variation

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. The act, process, or result of varying.
2. n. The state or fact of being varied. See Synonyms at difference.
3. n. The extent or degree to which something varies: a variation of ten pounds in weight.
4. n. Magnetic declination.
5. n. Something slightly different from another of the same type.
6. n. Biology Marked difference or deviation from the normal or recognized form, function, or structure.
7. n. Biology An organism or plant exhibiting such difference or deviation.
8. n. Mathematics A function that relates the values of one variable to those of other variables.
9. n. Music A form that is an altered version of a given theme, diverging from it by melodic ornamentation and by changes in harmony, rhythm, or key.
10. n. Music One of a series of forms based on a single theme.
11. n. A solo dance, especially one forming part of a larger work.

Century Dictionary and Cyclopedia

1. n. The difference of offspring from the parent.
2. n. Statistical or formal abnormality in living beings, or the departure of individual organisms from the mean, average, or rule for the race, considered as a fixed standard or logical species which individual animals approach or from which they recede.
3. n. A change in a living being which is dne to its own activity as an individual, as contrasted with a change which is inherited. See the extract.
4. n. A congenital or germinal change in a living being, which is not due to its own activity and is transmitted to descendants, as contrasted with a change which comes about in it by its own activity and is not transmitted to descendants.
5. n. A change that may take place in an individual or a variety or species when its habitat changes.
6. n. The amount of change which a quantity suffers in an hour: as, the hourly variation of the sun's declination.
7. n. Variation which arises during the larval and later stages of development, as contrasted with variation which arises during the early embryonic stages.
8. n. The act or process of varying; partial change in form, position, state, or qualities; alteration; mutation; diversity; variance; modification: as, variations of color; the slow variation of language.
9. n. The extent to which a thing varies; the degree, interval, or amount of departure from a former condition, position, or relation; amount or rate of change: as, a variation of two degrees; a variation of twopence in the pound.
10. n. Difference.
11. n. Variance; dissension; discord.
12. n. In grammar, change of form of words, as in declension, conjugation, etc.; inflection.
13. n. In astronomy, any deviation from the mean orbit or mean motion of a heavenly body, occasioned by another disturbing body. When these deviations are compensated in comparatively short periods of time they are called periodic variations, but when the compensation requires an immense period of time for its consummation the variation is called a secular variation.
14. n. In physics and navigation, the deviation of a magnetic needle from the true north, denoted by the angle which the vertical plane passing through the poles of the needle freely suspended, and undisturbed by local attraction, makes with the geographical meridian of the place: generally and more properly called declination. The variation of the compass does not remain constantly the same in the same place, but undergoes certain diurnal, secular, and accidental changes. Of these the diurnal changes amount to only a small fraction of a degree; the secular change, however, may amount to 20 or 30 or more, and goes through a long cycle requiring for its completion some three or four centuries. Thus, in the year 1576, in London, the variation was 11' 15' east; in 1652 the needle pointed due north, after which time it traveled about 24½ to the westward (the maximum being in 1815); the variation is now considerably less, and is continually decreasing. It is very different, however, in different parts of the globe. In the eastern part of the United States the variation is now westerly, and has been increasing since the last decade of the eighteenth century; but the annual change is now less than it was fifty years ago. In the western United States the variation is easterly, and has been in general diminishing; for a region in the extreme southwest, however, the needle is now stationary. The accidental variations are such as accompany magnetic storms, and are most frequent and violent at periods of about eleven and a half years, corresponding to the sun-spot period. See declination, agonic, isogonic.
15. n. In biology, the act, process, or result of deviation from a given type of form or structure in a plastic vegetable or animal organization, by means of natural selection; or the sum of the phenomena resulting from the influence of conditions of environment, as opposed to those which would have been exhibited had the law of heredity alone been operative. See variability, 2, and variety, 6. Variation in the biological sense is the accomplishment of that which variability permits, environment requires, and selection directs; it covers the whole range of deviation from a given type, stock, or parent-form. Individual variation may be teratological, resulting in malformations or monstrosities, which are quite aside from the normal course of evolution, and probably never in perpetuity, though some freaks of nature, not decidedly pathological or morbid, are sometimes transmitted, as polydactylism in man, and the like. Another series of variations, less decidedly at variance with an ordinary development, and if not useless at least not hurtful to the organism, result in numberless sports, especially of cultivated plants and domesticated animals, which tend to perpetuation or may be perpetuated artificially. (See selection, 3 (artificial and methodical), sport, n., 8, and strain, 1.) The usual course of variation on a grand scale is believed to be by the natural selection of useful characters to be preserved and increased, with such decrease or extinction of their opposites as tends to their further improvement. The first decided steps in this direction are seeu in the (mainly geographical or climatic) varieties, races, subspecies, and conspecies of ordinary descriptive zoölogy and botany; a step further brings us to the species; and most biologists hold thatsuch increments of differences by insensible degrees have in fact resulted in the genus, the family, and all other distinctions which can be predicated among animals and plants. Variation is used in a more abstract sense, as nearly synonymous with variability: as, a theory of variation; and in a more concrete sense, like variety: as, this specimen is a variation of that one.
16. n. In music, a tune or theme repeated with changes, elaborations, or embellishments, especially when made one of a series of movements aiming to develop the capacities of a given subject. The impulse to compose sets of variations of a melody was one of the early fruits of the desire for extended works in which an artistic unity should be manifest. In the beginning of this century this impulse was doubtless indulged to excess, ingenuity of mechanical invention and the desire for executive display being unduly prominent. But essentially the idea of the repetition of a given theme with decoration and transformation is involved in the whole theory of thematic development. The particular devices used to produce variations—such as melodic figuration, alteration of harmonic structure, change of mode or tonality, change of rhythm, etc.—are too many to be enumerated. Variations were formerly called doubles.
17. n. In the calculus, an infinitesimal increment of a function, due to changes in the values of the constants, and affecting it, therefore, in different amounts for different values of the variables.
18. n. In algebra: The following of a + sign after a—sign, or vice versa, in a row of signs.
19. n. A linear arrangement of some of a given set of objects or of all. Thus, there are fifteen variations of the letters A, B, C, as follows: A, B, C, AB, BA, BC, CB, CA, AC, ABC, BCA, CAB, CBA, BAC, ACB.

