In Chapter VI we traced the beginnings of polyphony in the stiff organum, and the growth of the so-called mensural system by which all music was reduced to triple rhythm and bound by mathematical laws, indifferent to beauty, relentlessly rigid and monotonous. During this period the musical centre of Europe was Paris, where the organists of Notre Dame were the most influential composers. Here the reaction against the system found voice in theoretical discussion, though this again was probably only the reflection of what had been going on in actual practice, both in France and elsewhere. Indeed, it is claimed by some writers (notably Riemann) that certain composers of Florence, under the direct influence of Troubadour song, were the first to throw off the fetters of musical dogma; England, too, has a serious claim for priority in the new movement,[86] which was influenced everywhere by the spontaneous florescence of secular song. But the name _ars nova_, by which the reform was designated by its protagonists in contradistinction to the _ars antiqua_ of their Franconian predecessors, has led historians to connect it with the probable author of the treatise entitled 'The Ars Nova.’ Philippe de Vitry, bishop of Meaux (1290-1361), is said to be the author of this treatise, as well as of several others dealing with measured music, 'proportions’ and the relative value of the symbols of notation. In it he advocates counterpoint for several voices, rhythmic variety of a free use of chromatic alterations. None of his own compositions has been preserved to us, however. Another writer, known by the name of Jean de Muris, left several works of similarly radical character. He is not to be confused, however, with a theorist of the same name designated as 'the Norman,’ who taught at the Sorbonne from 1321 on, and whose teaching was so conservative as really to constitute a reaction against the new method--the ars nova. This effort toward freedom was characterized, first by the reintroduction of duple time into church music, in which triple time, on account of its symbolistic connection with the Trinity, had long held the field; secondly, by the emancipation of individual voices by means of a greater variety of rhythm; thirdly, by the prohibition of parallel octaves and fifths;[87] and lastly, by the differentiation between half and full cadences,[88] which, in homophonic music--in plain-chant and in secular song--had long been recognized.