Baroque musicBaroque music (UKbəˈrɒk or USbəˈroʊk) refers to the period or dominant style of Western classical music composed from about 1600 to 1750. The Baroque style followed the Renaissance period, and was followed in turn by the Classical period after a short transition (the galant style). The Baroque period is divided into three major phases: early, middle, and late. Overlapping in time, they are conventionally dated from 1580 to 1650, from 1630 to 1700, and from 1680 to 1750.
Statistical mechanicsIn physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, chemistry, and neuroscience.
Classical musicClassical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" also applies to non-Western art music. Classical music is often characterized by formality and complexity in its musical form and harmonic organization, particularly with the use of polyphony.
Sheet musicSheet music is a handwritten or printed form of musical notation that uses musical symbols to indicate the pitches, rhythms, or chords of a song or instrumental musical piece. Like its analogs – printed books or pamphlets in English, Arabic, or other languages – the medium of sheet music typically is paper (or, in earlier centuries, papyrus or parchment).
Ornament (music)In music, ornaments or embellishments are musical flourishes—typically, added notes—that are not essential to carry the overall line of the melody (or harmony), but serve instead to decorate or "ornament" that line (or harmony), provide added interest and variety, and give the performer the opportunity to add expressiveness to a song or piece. Many ornaments are performed as "fast notes" around a central, main note. There are many types of ornaments, ranging from the addition of a single, short grace note before a main note to the performance of a virtuosic and flamboyant trill.
Quantum statistical mechanicsQuantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.
Program musicProgram music or programmatic music is a type of instrumental art music that attempts to musically render an extramusical narrative. The narrative itself might be offered to the audience through the piece's title, or in the form of program notes, inviting imaginative correlations with the music. A well-known example is Sergei Prokofiev's Peter and the Wolf. The genre culminates in the symphonic works of Richard Strauss that include narrations of the adventures of Don Quixote, Till Eulenspiegel, the composer's domestic life, and an interpretation of Friedrich Nietzsche's philosophy of the Übermensch, Also Sprach Zarathustra.
Partition function (statistical mechanics)In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless.
Mutual informationIn probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable. The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.
Ensemble (mathematical physics)In physics, specifically statistical mechanics, an ensemble (also statistical ensemble) is an idealization consisting of a large number of virtual copies (sometimes infinitely many) of a system, considered all at once, each of which represents a possible state that the real system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The concept of an ensemble was introduced by J. Willard Gibbs in 1902.
Classical period (music)The Classical period was an era of classical music between roughly 1750 and 1820. The Classical period falls between the Baroque and the Romantic periods. Classical music has a lighter, clearer texture than Baroque music, but a more varying use of musical form, which is, in simpler terms, the rhythm and organization of any given piece of music. It is mainly homophonic, using a clear melody line over a subordinate chordal accompaniment, but counterpoint was by no means forgotten, especially in liturgical vocal music and, later in the period, secular instrumental music.
Scale (music)In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature.
Microstate (statistical mechanics)In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual particles or components that make up the system. Each microstate has a certain probability of occurring during the course of the system's thermal fluctuations. In contrast, the macrostate of a system refers to its macroscopic properties, such as its temperature, pressure, volume and density.
Chamber musicChamber music is a form of classical music that is composed for a small group of instruments—traditionally a group that could fit in a palace chamber or a large room. Most broadly, it includes any art music that is performed by a small number of performers, with one performer to a part (in contrast to orchestral music, in which each string part is played by a number of performers). However, by convention, it usually does not include solo instrument performances.
Music historyMusic history, sometimes called historical musicology, is a highly diverse subfield of the broader discipline of musicology that studies music from a historical point of view. In theory, "music history" could refer to the study of the history of any type or genre of music (e.g., the history of Indian music or the history of rock). In practice, these research topics are often categorized as part of ethnomusicology or cultural studies, whether or not they are ethnographically based.
Classical mechanicsClassical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The "classical" in "classical mechanics" does not refer classical antiquity, as it might in, say, classical architecture.
Interaction informationThe interaction information is a generalization of the mutual information for more than two variables. There are many names for interaction information, including amount of information, information correlation, co-information, and simply mutual information. Interaction information expresses the amount of information (redundancy or synergy) bound up in a set of variables, beyond that which is present in any subset of those variables. Unlike the mutual information, the interaction information can be either positive or negative.
Conditional mutual informationIn probability theory, particularly information theory, the conditional mutual information is, in its most basic form, the expected value of the mutual information of two random variables given the value of a third. For random variables , , and with support sets , and , we define the conditional mutual information as This may be written in terms of the expectation operator: . Thus is the expected (with respect to ) Kullback–Leibler divergence from the conditional joint distribution to the product of the conditional marginals and .
Variation of informationIn probability theory and information theory, the variation of information or shared information distance is a measure of the distance between two clusterings (partitions of elements). It is closely related to mutual information; indeed, it is a simple linear expression involving the mutual information. Unlike the mutual information, however, the variation of information is a true metric, in that it obeys the triangle inequality. Suppose we have two partitions and of a set into disjoint subsets, namely and .
Information theoryInformation theory is the mathematical study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field, in applied mathematics, is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering, and electrical engineering. A key measure in information theory is entropy.