Wiktionary

1. n. The act or state of varying; a partial change in the form, position, state, or qualities of a thing; modification; alternation; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.
2. n. A related but distinct thing.
3. n. nautical The angular difference at the vessel between the direction of true north and magnetic north. Also called magnetic declination.
4. n. board games a line of play that differs from the original
5. n. music a technique where material is repeated with alterations to the melody, harmony, rhythm, timbre, texture, counterpoint or orchestration.

GNU Webster's 1913

1. n. The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alteration; mutation; diversity; deviation.
2. n. Extent to which a thing varies; amount of departure from a position or state; amount or rate of change.
3. n. (Gram.) Change of termination of words, as in declension, conjugation, derivation, etc.
4. n. (Mus.) Repetition of a theme or melody with fanciful embellishments or modifications, in time, tune, or harmony, or sometimes change of key; the presentation of a musical thought in new and varied aspects, yet so that the essential features of the original shall still preserve their identity.
5. n. (Alg.) One of the different arrangements which can be made of any number of quantities taking a certain number of them together.

WordNet 3.0

1. n. an artifact that deviates from a norm or standard
2. n. an activity that varies from a norm or standard
3. n. the angle (at a particular location) between magnetic north and true north
4. n. a repetition of a musical theme in which it is modified or embellished
5. n. the process of varying or being varied
6. n. (ballet) a solo dance or dance figure
7. n. the act of changing or altering something slightly but noticeably from the norm or standard
8. n. (biology) an organism that has characteristics resulting from chromosomal alteration
9. n. something a little different from others of the same type
10. n. (astronomy) any perturbation of the mean motion or orbit of a planet or satellite (especially a perturbation of the earth's moon)
11. n. an instance of change; the rate or magnitude of change