Parameter

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A parameter (), generally, is any characteristic that can help in defining or classifying a particular
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
(meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including
mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...
,
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
,
statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
,
logic Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
,
linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'.

# Modelization

When a
system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and expres ...
is modeled by equations, the values that describe the system are called ''parameters''. For example, in
mechanics Mechanics (from Ancient Greek: wikt:μηχανική#Ancient_Greek, μηχανική, ''mēkhanikḗ'', "of machine, machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among Ph ...
, the masses, the dimensions and shapes (for solid bodies), the densities and the viscosities (for fluids), appear as parameters in the equations modeling movements. There are often several choices for the parameters, and choosing a convenient set of parameters is called ''parametrization''. For example, if one were considering the movement of an object on the surface of a sphere much larger than the object (e.g. the Earth), there are two commonly used parametrizations of its position: angular coordinates (like latitude/longitude), which neatly describe large movements along circles on the sphere, and directional distance from a known point (e.g. "10km NNW of Toronto" or equivalently "8km due North, and then 6km due West, from Toronto" ), which are often simpler for movement confined to a (relatively) small area, like within a particular country or region. Such parametrizations are also relevant to the modelization of geographic areas (i.e. map drawing).

# Mathematical functions

Mathematical function In mathematics, a function from a set (mathematics), set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the D ...
s have one or more
arguments An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...
that are designated in the definition by variables. A function definition can also contain parameters, but unlike variables, parameters are not listed among the arguments that the function takes. When parameters are present, the definition actually defines a whole family of functions, one for every valid set of values of the parameters. For instance, one could define a general
quadratic function In mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic polynomial. Before 20th century, the distinction was unclear between a polynomial ...
by declaring :$f\left(x\right)=ax^2+bx+c$; Here, the variable ''x'' designates the function's argument, but ''a'', ''b'', and ''c'' are parameters that determine which particular quadratic function is being considered. A parameter could be incorporated into the function name to indicate its dependence on the parameter. For instance, one may define the base-''b'' logarithm by the formula :$\log_b\left(x\right)=\frac$ where ''b'' is a parameter that indicates which logarithmic function is being used. It is not an argument of the function, and will, for instance, be a constant when considering the
derivative In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented ...
$\textstyle\log_b\text{'}\left(x\right) = \left(x\ln\left(b\right)\right)^$. In some informal situations it is a matter of convention (or historical accident) whether some or all of the symbols in a function definition are called parameters. However, changing the status of symbols between parameter and variable changes the function as a mathematical object. For instance, the notation for the falling factorial power :$n^=n\left(n-1\right)\left(n-2\right)\cdots\left(n-k+1\right)$, defines a
polynomial function In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in mo ...
of ''n'' (when ''k'' is considered a parameter), but is not a polynomial function of ''k'' (when ''n'' is considered a parameter). Indeed, in the latter case, it is only defined for non-negative integer arguments. More formal presentations of such situations typically start out with a function of several variables (including all those that might sometimes be called "parameters") such as :$\left(n,k\right) \mapsto n^$ as the most fundamental object being considered, then defining functions with fewer variables from the main one by means of
currying In mathematics and computer science, currying is the technique of translating the evaluation of a Function (mathematics), function that takes multiple Parameter (computer science), arguments into evaluating a sequence of functions, each with a sin ...
. Sometimes it is useful to consider all functions with certain parameters as ''parametric family'', i.e. as an
indexed family In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in m ...
of functions. Examples from probability theory are given further below.

