Cotto is rather indifferent and, of course, dry about the whole subject of _organum_. It occupied but a chapter in his rather long treatise. But the 'Anonymus’ is full of enthusiasm and loud in his praises of this method of part-singing and bold in his declaration of its superiority over the unaccompanied plain-song. Such enthusiasm smacks a little of the layman, and is but another indication of the real origin of _organum_ in the improvised descant of the people, quite out of the despotism of theory. The Anonymus gives a great many rules for the conduct of the organizing or improvising voice. He has divided the system into two modes, determined by the interval at which the voices start out. For instance, rules of the first mode state how the organizing voice must proceed when it starts in unison with the _cantus firmus_, or at the octave. If it starts at the fourth or fifth it is controlled by the rules of the second mode. There are three other modes which are determined by the various progressions of the parts in the middle of the piece. The division into modes and the rules are of little importance, for it is obvious that only the first few notes of a piece are definitely influenced by the position at which the parts start and that after this influence ceases to make itself felt the modes dissolve into each other. Thus, though the enthusiasm of the Anonymus points to the popularity of the current practice of organizing, whatever it may have been, his rules are but another example of the inability of theory to cope with it. Still this theoretical composition continued to claim the respect of teachers and composers late into the second half of the twelfth century.
A treatise by Guy, Abbot of Chalis, about this time, is concerned with essentially the same problems and presents no really new point of view. He is practically the last of the theorizing organizers. Organum gave way to a new kind of music. In the course of over two hundred years it had run perfectly within the narrow limits to which it had been inevitably confined, and the science of it was briefly this: to devise over any given melody a counter-melody which accompanied it note by note, moving, as far as possible, in contrary motion, sinking to meet the melody when it rose, rising away from it when it fell, and, with few exceptions, in strictest concord of octaves, fifth, fourths, and unison. Rules had been formulated to cover practically all combinations which could occur in the narrow scheme. The restricted, cramped art then crumbled into dust and disappeared. Again and again this process is repeated in the history of music. The essence of music, and, indeed, of any art, cannot be caught by rules and theories. The stricter the rules the more surely will music rebel and seek expression in new and natural forms. We cannot believe that music in the Middle Ages was not a means of expression, that it was not warm with life; and therefore we cannot believe that this dry organum of Hucbald and Odo, of Guido of Arezzo, of Guy of Chalis, which was still-born of scholastic theory, is representative of the actual practice of music, either in the church or among the people. On the other hand, these excellent old monks were pioneers in the science of polyphonic writing. Inadequate and confusing as their rules and theories may be, they are none the less the first rules and theories in the field, the first attempts to give to polyphony the dignity and regularity of Art.