In music, variation is a way of organizing a piece of music by taking a tune (a theme) and then repeating it in several different ways. It is often called Theme and Variations.
Many composers wrote pieces which are examples of Theme and Variations. Sometimes the theme is one they made up, at other times they took a theme that another composer had already written and then made variations on it.
There are lots of ways of varying a tune, and each variation will change it in a different way. A variation may play the tune much faster or much slower, it may change the tune by adding extra sharps and flats or other ornamental notes, or by playing the tune in octaves. It may change the harmony or the rhythm or use different instruments. It may combine the tune in different parts (counterpoint).
Composers have used variations in music for centuries. In the Renaissance and Baroque periods composers wrote variations on a short tune in the bass which was repeated again and again. This was called a ground bass or sometimes it was a passacaglia or chaconne. Renaissance composers also liked writing what they called “divisions”. This meant varying a tune by playing it, for example, at twice the speed or half the speed etc. so that crotchets (quarter notes) became minims (half notes) or quavers (eighth notes).
George Frideric Handel wrote a famous set of variations for harpsichord called Harmonious Blacksmith, and Johann Sebastian Bach wrote the Goldberg Variations, which was a set of 30 variations: a very long piece of music. It was written for a man who found it difficult to sleep at night, so he would ask his harpsichord player, whose name was Goldberg, to play to him.
Many composers from the Classical, Romantic and modern periods wrote sets of variations. Wolfgang Amadeus Mozart wrote several, one of which was based on a French folktune which we know in Britain as “Twinkle, twinkle little star”. Beethoven wrote several wonderful sets of variations. Many of them were for piano, but he also used the form in other pieces e.g. the slow movement of his Ninth Symphony. Schubert often wrote variations on tunes from his own songs.