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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
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)
all-interval tetrachord. Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b), respectively. The interval vector for both all-interval tetrachords
All-interval_tetrachord
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)
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
Topics referred to by the same term
manufacturer Interval vector in musical set theory KRISS Vector, a .45 ACP submachine gun Light verb, or vector verb, in grammar Parker Vector, pens Vector 2022
Vector
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)
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)
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
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)
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
Mathematical model combining space and time
momentum vector is extended to four dimensions. Added to the momentum vector is a time component that allows the spacetime momentum vector to transform
Spacetime
Similarity measure for number sequences
the interval [ − 1 , + 1 ] . {\displaystyle [-1,+1].} For example, two proportional vectors have a cosine similarity of +1, two orthogonal vectors have
Cosine_similarity
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 R n {\displaystyle
Vector_field
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)
Value that appears most often in a set of data
any random variable assuming values from a vector space, including the real numbers (a one-dimensional vector space) and the integers (which can be considered
Mode_(statistics)
Position that there is no relationship between two phenomena
H:\mu =100} . Inexact hypothesis Those specifying a parameter range or interval. Examples: H 1 : μ ≤ 100 {\displaystyle H_{1}:\mu \leq 100} ; H 2 : 95
Null_hypothesis
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
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
Operation in mathematical 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
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
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
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
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
Statistical test with teststatistic the number of signs of one type
"greater" or "less" conf.level = confidence level for the returned confidence interval. Examples of the sign test using the R function binom.test The sign test
Sign_test
Process of using data analysis for predicting population data from sample data
parameter of interest; an interval estimate, e.g. a confidence interval (or set estimate). A confidence interval is an interval constructed using data from
Statistical_inference
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
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)
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
Way of inferring information from cross-covariance matrices
of inferring information from cross-covariance matrices. If we have two vectors X = (X1, ..., Xn) and Y = (Y1, ..., Ym) of random variables, and there
Canonical_correlation
Comparison of two distributions
defines a parametric curve where the parameter is the index of the quantile interval. If the two distributions being compared are similar, the points in the
Q–Q_plot
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
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
Complete set of items that share at least one property in common
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Statistical_population
Processes that maintain quality at a constant level
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Quality_control
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
Concept in probability theory and statistics
vector eX (denoted rX in the accompanying graph), have a zero scalar product with the vector z generated by Z. This means that the residuals vector lies
Partial_correlation
Statistical model allowing for frequent zero values
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Zero-inflated_model
Relationship between items in a set
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Ranking
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
Statistics concept
degrees of freedom. We can therefore use this quotient to find a confidence interval for μ. This t-statistic can be interpreted as "the number of standard errors
Errors_and_residuals
Measure of statistical dispersion
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Interquartile_range
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
Compilation of information about a given population
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Census
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 mathematical model
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Statistical_model
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
Method of data analysis
space are a sequence of p {\displaystyle p} unit vectors, where the i {\displaystyle i} -th vector is the direction of a line that best fits the data
Principal_component_analysis
Metric for fit of statistical models
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Goodness_of_fit
Range to estimate an unknown parameter
According to frequentist inference, a confidence interval (CI) is a range of values which is likely to contain (in repeated sampling) the true value of
Confidence_interval
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
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)
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
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
Expression that may be integrated over a region
{\displaystyle f(x)\,dx} is an example of a 1-form, and can be integrated over an interval [ a , b ] {\displaystyle [a,b]} contained in the domain of f {\displaystyle
Differential_form
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
Statistical methods to build mathematical models of dynamical systems from measured data
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
System_identification
Design of tasks
legitimately and efficiently carried out. Contrasts can be represented by vectors and sets of orthogonal contrasts are uncorrelated and independently distributed
