French composers of the ars nova, such as Phillipe de Vitry and Guillaume de Machaut, used isorhythm as a means of unifying their compositions.
By the early fourteenth century, composers began to treat rhythm independently of pitch and text. The music theorist Franco of Cologne established rules for the time values of single notes, ligatures, and rests in his treatise Arts canus mensurabilis (ca. By the thirteenth century, formalized music composition began to replace improvisation and the role of composer and performer became increasingly distinct. Prior to the development of the score, music was learned by rote and generally improvised and embellished by the performing musician. His system employed a staff accompanied by a clef making it possible for a composer to notate a score so that it could be performed by someone other than the composer. Over a thousand years later, the work of music theorists such as Guido d'Arezzo established the framework for our conventional system of music notation. Although we have numerous treatises on music theory dating from Greek antiquity, the Greeks left no clues if mathematical procedures were applied to the composition of music. Their educational system, the quadrivium, was based on the study music, arithmetic, geometry, and astronomy.
The Greeks believed that the understanding of numbers was key to understanding the universe. 500 B.C.) documented the relationship between music and mathematics that laid the foundation for our modern study of music theory and acoustics. The Greek philosopher, mathematician, and music theorist Pythagoras (ca. 2.2 A Brief History of Algorithmic Processes Applied to Music Composition
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