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, in music
variation, in music, a compositional device in which certain features of a musical unit, e.g., phase, are altered while others are retained in a subsequent statement of the unit. Modifications include melodic, harmonic, and rhythmic. Variation is fundamental in Western music, serving to identify the unique features of a composition by partitioning those features. Gregorian chant exhibits much melodic variation, and all music from the Middle Ages through the 20th cent. employs the technique in some form. Specifically the term refers to a musical form, also called “theme and variations,” in which the varied item is an entire brief movement. The form originated in baroque dance suites, in which all movements have the same theme, and was popular during the 18th and 19th cent. Bach's Goldberg Variations and Beethoven's Diabelli Variations are famous examples of the genre.
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The periodic inequality in the Moon's motion that results from the combined gravitational attraction of the Earth and Sun. Its period is half the synodic month, i.e. 14.77 days, and the maximum longitude displacement is 39′29″.9. See also annual equation; evection; parallactic inequality; secular acceleration.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006


Repetition of a theme with embellishments in rhythm, details, and materials while keeping the essential characteristics of the original. See also: Theme
Illustrated Dictionary of Architecture Copyright © 2012, 2002, 1998 by The McGraw-Hill Companies, Inc. All rights reserved
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



(biology), the diversity of characters in individuals and groups of individuals of any degree of kinship. Variation is characteristic of all living organisms; hence, there are no individuals in nature that are identical in all characters. The term “variation” is also used to designate the ability of living organisms to respond to environmental influences with morphophysio-logical changes and to characterize the transformation of the forms of living organisms in the process of their evolution.

Variation may be classified according to the causes, nature, and character of the variability and also according to the purposes and methods of research. The following types of variation are distinguished: genetic variation (genotypic) and nongenetic variation (paratypic), individual and group variation, discontinuous (discrete) and continuous variation, qualitative and quantitative variation, independent variation of various characters and correlative variation, directed (determined, according to C. Darwin) and undirected (undetermined, according to C. Darwin) variation, and adaptive and nonadaptive variation. The most significant types of variation for solving the general problems of biology, and especially of evolution, are genetic and nongenetic variation on the one hand and individual and group variation on the other. All types of variation may be found under genetic and nongenetic variation and group and individual variation.

Genetic variation arises as a result of various types of mutations and their combinations in subsequent interbreeding. In every group of individuals existing over a sufficiently long period of time (sequences of generations) various mutations arise spontaneously and undirected, which subsequently combine, more or less randomly, with characters already present in the genetic pool. Variation resulting from the appearance of mutations is called variation through mutation while that conditioned by subsequent recombination of genes as a result of interbreeding is called variation through recombination.

The multiplicity of individual differences is based on genetic variation, including (1) distinct qualitative differences that are not connected to one another by transitional forms, as well as purely quantitative differences that form continuous sequences in which close members of the sequence may differ very little from one another; (2) changes in certain isolated characters (independent variation), as well as interrelated changes in a series of characters (correlative variation); and (3) changes that have adaptive significance (adaptive variation), as well as “indifferent” changes or even ones that decrease the vitality of their bearers (nonadaptive lethal variation). All these types of genetic changes constitute the substance of the evolutionary process. In the individual development of an organism, the manifestation of hereditary characters is always determined not only by the basic genes responsible for the given characters but also by their interaction with many other genes that make up the genotype of the individual and by the conditions of the external environment in which the organism develops.

The concept of nongenetic variation includes those changes in characters that are produced in individuals or in certain groups of individuals by the action of external factors (nutrition, temperature, light, humidity). Such nongenetic characters (modifications) are not transmitted by heredity in their concrete manifestations in each individual. They develop in individuals of succeeding generations only under the same conditions in which they arose. Such variation is also called epigenetic variation. For example, the coloration of many insects darkens at low temperatures and lightens at high ones; however, their offspring will have the coloration in accordance with the temperature at which it has developed, regardless of the coloration of the parents. There exists still another form of nongenetic variation—so-called protracted modifications—often found in unicellular organisms and occasionally in multicellular ones. They arise under the influence of external factors (for example, temperature or chemical factors) and are expressed in qualitative or quantitative deviations from the original form, which usually gradually disappear in subsequent reproduction. Protracted modifications are apparently based on changes of the stable cytoplasmic structures.

There is a close connection between nongenetic and genetic variation. There are no nongenetic (in the literal sense) characters, since nongenetic changes are a reflection of the genetically conditioned capacity of organisms to respond with definite changes in their characters to various factors in the external environment. At the same time, the limits of nongenetic changes are determined by the reaction norm of the genotype to environmental conditions.

