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Interval content of a given set in musical set theory
include: ic vector (or interval-class vector), PIC vector (or pitch-class interval vector) and APIC vector (or absolute pitch-class interval vector, which
Interval_vector
Method for bounding the errors of numerical computations
Interval arithmetic (also known as interval mathematics, interval analysis or interval computation) is a mathematical technique used to mitigate rounding
Interval_arithmetic
Topics referred to by the same term
covering digital humanities Interval vector in musical set theory Vector (album), 2018, by Haken Vector (band), 1980s Vector (rapper) (b. 1983), Nigerian
Vector
respectively, as single characters. Because, for any given set, its interval-class vector is independent of the version (cyclic permutation) considered, for
List_of_set_classes
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
5,6] (4-Z15b) and [0,4,6,7] (4-Z29b), respectively. The interval vector for both all-interval tetrachords is <1,1,1,1,1,1>. In the examples below, the
All-interval_tetrachord
Algorithm for partial ordering of events and detecting causality in distributed systems
processes. In 2008, Almeida et al. introduced Interval Tree Clocks. This mechanism generalizes Vector Clocks and allows operation in dynamic environments
Vector_clock
All numbers between two given numbers
between is an interval, denoted [0, 1] and called the unit interval. An interval may contain neither endpoint (called an open interval), both endpoints
Interval_(mathematics)
Class of problems in computer science
// The vectors are already sorted from earliest to latest finish time. int v[numOfVectors + 1]; // list of interval vectors int w[numOfVectors + 1]; //
Interval_scheduling
Branch of music theory
which obtains between two sets that share the same total interval content, or interval vector—but are not transpositionally or inversionally equivalent
Set_theory_(music)
Vector relating the initial and the final positions of a moving point
motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude
Displacement_(geometry)
Musical scale with seven pitches
juxtapositions of tetrachords. All heptatonic scales have all intervals present in their interval vector analysis, and thus all heptatonic scales are both hemitonic
Heptatonic_scale
Similarity measure for number sequences
always belongs to the interval [−1,+1]. For example, two proportional vectors have a cosine similarity of +1, two orthogonal vectors have a similarity of
Cosine_similarity
Algebraic structure in linear algebra
operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces
Vector_space
and they share the interval vector of <3,2,2,3,3,2>. It appears in pieces by Robert Morris and Elliott Carter. Carter uses all-interval twelve-tone sets
All-trichord_hexachord
Assignment of a vector to each point in a subset of Euclidean space
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space ℝn. A vector field
Vector_field
Topics referred to by the same term
Integrity check value, another name for a checksum Interval count vector in music theory, see Interval vector Infantry combat vehicle, see infantry fighting
ICV
Mechanism for tracking data changes
some settings, but can be replaced by Interval Tree Clocks. Interval Tree Clocks generalize version vectors and vector clocks and allows dynamic numbers of
Version_vector
Mathematical model combining space and time
same time interval, positive intervals are always timelike. If s2 is negative, the spacetime interval is said to be spacelike. Spacetime intervals are equal
Spacetime
Vector of length one
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase
Unit_vector
11 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 Source: Equal-interval chord Identity (music) Interval vector Octatonic scale Whittall, Arnold. 2008. The Cambridge
Interval_cycle
Operation in calculus
The collection of Riemann-integrable functions on a closed interval [a, b] forms a vector space under the operations of pointwise addition and multiplication
Integral
Mathematical function defined piecewise by polynomials
ith knot. For a given interval [a,b] and a given extended knot vector on that interval, the splines of degree n form a vector space. Briefly this means
Spline_(mathematics)
Property shared by codirectional lines
etc. On the plane, it corresponds to an angular interval. Body-relative direction Euclidean vector Directional statistics Tangent direction Not strictly
Direction_(geometry)
Algorithm for finding a zero of a function
values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values, then selecting the subinterval in which the function
Bisection_method
Vector space with a partial order
ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations
Ordered_vector_space
Whose values lie in an infinite-dimensional vector space
[a,b]} is an interval contained in the domain of a curve f {\displaystyle f} that is valued in a topological vector space then the vector f ( b ) − f (
Infinite-dimensional vector function
Infinite-dimensional_vector_function
Forte’s definition in 1965; while Clough agreed with the utility of interval-vector analysis and prime forms, he argued that Forte's method groups sets
Equivalence_class_(music)
Concept in Bayesian statistics
In Bayesian statistics, a credible interval is an interval used to characterize a probability distribution. It is defined such that an unobserved parameter
Credible_interval
Set of vectors used to define coordinates
(real or complex) vector space of all (real or complex valued) functions on the interval [0, 2π] that are square-integrable on this interval, i.e., functions
Basis_(linear_algebra)
Classification of pitch class sets
same Forte number have identical interval vectors. Those that have different Forte numbers have different interval vectors with the exception of z-related
Forte_number
Magnitude of velocity
average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction
Speed
Range to estimate an unknown parameter
In frequentist inference, a confidence interval (CI) determines lower and upper bounds likely to contain (in repeated sampling) the true value of an unknown
Confidence_interval
property can be generated with any interval coprime with twelve. For example, the diatonic scale's interval vector contains: The common tone theorem describes
