Fundamentals of Sound



Fundamentals of Sound: definitions and scope of study
Sound, Music, Noise: essential and operational definitions
Basic Physical Variables and Units - Review





Fundamentals of Sound: definitions and scope of study



The study of sound is a multidisciplinary field that deals with the physical (e.g. vibrations, waves), physiological (e.g. construction of the ear), and perceptual (e.g. auditory sensations) correlates of sound production, transmission, processing, storing, reproduction, and reception. It forges a link among the physical, physiological, and perceptual frames of reference, examining ways in which physical and physiological aspects interact to gives rise to auditory sensations/perceptions.
An extension of this general study of sound, Cognitive 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. Cognitive Psychology of Sound is addressed in more detail in RECA293 and will only be addressed here in passing.

"Frame of reference": A collection of concepts/definitions accepted by a particular field or bounded area of discourse, representing a particular world view.

In our study of sound will delve into several of the Acoustics Fields:

Physical Acoustics (vibrational/physical frame of reference): examination of sound in terms of generation, transmission and modification of acoustic waves.
How is sound produced and how is it influenced by sound source material, construction, and excitation?
How does sound wave transmission through the air, etc. modify the sound before it reaches our ears? 
What are the physical bases of our meaningful and emotional responses to sound?

Out of the many relevant areas, we will be touching on Musical, Architectural, and Environmental Acoustics.

Physiological Acoustics (biological/physiological frame of reference): human body reaction to sound vibrations.
How and with what accuracy do our ears process acoustic energy and how do they transform it into auditory sensations? 
What are the physiological bases of our meaningful and emotional responses to sound?

The combination of Physical and Physiological Acoustics outlines the discipline of Psychoacoustics.

Signal processing / Notation (symbolic frame of reference): examination of sound waves in terms of their electronic, graphic, and mathematical representations; a special case of semiotics, to which music notation also belongs. 
How does manipulating analogues/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?

In the context of our course, we will be limiting our investigation to a small subset of graphic representations of sound (i.e. sound signals & spectra) and to the conceptual understanding of digital audio basics.

In our study of sound we will identify

  1. sensation limits or absolute thresholds:
        absolute lowest/highest magnitudes (levels) of a vibration/wave that safely and reliably give rise to a corresponding sonic sensation

  2. relative sensation thresholds or difference thresholds or Just Noticeable Differences (JNDs):
        minimum amount of change in a physical variable, necessary to elicit a perceived change in sonic sensation

  3. type of relationship between physical and perceived changes
        (e.g. direct versus inverse relationship; linear versus nonlinear relationship; type of nonlinearity)

  4. changes in 1-3 due to a vibration's/wave's duration and level
        (e.g. issues of adaptation, fatigue, etc., related to the length and intensity of exposure to sonic stimuli)

  5. changes in 1-4 due to context and stimulus interactions
        (e.g. due to the simultaneous, past, or future presence of additional stimuli, whether sonic or otherwise)



Sound, Noise, Music: essential and 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, within a given context
(b) uniquely identifies it (i.e. no other concept shares exactly the same defining components, within a given context).
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, within a given context.


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)
For this course, we adopt the following definition
Sound is the sensation arising when vibrational energy within the response limits of the human hearing mechanism (i.e. sonic energy) reaches the ear.

Sonic Energy Visualization 1 (click above)

[Sonic Energy Visualization 2]
[Sonic Energy Visualization 3]



The term "noise" is defined differently depending on frame of reference (physics vs. communication). While "noise" is subsumed under the broader concepts of "sound" and "signal," it is often approached in opposition to these concepts. In such cases, "noise" refers to "undesired signal/sound." Then, there is the relatively new concept of Noise Music that essentially undoes all definition efforts. Watch, for example, the following video (optional)

In our course, we will be alternating between the two definitions, below, depending on ... context.
Noise is:
(a) auditory sensation arising in response to non-periodic sound waves/signals, with flat and dense spectral distributions
(vibrational/physical frame of reference, focusing on objectively measurable variables)


(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 and subjectively measureable variables)

(image source)



For the purposes of this course, we adopt the following operational definition:
Music is temporally organized sound and silence, a-referentially communicative within a context.
Emphasis is on the temporal and communicative aspects of music. Music is an essentially temporal art [music as virtual time (S. Langer) - music as articulating our emotional dimension (J. 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 intonation 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.
Analogously to abstract animation, the potential of music to communicate a-referentially, that is without necessarily having to refer/point to anything other the sounds themselves, distinguishes it from linguistic communication. Music may be seen as a "noun-less" language, made just from verbs (potential, motion, action, narrative: time).