Genetic and nongenetic variation are studied by investigating the differences in characters among certain individuals of a population (individual variation) and the differences among populations (group variation); individual variation also underlies any intergroup difference. Even within a closely related group there are no absolutely identical individuals that would not vary in the degree of expression of any genetic or nongenetic character. In view of the complexity of the organization of living systems, even in genotypically identical (for example, monozygotic twins) individuals that develop under practically identical conditions one can always discover insignificant morphophysiological differences associated with inevitable fluctuations in environmental conditions and in the processes of individual development.

Group variation includes the differences among aggregates of any rank—from differences among small groups of individuals within a population to differences among the kingdoms of living nature (animals and plants). In essence, the entire taxonomy of organisms is constructed on the comparative study of group variation. Of special significance in studying the triggering mechanisms of the evolutionary process are various forms of intraspecific group variation. Most of the species are divided into subspecies or geographic races. In the event of the complete isolation of geographic forms, they may differ markedly in one or several characters. Populations that inhabit extensive territories and are not separated by sharply isolating barriers may (owing to mixing and interbreeding) gradually merge, forming a quantitative gradient in certain characters (clinal variation). Geographic variation, including clinal variation, under natural conditions is the result of the effect of isolation, natural selection, and other factors of evolution that lead to the division of an original group of individuals in the course of historical formation into two or several groups differing in the numerical proportions of their genotypes.

In some instances, the differences among groups of individuals within a species are unrelated to the differences in their genotypic composition but are conditioned by modificatory variation (various reactions of similar genotypes to different external conditions). So-called seasonal variation occurs as a result of the influence of various weather conditions on the development of certain generations (for example, in some insects and herbaceous plants that produce two generations per year, the spring and autumn populations differ from one another in a number of characters). Sometimes, seasonal forms may be the result of the selection of different genotypes (for example, early- and late-flowering forms of grasses on haymaking meadows: over many generations, individuals that flowered in the summer, the time of hay mowing, were eliminated). Of great interest is ecological variation—differences between groups of individuals of one species that grow or live in different places (highlands and lowlands, marshy and dry areas). Often such forms are called ecotypes. The emergence of ecotypes may also be the result of modificatory changes, as well as of the selection of genotypes that are better adapted to local conditions. Various forms of polymorphism (variability within a population) are conditioned by genetic variation. In some populations, one observes the existence of two or more clearly distinguishable forms (for example, in almost all populations of bipunctate ladybugs, one finds the black form with red dots and the red form with black dots). Various evolutionary mechanisms may underlie this phenomenon: different adaptation of coexisting forms to conditions of various seasons of the year; increased viability of heterozygotes, in whose offspring both homozygotic forms are constantly split; or other, as yet insufficiently studied, mechanisms. Thus, both group and individual variation include changes that are genetic as well as nongenetic in nature.

Contrasted to the independent variation of characters is correlative variation—interrelated change of various characters: the relationship between growth and weight of the individual (positive correlation) or between the rate of cell division and the size of the cells (negative correlation). Correlations may be conditioned by purely genetic causes (pleiotropy), or by the interde-pendencies of processes of establishing certain characters in the development of the individual (ontogenetic correlation), or by similar reactions of various characters to the same external influences (physiological correlation). Finally, correlations may reflect the history of the origins of populations from a mixture of two or more forms, each of which contribute complexes of interrelated characters rather than separate characters (historical correlation). The study of correlative variation has great significance in paleontology (for example, in reconstructing extinct forms from certain fossil remains), anthropology (in reconstructing facial features from a study of the skull), selection and medicine.

The principal methods of studying variation are the comparative-descriptive and the biometric methods. These two methods permit investigation of the paratypic as well as genotypic components of the integral phenotypic variation. Thus, the former may be studied by comparing genotypically identical clones and pure lines developing under different conditions. It is more difficult to distinguish purely genotypic variation from the phenotypic variation. It is possible to do this on the basis of biometric analysis. The determination of the percent of convergence of certain characters in monozygotic and dizygotic twins is used in medical genetics for the same purposes.

Heredity and variation of living organisms are sometimes juxtaposed as “conservative” and “evolutionary” principles. In reality, however, they are very closely connected. Relative instability of the genotype favors mutations that lead to variation through recombination—that is, genotypic variation as a whole. Paratypic (nongenetic) variation is merely the result of the relative stability of the genotype in determining the reaction norms in ontogenesis during the development of the characters of individuals. The possibility of the experimental influence on genetic as well as nongenetic variation follows from this. The former may be strengthened by the influence of mutagenic factors (radiation, temperature, chemical substances). The scope and direction of variation through recombination may be controlled by means of artificial selection. Nongenetic variation may be influenced by changing the environmental conditions (nutrition, light, humidity) under which the development of the organism occurs.

A precise conception of the categories and forms of variation is necessary in the construction of evolutionary schemes and theories (since the phenomena of heredity and variation lie at the root of the evolutionary process) and in the practical selection of plants and animals and in the study of various problems in medical geography and population anthropology.