Design_of_experiments
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)
Study of collection and analysis of data
bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical if a two-sided interval is built violating symmetry around
Statistics
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)
Statistical interpretation with many tests
confidence intervals simultaneously, each with 95% coverage probability, the expected number of non-covering intervals is 5. If the intervals are statistically
Multiple_comparisons_problem
Vector space consisting of affine subsets
In linear algebra, the quotient of a vector space V {\displaystyle V} by a subspace U {\displaystyle U} is a vector space obtained by "collapsing" U {\displaystyle
Quotient space (linear algebra)
Quotient_space_(linear_algebra)
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
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
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
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
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
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
confidence interval (CI) In inferential statistics, a range of plausible values for some unknown parameter, such as a population mean, defined as an interval with
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Number of occurrences in an experiment or study
also equal to the frequency density of the interval, i.e., the frequency divided by the width of the interval. The total area of the histogram is equal
Frequency_(statistics)
Ratio of competing statistical models
of the two different models M1 and M2, parametrised by model parameter vectors θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} , is
Bayes_factor
Differential operator in mathematics
the vector Laplacian applies to a vector field, returning a vector quantity. When computed in orthonormal Cartesian coordinates, the returned vector field
Laplace_operator
Statistical test for normality of data
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Lilliefors_test
Measures of the characteristics of, or changes to, a population
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Demographic_statistics
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
Mathematical set with an ordering
and an ideal of L. An interval in a poset P is a subset that can be defined with interval notation: For a ≤ b, the closed interval [a, b] is the set of
Partially_ordered_set
Mathematical function
domain contain an interval of non-empty interior, and may be continuous, or have some degree of smoothness, over one or more intervals, each of non-empty
Function_of_a_real_variable
Graphical representation of the distribution of numerical data
series of intervals—and then count how many values fall into each interval. The bins are usually specified as consecutive, non-overlapping intervals of a variable
Histogram
Probabilistic problem-solving algorithm
optimization. The problem is to minimize (or maximize) functions of some vector that often has many dimensions. Many problems can be phrased in this way:
Monte_Carlo_method
Function related to statistics and probability theory
comprise an interval of real values. If the region does comprise an interval, then it is called a likelihood interval. Likelihood intervals, and more generally
Likelihood_function
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
Plan for research in clinical medicine
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Clinical_study_design
Way to determine a preliminary orbit from initial observations in astronomy
{\displaystyle \tau _{n}} is the time interval R n {\displaystyle R_{n}} is the respective observer position vector ρ ^ n {\displaystyle \mathbf {{\hat
Gauss's_method
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
Theorem of stationary processes
{\displaystyle \{b_{j}\}} . b {\displaystyle b} is the possibly infinite vector of moving average weights (coefficients or parameters) η t {\displaystyle
Wold's_theorem
Measure of the shape of a function
is the kurtosis. For a distribution of mass or probability on a bounded interval, the collection of all the moments (of all orders, from 0 to ∞) uniquely
Moment_(mathematics)
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
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
Specialized form of regression analysis, in statistics
loss of power in hypothesis tests and to unnecessarily wide confidence intervals on estimated parameters. Another consequence of the inefficiency of the
Robust_regression
Mathematical function of two positive real arguments
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Arithmetic–geometric_mean
Type of scatter plot
Median unbiased Plug-in Interval estimation Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Volcano_plot_(statistics)
Probability distribution
the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression
Student's_t-distribution
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
Variable representing a random phenomenon
to whether a random variable is valued in a countable subset or in an interval of real numbers. There are other important possibilities, especially in
Random_variable
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
INTERVAL VECTOR
INTERVAL VECTOR
Girl/Female
American, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Plucked Flower; Voice of Heart; Woman; Intellect; Behold of Any Beautiful Scene; Internal Beauty
Male
Greek
(ἈπολλÏων) Greek name APOLLYÅŒN means "destroyer." In the New Testament bible, this is the name of the angel-prince of the infernal regions, the minister of death and author of havoc on earth. He is also known by the name AbaddÅn.
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Punjabi, Sikh, Sindhi, Telugu
Heart; Inner Beauty; Fame; Internal Nature; Wisdom
Surname or Lastname
English and French
English and French : nickname for a handsome man (perhaps also ironically for an ugly one), from Old French beu, bel ‘fair’, ‘lovely’ (Late Latin bellus).Hungarian (Bél) : from the old secular Hungarian name Bél, or alternatively from bél ‘internal part’, probably an occupational name for a servant who worked in the household.Czech (BÄ›l) from Czech bÃlý ‘white’.
