variation

One of the earliest musical forms. A theme or melody is first presented in a straightforward manner and then repeated as often as the composer wishes but each time it is varied in one or more ways. The theme is usually easily recognizable; it may be a popular tune or – as a gesture of respect – the work of a fellow composer; for example, Johannes Brahms's Variations on a Theme by Haydn (1873), based on a theme known as the St Antony Chorale, although it may also be an original composition. The principle of variations has been used in larger-scale and orchestral works by modern composers, for example Arnold Schoenberg's Variations for Orchestra (1928).

variation

In ballet, a solo dance, unless otherwise designated.

variation

In biology, a difference between individuals of the same species, found in any sexually reproducing population. Variations may be almost unnoticeable in some cases, obvious in others, and can concern many aspects of the organism. Typically, variations in size, behaviour, biochemistry, or colouring may be found. The cause of the variation is genetic (that is, inherited), environmental, or more usually a combination of the two. Some variation is the result of the environment modifying inherited characteristics. The origins of variation can be traced to the recombination of the genetic material during the formation of the gametes, and, more rarely, to mutation.

An example of inherited variation is blood groups in humans. An extreme example of variation produced by the environment is the loss of a part of the body from injury. An example of variation that involves the environment modifying inherited characteristics is height. The characteristic of being tall or short is inherited, but the availability of food in the environment determines the actual height of the individual.

Inherited variation If the variation is inherited, a variant can become more common over a number of generations as a result of natural selection. This is evolution. Inherited variation is needed for evolution to be able to occur. Variation that can be inherited is produced in several ways. Accidental changes in DNA or chromosomes (mutation) produce variation.

In sexual reproduction male and female gametes (see ovum) combine. Gametes are produced by meiosis. Usually the male and female gametes are produced by two different individuals. If so, sexual reproduction combines inherited information from the two parents. It produces new combinations of genes, which may never have occurred before. This results in variation.

Artificial selection Artificial selection by humans can create new varieties of plant and animal from the natural variation in a species.

variation

In mathematics, a practical relationship between two variables. Direct variation (when the values of the variables maintain a constant ratio) corresponds to y = kx on a straight line graph, for example distance travelled at a steady speed. Inverse variation (when an increase in the value of one variable results in a decrease in that of the other) corresponds to y =k/x on a rectangular hyperbolic graph, for example the price of an article and the quantity that can be bought for a fixed sum of money. In problems of direct and inverse variation, the first step is to find the value of k.