Filipchenko, Iu. A. Izmenchivost’ i melody ee izucheniia, 2nd ed. Leningrad, 1926.
Chetverikov, S. S. “O nekotorykh momentakh evoliutsionnogo protsessa s tochki zreniia sovremennoi genetiki. ”Zhurnal eksperimenta’noi biologii, 1926, vol. 2, no. 1.
Johannsen, W. Elementy tochnogo ucheniia ob izmenchivosti i nasledst-vennosti s osnovami variatsionnoi statistiki. Moscow-Leningrad, 1933.
Johannsen, W. O nasledovanii v populiatsiiakh i chistykh liniiakh. Moscow-Leningrad, 1935.
Haldane, J. Faktory evoliutsii. Moscow-Leningrad, 1935. (Translated from English.)
Darwin, C. “Proiskhozhdenia vidov….” Soch., vol. 3. Moscow, 1939.
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Variation in microorganisms. In microorganisms, as in other organisms, a distinction is made between nongenetic and genetic variation. Any morphological or physiological character may undergo change: the size and shape of microorganisms and the form and pigmentation of their colonies, their ability to assimilate or synthesize various organic substances, their pathogenicity, and so forth.

Genetic variation in microorganisms is the result of mutations that arise spontaneously or are produced by physical or chemical mutagens (ultraviolet rays, ionizing radiation, ethylenimine). In mutants such quantitative characters as the ability to biosynthe-size amino acids, antibiotics, enzymes, vitamins, and the like may be sharply intensified or decreased. There also arise deficient mutants, which are capable of growing only with the addition of certain amino acids, purines, pyrimidines, and the like to the medium.

Microorganisms multiply very rapidly. It is therefore much easier to study all forms of variation in them and to effect artificial selection of beneficial mutants. Thus, in continuous cultur-ing in a medium containing, for example, an antibiotic, phenol, or mercuric chloride, one may readily obtain forms that are resistant to the given substance (adaptive variation). Also observed in microorganisms are interrelated changes (correlative variation). Thus, the emergence in pathogenic microbes of rough colonies is accompanied by a decrease in their immunogenicity. In microorganisms that have a true sexual process (certain molds and sporogenic yeasts), crossbreeding is possible, accompanied by a recombination of genes and the production of hybrids. Such hybrids cannot be produced in Fungi Imperfecti and in bacteria, which lack a true sexual process.


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


McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


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The angular difference between the direction of true north and magnetic north at any given point. It is measured in degrees east or west according to whether magnetic north lies east or west of this north. Variation is determined by the geographical location of the aircraft and is not affected by the aircraft heading. The variation indicated on a map or a chart is not a fixed quantity but is subject to change. Variation is indicated by dashed lines on maps and charts. All maps and charts also indicate the rate of the annual change of variation.
An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved


1. Music
a. a repetition of a musical theme in which the rhythm, harmony, or melody is altered or embellished
b. (as modifier): variation form
2. Biology
a. a marked deviation from the typical form or function
b. a characteristic or an organism showing this deviation
3. Astronomy any change in or deviation from the mean motion or orbit of a planet, satellite, etc., esp a perturbation of the moon
4. another word for magnetic declination
5. Ballet a solo dance
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
In stage 1, they used mutagenic PCR to increase variation in the YFP gene.
The Onodi cells lie in close proximity to the optic nerve and carotid canal, which emphasizes the importance of considering this anatomical variation prior to any surgical intervention in the vicinity.
The OECD identified a common set of medical procedures and interventions for analysis of intracountry variation, and some optional additional procedures.
Gage R&R =Variation due to R and R / (Measurement + part variation).
Although our study did not address it, we also wish to propose the consistent use of terms and symbols for several other aspects related to BV: analytical variation (imprecision, precision, and analytical variability), reference change value (critical difference), and index of individuality (individuality index).
(1) Regarding the concern about broad mean corpuscular volume (MCV) intraindividual biologic variation (CVi), we have reexamined our MCV data.
This issue does not consider the role of assembly process variation and measurement error in the assembly modelling, whereas, the effect of assembly process variation and measurement error on final product is the objective of next issue.
Sectional and en route charts contain dashed lines showing the amount of variation. These lines are called "isogonic lines" unless it is indicating a zero variation, then it is called an "agonic line." A pilot uses these lines to correct the true course he drew on a chart for variation.
Liebermann has a remarkable gift for texture, and can cast a haunting and hypnotic spell (the creeping eighth note counterpoint in variation V or the sense of suspension created in variation VII), generate breathless excitement (the parallel sixteenth note runs in variation III marked Presto), or convey an easy-going romp (the bi-tonal stride piano-style of variation VI).
The two greatest are undoubtedly Bach's Goldberg Variations and those Beethoven composed to an 1819 commission from the publisher Anton Diabelli, who had the shrewd idea of inviting various fashionable composers, including Schubert and the eightyear-old Liszt, each to compose a variation on a tawdry little waltz tune he himself had composed.