: Mechanical, electrical, chemical, thermal, etc.

Examples:
Potential energy for a spring with spring constant K (measure of a spring's stiffness) displaced from rest by y: Ep = (1/2)K*y2
Potential energy for a string with tension T and length L, displaced from rest by a distance yEp = 2T*y2/L

Power:  W = E/t (amount of energy production/consumption/transfer per unit time). 
                Unit
: 1 Watt (W).  1 W = 1 J/sec.
Power of 1 W means that energy of 1 J is produced/consumed/transferred every second.

[Pressure is more meaningful measure to hearing than force and Power is a more meaningful measure than Energy. Why? the answer is below. Intensity is a measure that combines the advantages to hearing of Pressure over Force and Power over Energy in a single measure]

Intensity:  I = W/A (power per unit area). 
                   Unit: 1 W/m2
Intensity of 1W/m2 represents the production/consumption/transfer of 1 J of energy through an area of 1 m2 each second.

As an expression of the amount of energy in a vibrational system, Intensity is more meaningful and useful that Energy or Power because it allows for energy comparisons irrespective of a vibration’s duration or the spatial spread of the resulting wave and is therefore better matched to the perceptual salience of rates of change over a given area rather than of absolute quantities, salience that is related to the auditory system's construction and function.

Smallest vibration intensity that can be perceived as sound: Iref = 10-12 W/m2.
In vibrations, Energy, Power, and Intensity are all proportional to the square of both frequency and amplitude (Can you derive this from the expression for Kinetic Energy?).
 
For waves in gases and liquids, Intensity is also proportional to the square of pressure I = kP2 (where k is a constant). More precisely:  P = (Iρc)0.5, where ρ is the medium's density and c the speed of wave propagation in the medium.

 

 


  

Columbia College, Chicago - Audio Arts & Acoustics