Surname or Lastname
Irish
Irish : reduced Anglicized form of either of two Gaelic names, Ó DuibhÃn ‘descendant of DuibhÃn’, a byname meaning ‘little black one’, or Ó DaimhÃn ‘descendant of DaimhÃn’, a byname meaning ‘fawn’, ‘little stag’. These are attenuated versions of Ó Dubháin and Ó Damháin, and are the phonetic origin of Anglicizations with an internal v (as opposed to w, as in Dewan, or monosyllabic forms with an o or u) (see Doane).English and French : nickname, of literal or ironic application, from Middle English, Old French devin, divin ‘excellent’, ‘perfect’ (Latin divinus ‘divine’).
Boy/Male
Indian
Internal Cleanliness
Male
English
Anglicized form of Greek ApollyÅn, APOLLYON means "destroyer." In the New Testament bible, this is the name of the angel-prince of the infernal regions, the minister of death and author of havoc on earth. He is also known by the name Abaddon.
Male
Greek
(á¾Î¹Î´Î·Ï‚) Greek name derived from the word aides, HAIDES means "unseen." In mythology, this is the name of the god of the underworld, brother of Zeus and husband of Persephone. In the Greek bible, Haides is associated with Orcus, the realm of the dead, the infernal regions where disembodied spirits live, a dark and dismal place in the depths of the earth. Only later was Haides described as the grave, death, and hell. Also spelled HadÄ“s.Â
Boy/Male
Gujarati, Hindu, Indian, Kannada, Punjabi, Sanskrit, Sikh, Traditional
Protector of All; Protector of God Indra; Gods Friends
Boy/Male
Sikh
Protector of Indra, Variant of Inder
INTERVAL VECTOR
INTERVAL VECTOR
Girl/Female
Hindu, Indian, Kannada, Marathi
A Bird; Voice of Bird
Boy/Male
Biblical
The work of the Lord.
Boy/Male
Indian, Marathi
God Name
Boy/Male
Hindu
Boy/Male
Tamil
A king
Boy/Male
Assamese, Hindu, Indian, Punjabi, Sikh
Goddess of Wealth; Seated in a Lotus
Boy/Male
Indian, Punjabi, Sikh
A Dwelling
Girl/Female
Gujarati, Hindu, Indian
Pearl
Girl/Female
Muslim
Luminous. Brilliant. Illuminating.
Male
Scandinavian
 Scandinavian form of Roman Latin Victor, VIKTOR means "conqueror." Compare with another form of Viktor.
INTERVAL VECTOR
INTERVAL VECTOR
INTERVAL VECTOR
INTERVAL VECTOR
INTERVAL VECTOR
n.
A small interval, less than any in actual practice, but used in the mathematical calculation of intervals.
n.
An interval.
a.
Pertaining to its own affairs or interests; especially, (said of a country) domestic, as opposed to foreign; as, internal trade; internal troubles or war.
a.
Derived from, or dependent on, the thing itself; inherent; as, the internal evidence of the divine origin of the Scriptures.
n.
An interval of a fifth; also, a part sung with such intervals.
n.
Alt. of Intervale
a.
Pertaining to, or proceeding by, integration; as, the integral calculus.
a.
Of or pertaining to, resembling, or inhabiting, hell; suitable for hell, or to the character of the inhabitants of hell; hellish; diabolical; as, infernal spirits, or conduct.
n.
Difference in pitch between any two tones.
n.
Space of time between any two points or events; as, the interval between the death of Charles I. of England, and the accession of Charles II.
n.
A space between things; a void space intervening between any two objects; as, an interval between two houses or hills.
a.
Inward; interior; being within any limit or surface; inclosed; -- opposed to external; as, the internal parts of a body, or of the earth.
n.
An interhyal ligament or cartilage.
n.
Interval; intermission.
a.
Internal.
v. t.
To interpel.
n.
An interval.
n.
Intervening space; interval.
n.
A brief space of time between the recurrence of similar conditions or states; as, the interval between paroxysms of pain; intervals of sanity or delirium.
n.
An inhabitant of the infernal regions; also, the place itself.