Set (music)

A set (pitch set, pitch-class set, set class, set form, set genus, pitch collection) in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example.

A set by itself does not necessarily possess any additional structure, such as an ordering. Nevertheless, it is often musically important to consider sets that are equipped with an order relation (called segments); in such contexts, bare sets are often referred to as "unordered", for the sake of emphasis.

Two-element sets are called dyads, three-element sets trichords (occasionally "triads", though this is easily confused with the traditional meaning of the word triad). Sets of higher cardinalities are called tetrachords (or tetrads), pentachords (or pentads), hexachords (or hexads), heptachords (heptads or, sometimes, mixing Latin and Greek roots, "septachords"—e.g.,), octachords (octads), nonachords (nonads), decachords (decads), undecachords, and, finally, the dodecachord.

Set construction

Set construction is the process by which a construction manager undertakes to build full scale scenery suitable for viewing by camera, as specified by a production designer or art director working in collaboration with the director of a production to create a set for a theatrical, film or television production. The set designer produces a scale model, scale drawings, paint elevations (a scale painting supplied to the scenic painter of each element that requires painting), and research about props, textures, and so on. Scale drawings typically include a groundplan, elevation, and section of the complete set, as well as more detailed drawings of individual scenic elements which, in theatrical productions, may be static, flown, or built onto scenery wagons. Models and paint elevations are frequently hand-produced, though in recent years, many Production Designers and most commercial theatres have begun producing scale drawings with the aid of computer drafting programs such as AutoCAD or Vectorworks.

Associative containers

In computing, associative containers refer to a group of class templates in the standard library of the C++ programming language that implement ordered associative arrays. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. The following containers are defined in the current revision of the C++ standard: set, map, multiset, multimap. Each of these containers differ only on constraints placed on their elements.

The associative containers are similar to the unordered associative containers in C++ standard library, the only difference is that the unordered associative containers, as their name implies, do not order their elements.

Design

Characteristics

Chess

Chess is a two-player board game played on a chessboard, a checkered gameboard with 64 squares arranged in an eight-by-eight grid. Chess is played by millions of people worldwide, both amateurs and professionals.

Each player begins the game with 16 pieces: one king, one queen, two rooks, two knights, two bishops, and eight pawns. Each of the six piece types moves differently. The most powerful piece is the queen and the least powerful piece is the pawn. The objective is to 'checkmate' the opponent's king by placing it under an inescapable threat of capture. To this end, a player's pieces are used to attack and capture the opponent's pieces, while supporting their own. In addition to checkmate, the game can be won by voluntary resignation by the opponent, which typically occurs when too much material is lost, or if checkmate appears unavoidable. A game may also result in a draw in several ways.

Chess is believed to have originated in India, some time before the 7th century; the Indian game of chaturanga is also the likely ancestor of xiangqi and shogi. The pieces took on their current powers in Spain in the late 15th century; the rules were finally standardized in the 19th century.

Chess annotation symbols

When annotating chess games, commentators frequently use widely recognized annotation symbols. Question marks and exclamation points that denote a move as bad or good are ubiquitous in chess literature. Some publications intended for an international audience, such as the Chess Informant have a wide range of additional symbols that transcend language barriers.

The common symbols for evaluating the merits of a move are "??", "?", "?!", "!?", "!", and "!!". In these cases, the corresponding symbol is juxtaposed in the text immediately after the move (e.g. Re7? or Kh1!?, see algebraic chess notation).

Use of these annotation symbols is subjective, as different annotators use the same symbols differently. Moreover, an annotator's use of symbols is often influenced by the player's strength: a positional misjudgment that an annotator might give a "??" if played by a strong grandmaster might pass unremarked if played by a beginner.

Annotators' use of punctuation also may possibly be influenced by the result of the game (regardless of the actual quality of the move); one possible example came in the 11th game of the 1972 World Championship, when Spassky played an unexpected move, 14.Nb1, retreating the knight to its initial square. Spassky won the game, and several annotators gave the move two exclamation points. Edmar Mednis asserted that if Spassky had lost the game, the move would likely have been given two question marks instead.

Computer chess

Computer chess is computer architecture encompassing hardware and software capable of playing chess autonomously without human guidance. Computer chess acts as solo entertainment (allowing players to practice and to better themselves when no sufficiently strong human opponents are available), as aids to chess analysis, for computer chess competitions, and as research to provide insights into human cognition.

Current chess engines are able to defeat even the strongest human players under normal conditions. Whether computation could ever solve chess remains an open question.

Availability

Chess-playing computers are now accessible to the average consumer. From the mid-1970s to the present day, dedicated chess computers have been available for purchase. There are many chess engines such as Stockfish, Crafty, Fruit and GNU Chess that can be downloaded from the Internet for free. These engines are able to play a game that, when run on an up-to-date personal computer, can defeat most master players under tournament conditions. Top programs such as the proprietary Shredder or Fritz or the open source program Stockfish have surpassed even world champion caliber players at blitz and short time controls. In October 2008 Rybka was rated top in the CCRL,CEGT, CSS,SSDF, and WBEC rating lists and has won many recent official computer chess tournaments such as CCT 8 and 9, the 2006 Dutch Open Computer Championship, the 16th IPCCC, and the 15th World Computer Chess Championship. As of February 03, 2016, Stockfish is the top rated chess program on the IPON rating list.