## Examples

* In a section on frequently misused words in his book ''The Writer's Art'', James J. Kilpatrick quoted a letter from a correspondent, giving examples to illustrate the correct use of the word ''parameter'':
W.M. Woods ... a mathematician ... writes ... "... a variable is one of the many things a ''parameter'' is not." ... The dependent variable, the speed of the car, depends on the independent variable, the position of the gas pedal.
ilpatrick quoting Woods"Now ... the engineers ... change the lever arms of the linkage ... the speed of the car ... will still depend on the pedal position ...'' but in a ... different manner''. You have changed a parameter"
* A parametric equaliser is an
audio filter An audio filter is a frequency dependent circuit, working in the audio frequency range, 0 Hz to 20 kHz. Audio filters can amplify (boost), pass or attenuate (cut) some frequency ranges. Many types of filters exist for different audio a ...
that allows the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in Hertz (unit), hertz (H ...
of maximum cut or boost to be set by one control, and the size of the cut or boost by another. These settings, the frequency level of the peak or trough, are two of the parameters of a frequency response curve, and in a two-control equaliser they completely describe the curve. More elaborate parametric equalisers may allow other parameters to be varied, such as skew. These parameters each describe some aspect of the response curve seen as a whole, over all frequencies. A
graphic equaliser Equalization, or simply EQ, in sound recording and reproduction is the process of adjusting the volume of different frequency bands within an audio signal. The circuit or equipment used to achieve this is called an equalizer. Most hi-fi equ ...
provides individual level controls for various frequency bands, each of which acts only on that particular frequency band. * If asked to imagine the graph of the relationship ''y'' = ''ax''2, one typically visualizes a range of values of ''x'', but only one value of ''a''. Of course a different value of ''a'' can be used, generating a different relation between ''x'' and ''y''. Thus ''a'' is a parameter: it is less variable than the variable ''x'' or ''y'', but it is not an explicit constant like the exponent 2. More precisely, changing the parameter ''a'' gives a different (though related) problem, whereas the variations of the variables ''x'' and ''y'' (and their interrelation) are part of the problem itself. * In calculating income based on wage and hours worked (income equals wage multiplied by hours worked), it is typically assumed that the number of hours worked is easily changed, but the wage is more static. This makes ''wage'' a parameter, ''hours worked'' an
independent variable Dependent and independent variables are variables in mathematical modeling, statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample d ...
, and ''income'' a dependent variable.

## Mathematical models

In the context of a
mathematical model A mathematical model is a description of a system using mathematical concepts and language Language is a structured system of communication. The structure of a language is its grammar and the free components are its vocabulary. Languag ...
, such as a
probability distribution In probability theory and statistics, a probability distribution is the mathematical Function (mathematics), function that gives the probabilities of occurrence of different possible outcomes for an Experiment (probability theory), experiment. ...
, the distinction between variables and parameters was described by Bard as follows: :We refer to the relations which supposedly describe a certain physical situation, as a ''model''. Typically, a model consists of one or more equations. The quantities appearing in the equations we classify into ''variables'' and ''parameters''. The distinction between these is not always clear cut, and it frequently depends on the context in which the variables appear. Usually a model is designed to explain the relationships that exist among quantities which can be measured independently in an experiment; these are the variables of the model. To formulate these relationships, however, one frequently introduces "constants" which stand for inherent properties of nature (or of the materials and equipment used in a given experiment). These are the parameters.

## Analytic geometry

In
analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...
, a
curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ...
can be described as the image of a function whose argument, typically called the ''parameter'', lies in a real interval. For example, the
unit circle In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented i ...
can be specified in the following two ways: * ''implicit'' form, the curve is the locus of points in the
Cartesian plane A Cartesian coordinate system (, ) in a plane is a coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the Position (geometry), position of the Point (geometry ...
that satisfy the relation $x^2 + y^2 = 1.$ * ''parametric'' form, the curve is the image of the function $t \mapsto (\cos t, \sin t)$

with parameter As a parametric equation this can be written

$(x,y)=(\cos t,\sin t).$

The parameter in this equation would elsewhere in mathematics be called the ''

independent variable Dependent and independent variables are variables in mathematical modeling, statistical model A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample d ...
''.

## Mathematical analysis

In mathematical analysis, integrals dependent on a parameter are often considered. These are of the form :$F\left(t\right)=\int_^f\left(x;t\right)\,dx.$ In this formula, ''t'' is the argument of the function ''F'', and on the right-hand side the ''parameter'' on which the integral depends. When evaluating the integral, ''t'' is held constant, and so it is considered to be a parameter. If we are interested in the value of ''F'' for different values of ''t'', we then consider ''t'' to be a variable. The quantity ''x'' is a '' dummy variable'' or ''variable of integration'' (confusingly, also sometimes called a ''parameter of integration'').

