Graph theoryIn mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
Indian classical musicIndian classical music is the classical music of the Indian subcontinent. It is generally described using terms like Marg Sangeet and Shastriya Sangeet. It has two major traditions: the North Indian classical music known as Hindustani and the South Indian expression known as Carnatic. These traditions were not distinct until about the 15th century. During the period of Mughal rule of the Indian subcontinent, the traditions separated and evolved into distinct forms.
Musical theatreMusical theatre is a form of theatrical performance that combines songs, spoken dialogue, acting and dance. The story and emotional content of a musical – humor, pathos, love, anger – are communicated through words, music, movement and technical aspects of the entertainment as an integrated whole. Although musical theatre overlaps with other theatrical forms like opera and dance, it may be distinguished by the equal importance given to the music as compared with the dialogue, movement and other elements.
AtonalityAtonality in its broadest sense is music that lacks a tonal center, or key. Atonality, in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a single, central triad is not used, and the notes of the chromatic scale function independently of one another. More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized European classical music between the seventeenth and nineteenth centuries.
Nonchord toneA nonchord tone (NCT), nonharmonic tone, or embellishing tone is a note in a piece of music or song that is not part of the implied or expressed chord set out by the harmonic framework. In contrast, a chord tone is a note that is a part of the functional chord . Non-chord tones are most often discussed in the context of the common practice period of classical music, but they can be used in the analysis of other types of tonal music as well, such as Western popular music.
TonalityTonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is called the tonic. The root of the tonic chord forms the name given to the key, so in the key of C major, the note C can be both the tonic of the scale and the root of the tonic chord (when it is C–E–G). The tonic can be a different note in the same scale, when the work is said to be in one of the modes of the scale.
Music of IndiaOwing to India's vastness and diversity, Indian music encompasses numerous genres in multiple varieties and forms which include classical music, folk, rock, and pop. It has a history spanning several millennia and developed over several geo-locations spanning the sub-continent. Music in India began as an integral part of socio-religious life. Music in ancient India The 30,000-year-old paleolithic and neolithic cave paintings at the UNESCO world heritage site at Bhimbetka rock shelters in Madhya Pradesh show a type of dance.
Music genreA music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions. It is to be distinguished from musical form and musical style, although in practice these terms are sometimes used interchangeably. Music can be divided into genres in varying ways, such as popular music and art music, or religious music and secular music. The artistic nature of music means that these classifications are often subjective and controversial, and some genres may overlap.
Line graphIn the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.
MusicMusic is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm, or otherwise expressive content. Definitions of music vary depending on culture, though it is an aspect of all human societies and a cultural universal. While scholars agree that music is defined by a few specific elements, there is no consensus on their precise definitions. The creation of music is commonly divided into musical composition, musical improvisation, and musical performance, though the topic itself extends into academic disciplines, criticism, philosophy, and psychology.
Musical instrumentA musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who plays a musical instrument is known as an instrumentalist. The history of musical instruments dates to the beginnings of human culture. Early musical instruments may have been used for rituals, such as a horn to signal success on the hunt, or a drum in a religious ceremony.
Musical formIn music, form refers to the structure of a musical composition or performance. In his book, Worlds of Music, Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a piece of music, such as "the arrangement of musical units of rhythm, melody, and/or harmony that show repetition or variation, the arrangement of the instruments (as in the order of solos in a jazz or bluegrass performance), or the way a symphonic piece is orchestrated", among other factors.
Graph (abstract data type)In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points), together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as edges (also called links or lines), and for a directed graph are also known as edges but also sometimes arrows or arcs.
Variation (music)In music, variation is a formal technique where material is repeated in an altered form. The changes may involve melody, rhythm, harmony, counterpoint, timbre, orchestration or any combination of these. Mozart's Twelve Variations on "Ah vous dirai-je, Maman" (1785), known in the English-speaking world as "Twinkle, Twinkle, Little Star" exemplifies a number of common variation techniques.
Nearest neighbor searchNearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest-neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M, find the closest point in S to q. Donald Knuth in vol.
HierarchyA hierarchy (from Greek: ἱεραρχία, from hierarkhes, 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science, organizational theory, systems theory, systematic biology, and the social sciences (especially political science).
Tonic (music)In music, the tonic is the first scale degree () of the diatonic scale (the first note of a scale) and the tonal center or final resolution tone that is commonly used in the final cadence in tonal (musical key-based) classical music, popular music, and traditional music. In the movable do solfège system, the tonic note is sung as do. More generally, the tonic is the note upon which all other notes of a piece are hierarchically referenced. Scales are named after their tonics: for instance, the tonic of the C major scale is the note C.
Graph coloringIn graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edge so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face or region so that no two faces that share a boundary have the same color.
Medieval musicMedieval music encompasses the sacred and secular music of Western Europe during the Middle Ages, from approximately the 6th to 15th centuries. It is the first and longest major era of Western classical music and followed by the Renaissance music; the two eras comprise what musicologists generally term as early music, preceding the common practice period. Following the traditional division of the Middle Ages, medieval music can be divided into Early (500–1150), High (1000–1300), and Late (1300–1400) medieval music.
Motif (music)In music, a motif IPA: (/moʊˈtiːf/) (also motive) is a short musical idea, a salient recurring figure, musical fragment or succession of notes that has some special importance in or is characteristic of a composition. The motif is the smallest structural unit possessing thematic identity. The Encyclopédie de la Pléiade regards it as a "melodic, rhythmic, or harmonic cell", whereas the 1958 Encyclopédie Fasquelle maintains that it may contain one or more cells, though it remains the smallest analyzable element or phrase within a subject.
