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Related to notation: scientific notation


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 ?
Some opponents of notation argue that a transcript notation serves as a permanent scarlet letter for a student and could forever disadvantage them in both the academic and employment sectors.
In Rankin's discussion of neumatic notations, she shows the strength of working on one centre of music notation and individual scribes, saying 'Because of the relation between music scripts and what they seek to record, those who wrote neumatic notation could exercise personal judgement about how they notated melodies, using writing to highlight specific musical issues, whether that be habits of performance practice or momentary reminders.
The practice of this oral heritage has been largely unbroken for centuries even within the reformed Chrysanthine notation of the nineteenth century.
Adopting a multi-linear development pattern allows Chrisomalis to show that numerical notation systems did not all stem from one source.
In composing the notation, Peter aimed to develop a system, which would allow people across the world to learn and perform African rhythms.
In the edition of The Standard Course that year Curwen allowed the tonic sol-fa notation to stop being merely a mnemonic aid to sight singing from the staff and to become an end in itself.
I revised the notation to make the quarter note the basic beat.
Gasser transcribes several pieces into modern notation that reveals a flexible rhythmic feeling.
However, my simplified notation would not take into account all the elements involved in remembering.
Coverage of more sheet music repertoires, including Chinese jianpu numbered notation, Turkish maqam music, Persian and Iranian music, and improved support for educational music.
ScoreCleaner Notes enables anyone who can whistle or sing a tune to have it rendered instantly into correct notation and MIDI through their iPhone or iPad, publish to social media, sync it with ScoreCleaner, and extend it into a full score using ScoreCleaner or any other notation tool of choice.