## Statistics and econometrics

In
statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
and
econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...
, the probability framework above still holds, but attention shifts to estimating the parameters of a distribution based on observed data, or testing hypotheses about them. In frequentist estimation parameters are considered "fixed but unknown", whereas in Bayesian estimation they are treated as random variables, and their uncertainty is described as a distribution. In
estimation theory Estimation theory is a branch of statistics that deals with estimating the values of Statistical parameter, parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such ...
of statistics, "statistic" or
estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, th ...
refers to samples, whereas "parameter" or estimand refers to populations, where the samples are taken from. A
statistic A statistic (singular) or sample statistic is any quantity computed from values in a Sample (statistics), sample which is considered for a statistical purpose. Statistical purposes include Estimation, estimating a Statistical population, populat ...
is a numerical characteristic of a sample that can be used as an estimate of the corresponding parameter, the numerical characteristic of the
population Population typically refers to the number of people in a single area, whether it be a city A city is a human settlement of notable size.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Penguin.Kuper, A. and Kuper, ...
from which the sample was drawn. For example, the
sample mean The sample mean (or "empirical mean") and the sample covariance are statistics computed from a Sample (statistics), sample of data on one or more random variables. The sample mean is the average value (or mean, mean value) of a sample (statistic ...
(estimator), denoted $\overline X$, can be used as an estimate of the ''mean'' parameter (estimand), denoted ''μ'', of the population from which the sample was drawn. Similarly, the
sample variance In probability theory and statistics, variance is the expected value, expectation of the squared Deviation (statistics), deviation of a random variable from its population mean or sample mean. Variance is a measure of statistical dispersion, di ...
(estimator), denoted ''S''2, can be used to estimate the ''variance'' parameter (estimand), denoted ''σ''2, of the population from which the sample was drawn. (Note that the sample standard deviation (''S'') is not an unbiased estimate of the population standard deviation (''σ''): see Unbiased estimation of standard deviation.) It is possible to make statistical inferences without assuming a particular parametric family of
probability distribution In probability theory and statistics, a probability distribution is the mathematical Function (mathematics), function that gives the probabilities of occurrence of different possible outcomes for an Experiment (probability theory), experiment. ...
s. In that case, one speaks of ''
non-parametric statistics Nonparametric statistics is the branch of statistics that is not based solely on Statistical parameter, parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based ...
'' as opposed to the parametric statistics just described. For example, a test based on
Spearman's rank correlation coefficient In statistics, Spearman's rank correlation coefficient or Spearman's ''ρ'', named after Charles Spearman and often denoted by the Greek letter rho (letter), \rho (rho) or as r_s, is a Nonparametric statistics, nonparametric measure of rank corre ...
would be called non-parametric since the statistic is computed from the rank-order of the data disregarding their actual values (and thus regardless of the distribution they were sampled from), whereas those based on the
Pearson product-moment correlation coefficient In statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, a ...
are parametric tests since it is computed directly from the data values and thus estimates the parameter known as the population correlation.

## Probability theory

In
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
, one may describe the distribution of a
random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the p ...
as belonging to a ''family'' of
probability distribution In probability theory and statistics, a probability distribution is the mathematical Function (mathematics), function that gives the probabilities of occurrence of different possible outcomes for an Experiment (probability theory), experiment. ...
s, distinguished from each other by the values of a finite number of ''parameters''. For example, one talks about "a
Poisson distribution In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known co ...
with mean value λ". The function defining the distribution (the
probability mass function In probability theory, probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete density function. T ...
) is: :$f\left(k;\lambda\right)=\frac.$ This example nicely illustrates the distinction between constants, parameters, and variables. ''e'' is Euler's number, a fundamental
mathematical constant A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an Letter (alphabet), alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematic ...
. The parameter λ is the
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude (mathematics), magnitude and sign (mathematics), sign) of a gi ...
number of observations of some phenomenon in question, a property characteristic of the system. ''k'' is a variable, in this case the number of occurrences of the phenomenon actually observed from a particular sample. If we want to know the probability of observing ''k''1 occurrences, we plug it into the function to get $f\left(k_1 ; \lambda\right)$. Without altering the system, we can take multiple samples, which will have a range of values of ''k'', but the system is always characterized by the same λ. For instance, suppose we have a
radioactive Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nucl ...
sample that emits, on average, five particles every ten minutes. We take measurements of how many particles the sample emits over ten-minute periods. The measurements exhibit different values of ''k'', and if the sample behaves according to Poisson statistics, then each value of ''k'' will come up in a proportion given by the probability mass function above. From measurement to measurement, however, λ remains constant at 5. If we do not alter the system, then the parameter λ is unchanged from measurement to measurement; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase. Another common distribution is the
normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real number, real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The param ...
, which has as parameters the mean μ and the variance σ². In these above examples, the distributions of the random variables are completely specified by the type of distribution, i.e. Poisson or normal, and the parameter values, i.e. mean and variance. In such a case, we have a parameterized distribution. It is possible to use the sequence of moments (mean, mean square, ...) or
cumulant In probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expres ...
s (mean, variance, ...) as parameters for a probability distribution: see
Statistical parameter In statistics, as opposed to its general parameter, use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a popu ...
.

