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musical notation

musical 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. 525) applied the first 15 letters of the alphabet to the notes in use at the end of the Roman period. Notation of Gregorian chant was by means of neumes, which are thought to have been derived from symbols used in the Greek language to indicate pitch inflection. Neumes were certainly in use by the 6th cent., although the earliest extant manuscripts containing them are fragmentary ones from the 8th cent. These neumes indicated only the grouping of sounds in a given melody, evidently to recall to a singer the approximate shape of a melody already learned by ear.

Heighted neumes, arranged above and below a line, made the intervals of a melody more discernible in 10th-century notation, and by the end of the 12th cent. the staff perfected by Guido d'Arezzo was in use. Guido placed letters on certain lines to indicate their pitch, and thereby the pitch of the remaining lines and spaces. The letters evolved into the clef signs used today. Guido also invented a system of naming scale degrees using the initial syllables of the lines of a Latin hymn (ut, re, mi, fa, sol, la). Originally used for teaching sight singing, these or their derivatives are also used in some languages for naming absolute pitches.

A staff of five lines for vocal music was adopted in France and one of six lines in Italy. Instrumental music employed staves of varying numbers of lines until the 16th cent., when the five-line staff became the standard. Signs for chromatic alteration of tones appear almost from the beginning and had assumed their present shapes by the end of the 17th cent. The essential problems in pitch notation, the use of both lines and spaces to indicate successive scale degrees and the use of extra symbols to indicate raising or lowering a tone by a half step, were solved comparatively rapidly.

However, the evolution of the rhythmic notation used today took much longer than that for pitch. Mensural notation, in which each note has a specific time value, became a necessity with the development of polyphony. At first, certain patternings of neumes were used to represent the various rhythmic modes; later, in his Ars cantus mensurabilis (c.1280), Franco of Cologne created a clear indication for each note of its exact rhythmic length and selected certain neumes to represent tones of long and short duration. In his system, the long value was in principle equal to three of the short values.

In the 14th cent. Philippe de Vitry, author of Ars nova, which expands the system of Franco, codified the ready availability of duple divisions of the long and short notes. At the various rhythmic levels of a given piece either a 2:1 or a 3:1 relationship was implied, and a system of signs and colored notes developed for indicating which relationships were in force or were being temporarily altered.

In the 15th cent. numbers with the appearance of fractions indicated that one proportionality of rhythmic values was temporarily being substituted for another. Modern signatures evolved from these numbers. Bar lines, expression signs, and Italian terms to indicate tempo and dynamics came into use in the 17th cent. With the adoption of equal temperament and the major and minor modes, signatures indicating a major key or its relative minor became conventional. They assumed their present form during the baroque period.

The advent of aleatory music has produced notation systems, varying from piece to piece, indicating only approximate pitch, duration, and dynamic relations. Notation for electronic music is still not standardized but generally uses traditional reference symbols (staff and clef signs) in conjunction with specially adapted pitch and rhythm notation.

For a system of notation of lute and keyboard music, see tablature. See also score.


See W. Apel, The Notation of Polyphonic Music, 900–1600 (5th ed. 1961); C. F. A. Williams, The Story of Notation (1903, repr. 1969); E. Karkoschka, Notation in New Music (1972), G. Read, Music Notation (3d ed. 1972).

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A group of spectal lines usually in an emission spectrum that identifies a chemical – an atom or molecule, possibly ionized and/or in a rare isotopic form – in a star, stellar environment, galaxy, etc.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



in mathematics, a number characterizing a quadratic form. Every quadratic form with real coefficients can be reduced by a nonsingular linear transformation of variables with real coefficients to the form

The difference ρ – q between the number of positive and negative terms in this expression is called the signature of the quadratic form. The numbers ρ and q are independent of the means by which the quadratic form is reduced to the form (*).



a number placed at the lower left-hand corner of the first page of each sheet of printed pages and repeated with an asterisk on the third page. The signature is used as a control in arranging the sections of a publication before binding.

