Bartolomé Ramos de Pareja

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Bartolomé Ramos de Pareja[1] (ca. 1440 – 1522) was a Spanish mathematician, music theorist, and composer. His only surviving work is the Latin treatise Musica practica.[2] By his own testimony at the end of his Musica practica, Ramos de Pareja was born in Baeza, possibly around 1440. Most of the biographical details of his life must be culled from this treatise. He says that he was a student of Juan de Monte and that he obtained the chair of music at the University of Salamanca for his commentaries on the works of Boethius (cum Boetium in musica legeremus). At Salamanca he had many debates with Pedro de Osma concerning his musical theories. In 1482, when he published his Musica, he revolutionarily proposed a new, five-limit division of the monochord, breaking from the Pythagorean system that had dominated the medieval ars antiqua through Boethius and Guido of Arezzo. This system of musical tuning yielded consonant perfect fourths and fifths, but the thirds and sixths were rough.[3] Ramos de Pareja's new division was only slowly accepted. Afterwards he worked in Italy, primarily at Bologna, where his theories engendered serious controversy, even polemics, from conservatives such as Franchino Gaffurio. After a long stay there he moved to Rome, where he died shortly after 1521. Ramos de Pareja sought to heal the divide between music in theory and in practice. To this end he sought to render the dissonant thirds and sixths consonant. He proposed the intervals 5/4, 6/5, 5/3, and

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