1.
Plus-Minus (Stockhausen)
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Plus-Minus,2 ×7 pages for realisation, is a composition for one or several performers by Karlheinz Stockhausen, first written in 1963 and redrafted in 1974. It is Nr.14 in the catalogue of works. The score is dedicated to Mary Bauermeister, in it, various compositional premises of Stockhausen’s are presented in such a way as to enable the most radically different concrete results. (Id discussed all the transformations of the seven musical types that occur in the score with Mary. Stockhausens intention was to enable a music that reproduces itself, within a strict framework, the first public performance was given in Rome in June 1964 by Cornelius Cardew and Frederic Rzewski, each of whom realised one page of the score. The course of the work is based on polarities of attraction and repulsion, of growth, material is systematically accumulated and eroded, in a process resembling a game of chess, where central and secondary notes either expand and proliferate, or are reduced until they disappear. These oppositions include, for example, the confrontation of materials having definite pitch with others of indeterminate pitch, one or several layers of events can be worked out from these fourteen pages, and be combined according to particular rules. At that point, the event-type in question dies and may not be used again in the piece, the score of Plus-Minus is complicated, delivering the message that composing serial music is hard work. The openness of the score was seen at the end of the 20th century as a form of control, deterring all. At the first Cologne Courses, a student composer from Iceland, Atli Heimir Sveinsson, according to Stockhausen, There were just a few blips and blobs and then lots of silences … that was it. Recorded in the Levin Salen at the Norwegian State Academy of Music on August 14–15,1998, hamburg, Germany, TIM The International Music Company AG,2002. Charlotte Moorman, Nam June Paik, Terry Jennings, Benjamin Patterson, Philip Corner, Malcolm Goldstein, Jackson Mac Low, David Behrman. 1 for Adults Only, TV Cello Duets, Concerto for TV Cello and Videotapes, Waiting for Commercials, Karlheinz Stockhausen, Plus-Minus, Toshi Ichiyanagi, Charlotte Moorman interview by Harvey Matusow, BBC New York Studios, October 1969. Recorded between 1964 and 1982 in various locations, compact disc 4 sound discs Alga Marghen 27NMN.064. Disc with Plus-Minus also issued separately, as Charlotte Moorman, Cello Anthology, recorded 29 June–2 July 2002 at Theater Romein, Leeuwarden, Netherlands. Contemporary Music as Represented in Stockhausens Plus-Minus, International Review of the Aesthetics and Sociology of Music 2, no. Stockhausens Plus Minus, More or Less, Written in Sand, Karlheinz Stockhausen II, Die Werke 1950–1977, Gespräch mit Karlheinz Stockhausen, Es geht aufwärts. Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto, designing Programmes, Four Essays and an Introduction, with an introduction to the introduction by Paul Gredinger

2.
Plus and minus signs
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The plus and minus signs are mathematical symbols used to represent the notions of positive and negative as well as the operations of addition and subtraction. Their use has extended to many other meanings, more or less analogous. Plus and minus are Latin terms meaning more and less, respectively, though the signs now seem as familiar as the alphabet or the Hindu-Arabic numerals, they are not of great antiquity. In Europe in the early 15th century the letters P and M were generally used, the symbols appeared for the first time in Luca Pacioli’s mathematics compendium, Summa de arithmetica, geometria, proportioni et proportionalità, first printed and published in Venice in 1494. The + is a simplification of the Latin et, the − may be derived from a tilde written over m when used to indicate subtraction, or it may come from a shorthand version of the letter m itself. In his 1489 treatise Johannes Widmann referred to the symbols − and + as minus and mer, was − ist, das ist minus, und das + ist das mer. They werent used for addition and subtraction here, but to indicate surplus and deficit, the plus sign is a binary operator that indicates addition, as in 2 +3 =5. It can also serve as an operator that leaves its operand unchanged. This notation may be used when it is desired to emphasize the positiveness of a number, the plus sign can also indicate many other operations, depending on the mathematical system under consideration. Many algebraic structures have some operation which is called, or is equivalent to and it is conventional to use the plus sign to only denote commutative operations. Subtraction is the inverse of addition, directly in front of a number and when it is not a subtraction operator it means a negative number. For instance −5 is negative 5, a unary operator that acts as an instruction to replace the operand by its additive inverse. For example, if x is 3, then −x is −3, similarly, − is equal to 2. The above is a case of this. All three uses can be referred to as minus in everyday speech, further, some textbooks in the United States encourage −x to be read as the opposite of x or the additive inverse of x to avoid giving the impression that −x is necessarily negative. However, in programming languages and Microsoft Excel in particular, unary operators bind strongest, so in those cases −5^2 is 25. Some elementary teachers use raised plus and minus signs before numbers to show they are positive or negative numbers. For example, subtracting −5 from 3 might be read as positive three take away negative 5 and be shown as 3 − −5 becomes 3 +5 =8, in grading systems, the plus sign indicates a grade one level higher and the minus sign a grade lower