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see arithmeticarithmetic,
branch of mathematics commonly considered a separate branch but in actuality a part of algebra. Conventionally the term has been most widely applied to simple teaching of the skills of dealing with numbers for practical purposes, e.g.
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 and musical notationmusical notation,
symbols used to make a written record of musical sounds.

Two different systems of letters were used to write down the instrumental and the vocal music of ancient Greece. In his five textbooks on music theory Boethius (c.A.D. 470–A.D.
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The Columbia Electronic Encyclopedia™ Copyright © 2013, Columbia University Press. Licensed from Columbia University Press. All rights reserved.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



a system of graphic signs for the written expression of music; the writing down of music.

Notation originated in antiquity. The ancient Greeks used a system of letters that indicated the pitch but not the duration of sounds. This system was followed until the tenth century, when the Greek letters were replaced by Latin ones. In the 20th century, Latin letters are still used to designate individual sounds and tonalities. In the Middle Ages neumatic notation was widely used. Special symbols called neumes were written above the texts to remind the singer of the chant melodies.

Later, horizontal lines, which made possible the more precise indication of the pitch of sounds, came into use. In the 11th century the Italian music theoretician Guido d’Arezzo introduced a system of four lines, the prototype of the modern staff. At the beginning of the lines he placed a letter indicating the pitch of the sounds represented. (This was the forerunner of the modern clefs.) Subsequently, the number of lines was increased to five, and the neumes were replaced by notes with square heads. This system, which was widely used to notate Gregorian chant, was called Choralnotation. The next development in notation was mensural notation, which fixed both the pitch and the duration of sounds. In addition to mensural notation, a system of letters or numbers, the tablatures, was used during the 15th through 17th centuries for the written representation of instrumental music. Like the modern number system that is designed to simplify the teaching of certain folk instruments, the tablatures indicated not the sounds but the strings and frets. In the 17th and 18th centuries chords were indicated by means of numbers placed over or under the bass notes (the figured bass).

From the late tenth century staffless znamennoe, or kriukovoe, notation was used in the Orthodox Church in ancient Rus’. In the 16th and 17th centuries there was a gradual shift from kriukovoe notation to the five-line staff.

Modern notation graphically indicates the pitch of the notes and their metric and rhythmic relationship. Together with the well-developed system of markings for tempo, dynamics, and expression, it makes possible a precise but not overly restrictive representation of a musical work. Although the performer does not depart from the written notes, he lends his own interpretation to a work. Exponents of 20th-century avant-garde musical tendencies have introduced new markings for the performer; however, these are not widely used. Some 20th-century composers have almost entirely abandoned the traditional forms of notation, providing in the written music only hints for the performer. There is a special system of notation for the blind.


Niurnberg, M. Notnaia grafika. Leningrad, 1953.
Wolf, J. Handbuch der Notationskunde, vols. 1–2. Leipzig, 1913–19.


The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.


(computer science)
The use of symbols to denote quantities or operations.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


How a system of numbers, phrases, words or quantities is written or expressed. Positional notation is the location and value of digits in a numbering system, such as the decimal or binary system.
Copyright © 1981-2019 by The Computer Language Company Inc. All Rights reserved. THIS DEFINITION IS FOR PERSONAL USE ONLY. All other reproduction is strictly prohibited without permission from the publisher.
References in periodicals archive ?
10 Helmut Hell, 'Zu Rhythmus und Notierung des "Vi Ricorda" in Claudio Monteverdis Orfeo', Analecta musicologica, xv (1975), 87-157; Wolf Frobenius, 'Zur Notation eines Ritornells in Monteverdis L'Orfeo', Archiv fur Musikwissenschaft, xxviii (1971), 201-4; Carl Dahlhaus, 'Zur Geschichte des Taktschlagens im fruhen 17.
More significantly, he completely eliminated most of the step symbols from the notations, having outlined rules for `default' steps in the introductory material;(37) only nontravelling steps (jumps in place, balances and pas de rigaudon), and hand and arm motions, were notated.
Given the rivalry between Frege and Husserl, and the rivalry between the traditions that emanated from both thinkers, it is highly appropriate to provide such a notation for Husserl.
In contrast, the expert users of graphical notations were more consistent as a group, with different subjects choosing similar strategies.
The first sixty-one chapters provide accounts of Qing musical ceremonies, including procedures, lyrics, dance notation, instrumentation, and abundant pieces of jisiyue ([TEXT NOT REPRODUCIBLE IN ASCII], state sacrificial music), chaohuiyue ([TEXT NOT REPRODUCIBLE IN ASCII], court assembly music), yanxiangyue ([TEXT NOT REPRODUCIBLE IN ASCII], banquet and entertainment music), daoyingyue ([TEXT NOT REPRODUCIBLE IN ASCII], leading and welcoming music), and xingxingyue ([TEXT NOT REPRODUCIBLE IN ASCII], processional music).
The author goes far beyond the title of the book; he gives an introduction not only to the theory of neumes, but also to the history of monodic music of Byzantine, Slavonic, and Latin churches and the notations used by them.
A 2015 national survey of university registrars found that about 40 percent didn't support including disciplinary notations on transcripts.
Compositional strategies and musical creativity when composing with staff notations versus graphic notations among Korean students.
These are ordered based on SLOM notation (D.Narashiman et al.,2013).
L'agence de notation Fitch Ratings a confirme les notes nationales a long et court terme de premier rang non garanties de Servicom a 'B (tun)' et les a retirees de la notation sous surveillance negative (RWN ), avec perspective stable.
Part Two of this volume shows the need to study individual centres in order to understand fully the cultural climate in which early music notations originated.