"How Music Works" by David Byrne
seven short video interviews on the book with the same name
(book review by The Guardian)

AUDIO BOOK: Part 2 (Part 1 no longer available)  

"How Music Works" BBC4 Series - Howard Goodall (save to watch at a later time)



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), broadly defined. 
Music, as a form of communication, is possible only when the parties involved share some common explicit (i.e. describable) and implicit (i.e. unspoken) knowledge.  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 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 one-to-one 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 (to the listener) 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 where 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 contemporaneous cultural context. 

Sounds and sound patterns alone do not constitute music. 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 their privileged status ends, at least in terms of music perception.

THE WORLD OF MUSIC (or, sampling the depth and breadth of sonic and structural possibilities that can constitute music)

Excerpt from 'Raga Hameer'. Traditional piece arranged by Vilayat Khan. 'The Music of India and Pakistan' CD. The Rough Guide. World Music Network ©1995.

'Green Frog'. Arnhem Land, Northern Australia, Wangga song (A. Maralung: voice and clapsticks; P. Manaberu: didjeridu). 'The Garland Encyclopedia of World Music CD, Vol. 9: Australia and the Pacific Islands.' Garland Publishing ©1986.

'Caymmi Mostra Ao Mundo O Que A Bahia E Mangueira Tem'. Rio De Janeiro. Samba Enredo by Thobias Da Vai-Vai. 'The Music of Brazil' CD. The Rough Guide. World Music Network ©1998.

'Almamy Bocoum'. Senegal; West Africa. By Mansour Seck. 'West African Music' CD. The Rough Guide. World Music Network ©1995.
'Mauritania My Beloved Country'. Mauritania; West Africa. By Khalifa Ould Eide & Dimi Mint Abba. 'West African Music' CD. The Rough Guide. World Music Network ©1995.
'Jaya Semara'. Indonesian Gamelan (for Kebyar gong). UCLA Gamelan Ensemble.
'Three-part Bulgarian vocal piece'. Fieldwork recording by Timothy Rice.
'Jesu, Joy of Man's Desiring', from the Cantata 'Herz und Mund und Tat und Leben.' J. S. Bach (BWV 147). W. Basch: Trumpet; W. Rubsam: Organ. CD, Pro-Arte Records ©1986.
Sonata No. 2 for Cello and Piano (1994) - II: Allegro (in "Schnittke - Complete Works for Cello and Piano - Alexander Ivashkin, cello - Irina Schnittke, piano")- © 1998 Chandos Records Ltd.
Symphony No. 21 - Opening (Anton Webern - Excerpt)



Basic physical variables and units - Review

Math Symbols & Units - (source)


Acoustics is based on the following three fundamental concepts/measures/units. All other acoustical concepts/measures/units derive from these three:
Mass (kg: kilogram)
Length/Distance (m: meter)
Time (s: second)

According to the International System of Units (SI), there is a total of 7 base units. The above three plus: iv) electric current (A: ampere); v) thermodynamic temperature (K: kelvin); vi) amount of substance (mol: mole); and vii) luminous intensity (cd: candela)

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 Pa represents a force of 1 Newton applied over an area of 1 square meter.
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, thermal, chemical, etc.

Potential energy for a spring with spring constant K (measure of a spring's stiffness) displaced from rest by a distance y  --> Ep = (1/2)K*y2
Take-away: The energy stored in a spring is proportional to its stiffness and to the square of its compression/expansion away from rest.
Potential energy for a string with tension T and length L, displaced from rest by a distance y  --> Ep = 2T*y2/L
Take-away: Analogously to a spring, the energy stored in a string is proportional to its stiffness and to the square of its displacement away from rest but it is inversely proportional to its length

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 within a system every second.

In terms of hearing
a) Pressure is a more meaningful measure than Force and
b) Power is a more meaningful measure to hearing than Energy.
Why? The answer can be inferred further below.
Intensity combines in a single measure the advantages (with regards to hearing) of Pressure over Force and of Power over Energy.

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. This matches 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, consequently, Intensity are all proportional to the square of both frequency and amplitude.
(Optional: Can you infer this from the expression for Kinetic Energy?)
For waves in gases/liquids, intensity I is also proportional to the square of pressure: I = kP2 (where k is a constant).
(Optional: note that pressure P is proportional to the square root of the gas's density ρ  and of the speed of wave propagation c [i.e. P= (Iρc)0.5]).


Loyola Marymount University - School of Film & Television