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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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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.



(computer science)
The use of symbols to denote quantities or operations.


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.
References in periodicals archive ?
Of course I get pushback from some Conservatory-trained students who want to dig into technique or show off their theory prowess, but my response is always the same: graphic notation is what you need it to be.
Our new class notations are Lloyds Registers response to that evolution and ensure the role of class continues to deliver stakeholder assurance.
We are told in the preface that the aim of this volume is 'to fill an improbable lacuna: the study of the graphics of music, of notation as calligraphy'.
Troelsgard has attempted to produce a diplomatic transcription method of appeasement between West and East by including the Byzantine neumatic notation over his Western staff notation.
A characteristic of oral notations in India is that they tend to capture fully only one parameter of the music: in melodic notation, the sequence of basic pitches, without detailed indications of ornamentation, rhythm, or even octave register; in drum notations, the sequence of sonorities (produced by different techniques of striking the drum-heads), without precise indication of rhythm.
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.
Byzantine, Slavonic, and Latin neume notations are presented in three major chapters.
327 includes chant notated in Aquitanian notation and has characteristics supporting the likelihood of Iberian provenance around 1200.
As music teachers, we must make our students aware of the rhythm all around us, help them understand the importance of rhythm in the music they play and hear and teach them to respond correctly to the rhythmic notation they read--all while keeping ourselves energized and our students engaged.
Yet his collection of pencil and pen drawings, more than twenty of which were exhibited here alongside his better-known dance notations, does manage to surprise.
When Sergeyev died in 1951, he bequeathed all his scores and notations to Inglesby, who later sold them to the Harvard library, where they remain.
In particular, I hoped to show how recognition of the applicability of the traditional meanings of proportional notations immediately resolves ostensible inconsistencies in the notation and restores sense and regularity to music hitherto presented in transcriptions that are irregular and implausible, and also, in the case of the Sonata sopra Santa Maria, even makes possible the revelation of an underlying proportional foundation for the architecture of this movement.