Bright new history traces music through the ages; James Galway's Music in Time, by William Mann. New York: Henry N. Abrams. 384 pp. $22.50.

In an age when interest in personalities runs high, it is not surprising to find a history of music concentrating heavily on the lives of composers. This anecdotal survey of major eras and themes in the development of composed Western music was developed with the television series of the same name, hosted by flutist-conductor James Galway and written by London Times music critic William Mann.

Mann concentrates on the personal, social, and musical influences that shaped the composers' styles. ''Every piece of music ever composed was fired by a particular moment in history, and a place, and a creative individual,'' he says.

This is a lively narrative in which analytical and descriptive criticism is only rarely marred by less useful personal opinion written with judgmental fervor. We see the music of each composer take shape as a reflection of his life , his environment, and his contact with other composers. Guillaume Dufay, for instance, in 1474 senses death and writes his own funeral mass; Giuseppe Sammartini, an 18th-century oboist and composer, works as musician and major-domo of the household for the Prince of Wales; Joseph Haydn plays string quartets as first violin with violist Wolfgang Mozart, second violinist Ditters von Dittersdorf, and cellist Johann Vanhall; early 20th-century composers Stravinsky, Satie, and Hindemith struggle for new expression amid the horrors of the world wars and the innovations of the Machine Age.

Portraits or photographs, samples of handwritten scores, and quotations from personal letters make each person come to life.

Only the broadest outlines of music theory are suggested in this book, and only when necessary to understand compositional innovations. More detailed histories of selected instruments, and important styles of composition and performance, are left to italicized inserts in the text.

Mann seems to realize the difficulty of describing the quality of music in words. He concentrates more on composers' motivations than on wordy descriptions of their sound. For the dedicated reader, a list of recordings is provided to illustrate each chapter.

Throughout, the book reflects its title, ''Music in Time.'' Mann points out how vocal and instrumental music changes and develops as a product of history. He shows how fashion, circumstance, and pure chance help determine what music becomes famous and popular or what work of equal genius might lie neglected.

We see Pope Gregory's modes and the ancient pentatonic scale come full circle in the tunes of the Beatles. Improvisation reaches one peak in J. S. Bach and the High Baroque and another peak in 20th-century jazz.

Finally, we understand our own century as being unique in its persistent use of dissonance and in its reverence for ''old'' music (as opposed to that freshly composed for the moment). In conclusion, Mann suggests that ''our receptivity has to move forward'' while ''so much experiment in so many directions'' gradually sorts itself out ''along lines accessible to every interested listener.''