<P> Many composers have taken pieces composed by others as a basis for elaboration . John Dowland's Lachrimae was frequently used by other composers as a basis for sets of variations during the 17th century . Composed in 1700, the final movement of Arcangelo Corelli's Violin Sonata Op. 5 No. 9 opens with this rather sparse melodic line: </P> <P> Corelli's fellow - composer and former student Francesco Geminiani produced a "playing version" as follows: </P> <P> According to Nicholas Cook, in Geminiani's version "all the notes of Corelli's violin line...are absorbed into a quite new melodic organization . With its characteristic rhythmic pattern, Geminiani's opening is a tune in a way that Corelli's is not...whereas in the original version the first four bars consist of an undifferentiated stream of quarter - notes and make up a single phrase, Geminiani's version has three sequential repetitions of a distinctive one--bar phrase and a contrasted closing phrase, producing a strongly accented down - beat quality ." " </P> <P> Jazz arrangers frequently develop variations on themes by other composers . For example, Gil Evans' 1959 arrangement of George Gershwin's song "Summertime" from the opera Porgy and Bess is an example of variation through changing orchestral timbre . At the outset, Evans presents a single variation that repeats five times in subtly differing instrumental combinations . These create a compelling background, a constantly changing sonic tapestry over which trumpeter Miles Davis freely improvises his own set of variations . Wilfrid Mellers (1964) wrote that "It called for an improviser of Davis's kind and quality to explore, through Gil Evans' arrangement, the tender frailty inherent in the' Summer - time' tune...Between them, solo line and harmonic colour create a music that is at once innocent and tense with apprehension". </P>

What does theme and variation mean in music