Common_tone_(scale)
Definite integral of a scalar or vector field along a path
curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve). This weighting distinguishes
Line_integral
Estimate of an interval in which future observations will fall
inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain
Prediction_interval
Class of statistical models
multinomial distribution, and for the vector form of the categorical distribution, the expected values of the elements of the vector can be related to the predicted
Generalized_linear_model
different scale intervals (distance between points on the coastline at which measurements are taken). The smaller the scale interval (meaning the more
List of countries and dependencies by length of coastline
List_of_countries_and_dependencies_by_length_of_coastline
Ascending or descending sequence of musical tones
101010110101 = 2741. This binary representation permits easy calculation of interval vectors and common tones, using logical binary operators. It also provides
Scale_(music)
Graphical display of scientific results
these studies (often represented by a square) incorporating confidence intervals represented by horizontal lines. The graph may be plotted on a natural
Forest_plot
Mathematical set with an ordering
not an interval. An interval I is bounded if there exist elements a,b∈P such that I ⊆ [a, b]. Every interval that can be represented in interval notation
Partially_ordered_set
Partially ordered vector space, ordered as a lattice
is a vector lattice. An order interval in a partially ordered vector space is a convex set of the form [a,b]={x:a≤x≤b}. In an ordered real vector space
Riesz_space
large number of individually unlikely events that happen in a certain time interval. Related to this distribution are a number of other distributions: the
List of probability distributions
List_of_probability_distributions
In linear algebra, generated subspace
linear hull or just span) of a set S {\displaystyle S} of elements of a vector space V {\displaystyle V} is the smallest linear subspace of V {\displaystyle
Linear_span
Generalization of the one-dimensional normal distribution to higher dimensions
formula exist, as follows. The interval for the multivariate normal distribution yields a region consisting of those vectors x satisfying ( x − μ ) T Σ −
Multivariate normal distribution
Multivariate_normal_distribution
Family of linear transformations
coordinates in column vectors and the Minkowski metric η as a square matrix X′=[ct′x′y′z′],η=[−1000010000100001],X=[ctxyz] the spacetime interval takes the form
Lorentz_transformation
Grouping a set of objects by similarity
small distances between cluster members, dense areas of the data space, intervals or particular statistical distributions. Clustering can therefore be formulated
Cluster_analysis
Mathematical description of spacetime used in relativity
because of the invariance of the spacetime interval under Lorentz transformation. The set of all null vectors at an event of Minkowski spacetime constitutes
Minkowski_spacetime
Speed and direction of a motion
physical objects. Velocity is a vector quantity, meaning that both magnitude and direction are needed to define it (velocity vector). The scalar absolute value
Velocity
Topics referred to by the same term
Cisco's implementation of software-defined networking APIC vector (absolute pitch-class interval vector), in musical set theory Agreement on the Privileges and
APIC
Generalization of finite measure to Banach spaces
In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. It is a generalization
Vector_measure
Musical motif representing Arnold Schoenberg
complement is 6-Z19 (3478te or, in prime form, 013478). They have the interval vector of <3,1,3,4,3,1> in common. 6-Z44 lacks prime and inversional combinatoriality
Schoenberg_hexachord
Statistical model to calculate the value of multiple quantities as they change over time
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type
Vector_autoregression
Agent that carries and transmits pathogens
In epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen such as a parasite or microbe, to another living
Disease_vector
Chord
Viennese trichord Component intervals from root tritone minor second root Tuning 8:12:17 Forte no. / Complement 3-5 / 9-5 Interval vector <1,0,0,0,1,1>
Viennese_trichord
Way to determine a preliminary orbit from initial observations in astronomy
scalar quantities τn is the time interval Rn is the respective observer position vector 𝝆̂𝐧 is the respective unit vector Calculate the squared scalar distance
Gauss's_method
Musical scale containing no semitones
and B. Past this point in the projection series, no new intervals are added to the Interval vector analysis of the scale, but cohemitonia results. Adding
Anhemitonic_scale
Interval bounded by an upper and a lower limit statistics
In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a (sample) parameter of interest. This is in
Interval_estimation
Generalization of perpendicularity
perpendicularity to linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B {\displaystyle B} are orthogonal when B ( u
Orthogonality_(mathematics)
Method used in statistics, pattern recognition, and other fields
projection of multidimensional-space point x → {\displaystyle {\vec {x}}} onto vector w → {\displaystyle {\vec {w}}} (thus, we only consider its direction). In
Linear_discriminant_analysis
Fundamental space of geometry
plane, the oriented angle of two lines belongs to the interval [−π/2, π/2]. Every Euclidean vector space has an orthonormal basis (in fact, infinitely many
Euclidean_space
Data transformation of statistics into rank
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Ranking_(statistics)
Distinction between nominal, ordinal, interval and ratio variables
classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated
Level_of_measurement
and engineering, a Euclidean vector (sometimes called a geometric vector or spatial vector, or – as here – simply a vector) is a geometric object that
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Measure of covariance of components of a random vector
matrix giving the covariance between each pair of elements of a given random vector. Intuitively, the covariance matrix generalizes the notion of variance to
