variation, in biology: see Darwinism.

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.

In biology, any difference between cells, individual organisms, or groups of organisms within a species caused either by genetic differences (variation in genotype) or by the effect of environmental factors on the expression of genetic potentials (variation in phenotype). Variation may be shown in physical appearance, metabolism, fertility, mode of reproduction, behaviour, learning and mental ability, and other obvious or measurable characters. Genotypic variations are caused by differences in number or structure of chromosomes or by differences in the genes carried by the chromosomes. Eye colour, body form, and disease resistance are genotypic variations. Phenotypic variations may result from factors such as climate, food supply, and actions of other organisms. Phenotypic variations also include stages in an organism's life cycle and seasonal variations in an individual. Because they do not involve hereditary alteration and in general are not transmitted to future generations, phenotypic variations are not important in evolution. Seealso polymorphism.

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Genetic makeup of an organism. The genotype determines the hereditary potentials and limitations of an individual. Among organisms that reproduce sexually, an individual's genotype comprises the entire complex of genes inherited from both parents. Sexual reproduction guarantees that each individual has a unique genotype, except for identical twins, who come from the same fertilized egg. Seealso phenotype, variation.

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Variation means a change within population

• Biodiversity
• Genetic diversity, differences within a species

Physics:

• Magnetic variation, difference between magnetic north and true north, measured as an angle
• Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the Moon

Mathematics:

• Bounded variation
• Calculus of variations, a field of mathematics which deals with functions of functions.
• Permutation

Statistics:

• Coefficient of variation in statistics, the magnitude of variance relative to the mean.
• Statistical dispersion, a notion of the extent of spread in measurements of a variable, quantified in the variance.

Arts:

• Variation (ballet), solo dance or dance figure
• Variation (music), formal technique where material is altered during repetition
• Variations (album), composed by Andrew Lloyd Webber
• Variation on a theme, in art history

Other:

• Variation (linguistics)
• Variation (game), modifications made to a game by a community of players (as opposed to a central authority)
• Variation (game tree), particular series of moves