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


The characteristic pattern of a target as displayed by detection and classification equipment.
(graphic arts)
A folded, printed sheet, usually consisting of 16 or 32 pages, that forms a section of a book or a pamphlet; the sheet may have fewer pages, but is always in multiples of four.
For a quadratic or Hermitian form, the number of positive coefficients minus the number of negative coefficients when the form is reduced by a linear transformation to a sum of squares of absolute values.
For a symmetric or Hermitian matrix, the number of positive entries minus the number of negative entries when the matrix is transformed to diagonal form.
(naval architecture)
The graphic record of the magnetic properties of a vessel automatically traced as the vessel passes over the sensitive element of a recording instrument; more accurately called magnetic signature.
The identifying characteristics peculiar to each type of target which enable detecting apparatus, such as certain fuses, to sense and differentiate targets.
(quantum mechanics)
A quantum number α that characterizes a system with the symmetry of a prolate or oblate spheroid and satisfies the equation r = exp (-i πα), where r is the eigenvalue of the system under a rotation through 180° about an axis perpendicular to the symmetry axis.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


An example of infrared signature of a helicopter.
i. The characteristic pattern of a target displayed by detection and identification equipment. It can be a radar, IR (infrared), acoustic, or Doppler signature. See also radar signature.
ii. As it relates to air-photo interpretation, it is the visual characteristics of objects on an air photograph that allow one to differentiate them. These characteristics include the tone, shape, size, pattern, texture, and shadow. Tone refers to the relative brightness or colors of an object in an image. Generally, tone is a fundamental element for distinguishing between different targets or features. Variations in tone also allow the elements of the shape, texture, and pattern of objects to be distinguished. Shape refers to the general form, structure, or outline of individual objects. Shape can be a very distinctive clue for interpretation. Straight-edge shapes typically represent urban or agricultural targets, whereas natural features, such as forest edges, are generally more irregular in shape. The size of objects in an image is a function of scale. It is important to assess the size of a target relative to other objects in a scene to aid in the interpretation of that target. Pattern refers to the spatial arrangement of the visibly discernible objects. Typically, an orderly repetition of similar tones and texture will produce a distinctive and ultimately recognizable pattern. Orchards with evenly spaced trees and urban streets with regularly spaced houses are good examples of pattern. Texture refers to the arrangement and frequency of tonal variation in a particular area of the image. Rough textures would consist of a mottled tone where gray levels change abruptly in a small area, whereas smooth textures would have very little tonal variation. Shadow is also helpful in interpretation, as it may provide an idea of the profile and relative height of a target(s).
An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved


2. US the part of a medical prescription that instructs a patient how frequently and in what amounts he should take a drug or agent
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005


A set of function symbols with arities.


(Or sig) A few lines of information about the sender of an electronic mail message or news posting. Most Unix mail and news software will automagically append a signature from a file called .signature in the user's home directory to outgoing mail and news.

A signature should give your real name and your e-mail address since, though these appear in the headers of your messages, they may be munged by intervening software. It is currently (1994) hip to include the URL of your home page on the World-Wide Web in your sig.

The composition of one's sig can be quite an art form, including an ASCII logo or one's choice of witty sayings (see sig quote, fool file). However, large sigs are a waste of bandwidth, and it has been observed that the size of one's sig block is usually inversely proportional to one's prestige on the net.

See also doubled sig, sig virus.


A concept very similar to abstract base classes except that they have their own hierarchy and can be applied to compiled classes. Signatures provide a means of separating subtyping and inheritance. They are implemented in C++ as patches to GCC 2.5.2 by Gerald Baumgartner <>.
This article is provided by FOLDOC - Free Online Dictionary of Computing (


(1) See digital signature and email signature.

(2) A pattern used for matching. Also called a "fingerprint" or "definition." For example, antivirus companies maintain a database that contains the virus code (the "binary signature") of each of the known viruses. To detect a virus, the antivirus program looks for these code strings in executable programs. Spyware blockers that look for spyware and adware also use signature patterns.

An intrusion detection system also uses signatures, which are patterns that suggest an attack. For example, excessive logins that failed or the execution of certain programs.

(3) A unique number built into hardware or software for identification.

(4) A group of printed pages used in the construction of a book or booklet. Typically comprising 16 or 32 pages, signatures may also be 8, 12, 24, 48 or 64 pages long. The signature is printed on one large sheet of paper in a certain "imposition" order that, when cut and folded, results in the correct page sequence. The signatures are then bound together to make the final product.
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