Covariance_matrix
Theory and technique of psychological measurement
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Psychometrics
Diagnostic plot in multivariate statistics
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Scree_plot
System of moving vectors in differential geometry
{\displaystyle X} is a tangent vector field, this expression means that, for every t {\displaystyle t} in the interval, tangent vectors in X {\displaystyle X}
Parallel_transport
numerical analysis, the interval finite element method (interval FEM) is a finite element method that uses interval parameters. Interval FEM can be applied
Interval_finite_element
Generates a forecast of future values of a time series
T}{\ln(1-\alpha )}}} where Δ T {\displaystyle \Delta T} is the sampling time interval of the discrete time implementation. Some math libraries provide the function
Exponential_smoothing
Type of statistics
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Summary_statistics
Point not between two other points
extreme point of a convex set S {\displaystyle S} in a real or complex vector space or affine space is a point in S {\displaystyle S} that does not lie
Extreme_point
Property of two or more vectors that are orthogonal and of unit length
algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors. A unit vector means that the vector has a length of
Orthonormality
Rate of change of velocity
over an infinitesimal interval of time. In the terms of calculus, instantaneous acceleration is the derivative of the velocity vector with respect to time:
Acceleration
Branch of music theory
criticisms, continue to use broadly Lewinnian techniques. Pitch space Interval vector Musical transformation Jay Chung, Andrew (2012). Lewinian Transformations
Transformational_theory
Vector-based collection of geographic information system (GIS) data about Earth
The Vector Map (VMAP), also called Vector Smart Map, is a vector-based collection of geographic information system (GIS) data about Earth at various levels
Vector_Map
Topics referred to by the same term
that is equal to one Unit interval: the set of all real-numbered points on the closed interval [0,1] Unit vector: a vector normalized to length one for
Unit_distance
Vector space with generalized dot product
space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in the space is a scalar, often
Inner_product_space
Non-parametric statistic used to estimate the survival function
statistics that may be of use with this estimator are pointwise confidence intervals, the Hall-Wellner band and the equal-precision band. Mathematica: the
Kaplan–Meier_estimator
Measure of linear correlation
coordinates of an n-dimensional vector, and computing the cosine between these two vector directions. When the angle between the vectors is near zero, then the
Pearson correlation coefficient
Pearson_correlation_coefficient
Type of numerical analysis
the R package "cir". This package also provides analytical confidence-interval estimates. Kruskal, J. B. (1964). "Nonmetric Multidimensional Scaling:
Isotonic_regression
Statistical method
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Regression discontinuity design
Regression_discontinuity_design
Method of encoding digital data on multiple carrier frequencies
improved by Weinstein and Ebert in 1971 with the introduction of a guard interval, providing better orthogonality in transmission channels affected by multipath
Orthogonal frequency-division multiplexing
Orthogonal_frequency-division_multiplexing
Statistic of a given score
scored below the score of interest. Percentile ranks are not on an equal-interval scale; that is, the difference between any two scores is not the same as
Percentile_rank
Measure of the joint variability
mean and the covariance matrix of the random vector X {\displaystyle \textstyle \mathbf {X} } , a vector whose jth element ( j = 1 , … , K ) {\displaystyle
Covariance
Bias in causal inference
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Confounding
Closed interval [0,1] on the real number line
up unit interval in Wiktionary, the free dictionary. Interval notation Unit square, cube, circle, hyperbola and sphere Unit impulse Unit vector Robert
Unit_interval
Conserved physical quantity; rotational analogue of linear momentum
the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv in Newtonian mechanics.
Angular_momentum
Diagnostic test or benchmark
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Gold_standard_(test)
Heptatonic music scale
of the octatonic scale with an omitted ♭2 degree. It has the following interval structure in semitones: 3, 1, 2, 1, 2, 1, 2, giving it the notes C D♯ E
Hungarian_major_scale
Statistical method
Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This technique allows estimation
Bootstrapping_(statistics)
Method of data analysis
of p unit vectors, where the i-th vector is the direction of a line that best fits the data while being orthogonal to the first i−1 vectors. Here, a best-fitting
Principal_component_analysis
Statistical measure of association for two binary variables
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Phi_coefficient
Type of function
belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form
Orthogonal_functions
Type of signal in signal processing
independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated
White_noise
Type of chart
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Radar_chart
Tool to assess control of a manufacturing process
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Control_chart
Type of hexachord
"Ode-to-Napoleon" hexachord is the six-member set-class with the highest number of interval classes 3 and 4 yet lacks 2s and 6s. 6-20 maps onto itself under transposition
"Ode-to-Napoleon"_hexachord
Number of values in the final calculation of a statistic that are free to vary
domain of a random vector, or essentially the number of "free" components (how many components need to be known before the vector is fully determined)
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Function related to statistics and probability theory
they are parameterized by multiple parameters given as the components of a vector. For a probability function (or probability density function) Pr[x | θ]
Likelihood_function
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