Meanwhile, long before Guy of Chalis had written what may be taken as the final word on organum, the new art which was destined to supplant it was developing both in England and in France. Two little pieces, one _Ut tuo propitiatus_, the other _Mira lege, miro modo_, have survived from the first part of the twelfth century. Both are written in a freely moving style in which the use of concords and discords appears quite unrestricted. Moreover, the second of them is distinctly metrical, and in lively rhythm. It is noted with neumes on a staff and the rhythm is evident only through the words, for the neumes gave no indication of the length or shortness of the notes which they represented, but only their pitch. Now in both these little pieces there are places where the organizing voice sings more than one note to a note of the _cantus firmus_ or _vice versa_. So long as composers set only metrical texts to music the rhythm of the verse easily determined the rhythm in which the shorter notes were to be sung over the longer; but the text of the mass was in unmetrical prose, and if composers, in setting this to music in more than one part, wished one part to sing several notes to the other’s one, they had no means of indicating the rhythm or measure in which these notes were to be sung. Hence it became necessary for them to invent a standard metrical measure and a system of notation whereby it could be indicated. Their efforts in this direction inaugurated the second period in the history of polyphonic music, which is known as the period of measured music, and which extends roughly from the first half of the twelfth century to the first quarter of the fourteenth, approximately from 1150 to 1325. IV Our information regarding the development of the new art of measured music comes mainly from treatises which appeared in the course of these two centuries. Among them the most important are the two earliest, _Discantus positio vulgaris_ and _De musica libellus_, both anonymous and both belonging to the second half of the twelfth century; the _De musica mensurabili positio_ of Jean de Garlandia, written about 1245; and at last the great _Ars cantus mensurabilis_, commonly attributed to Franco of Cologne, about whose identity there is little certainty, and the work of Walter Odington, the English mathematician, written about 1280, _De speculatione musices_. As the earlier theorists succeeded in compressing a certain kind of music within the strict limits of mathematical theory, so the mensuralists finally bound up music in an exact arbitrary system from which it was again to break free in the so-called _Ars nova_. But the field of their efforts was much larger than that of the organum and the results of their work consequently of more lasting importance.