# Computer programming

In
computer programming Computer programming is the process of performing a particular computation (or more generally, accomplishing a specific computing result), usually by designing and building an executable computer program. Programming involves tasks such as anal ...
, two notions of
parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
are commonly used, and are referred to as parameters and arguments—or more formally as a formal parameter and an actual parameter. For example, in the definition of a function such as : y = ''f''(''x'') = ''x'' + 2, ''x'' is the ''formal parameter'' (the ''parameter'') of the defined function. When the function is evaluated for a given value, as in :''f''(3): or, ''y'' = ''f''(3) = 3 + 2 = 5, 3 is the ''actual parameter'' (the ''argument'') for evaluation by the defined function; it is a given value (actual value) that is substituted for the ''formal parameter'' of the defined function. (In casual usage the terms ''parameter'' and ''argument'' might inadvertently be interchanged, and thereby used incorrectly.) These concepts are discussed in a more precise way in
functional programming In computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied sc ...
and its foundational disciplines,
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computability, computation based on function Abstraction (computer science), abstraction and function application, application using variable ...
and combinatory logic. Terminology varies between languages; some computer languages such as C define parameter and argument as given here, while Eiffel uses an alternative convention.

# Artificial Intelligence

In
artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animal cognition, animals and human intelligence, humans. Example tasks in ...
, a
model A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a mea ...
describes the probability that something will occur. Parameters in a model are the weight of the various probabilities. Tiernan Ray, in an article on GPT-3, described parameters this way:

# Engineering

In
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more specializ ...
(especially involving data acquisition) the term ''parameter'' sometimes loosely refers to an individual measured item. This usage isn't consistent, as sometimes the term ''channel'' refers to an individual measured item, with ''parameter'' referring to the setup information about that channel. "Speaking generally, properties are those physical quantities which directly describe the physical attributes of the system; parameters are those combinations of the properties which suffice to determine the response of the system. Properties can have all sorts of dimensions, depending upon the system being considered; parameters are dimensionless, or have the dimension of time or its reciprocal." The term can also be used in engineering contexts, however, as it is typically used in the physical sciences.

# Environmental science

In
environmental science Environmental science is an interdisciplinary academic field that integrates physics, biology, and geography (including ecology, chemistry, plant science, zoology, mineralogy, oceanography, limnology, soil science, geology and physical geograp ...
and particularly in
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
and
microbiology Microbiology () is the scientific study of microorganisms, those being unicellular (single cell), multicellular (cell colony), or acellular (lacking cells). Microbiology encompasses numerous sub-disciplines including virology, bacteriolog ...
, a parameter is used to describe a discrete chemical or microbiological entity that can be assigned a value: commonly a concentration, but may also be a logical entity (present or absent), a
statistical Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
result such as a 95 percentile value or in some cases a subjective value.

# Linguistics

Within linguistics, the word "parameter" is almost exclusively used to denote a binary switch in a
Universal Grammar Universal grammar (UG), in modern linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of languag ...
within a
Principles and Parameters Principles and parameters is a framework within generative linguistics in which the syntax of a natural language is described in accordance with general ''principles'' (i.e. abstract rules or grammars) and specific ''parameters'' (i.e. markers, sw ...
framework.

# Logic

In
logic Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
, the parameters passed to (or operated on by) an ''open predicate'' are called ''parameters'' by some authors (e.g., Prawitz, "Natural Deduction"; Paulson, "Designing a theorem prover"). Parameters locally defined within the predicate are called ''variables''. This extra distinction pays off when defining substitution (without this distinction special provision must be made to avoid variable capture). Others (maybe most) just call parameters passed to (or operated on by) an open predicate ''variables'', and when defining substitution have to distinguish between '' free variables'' and '' bound variables''.

# Music

In music theory, a parameter denotes an element which may be manipulated (composed), separately from the other elements. The term is used particularly for pitch,
loudness In acoustics, loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The relation of ph ...
, duration, and
timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or musical tone, tone. Timbre distinguishes different types of sound production, such as choir voice ...
, though theorists or composers have sometimes considered other musical aspects as parameters. The term is particularly used in serial music, where each parameter may follow some specified series. Paul Lansky and George Perle criticized the extension of the word "parameter" to this sense, since it is not closely related to its mathematical sense, but it remains common. The term is also common in music production, as the functions of audio processing units (such as the attack, release, ratio, threshold, and other variables on a compressor) are defined by parameters specific to the type of unit (compressor, equalizer, delay, etc.).