Hardly a trace has survived of the development of music during the fifty years after the death of Guido, about 1050. The next works which cast light upon music were written about 1100. One is the _Musica_ of Johannes Cotto, the other the anonymous _Ad organum faciendum_ mentioned above. In both works a wholly new style of organum makes its appearance. In the first place, the organizing voice now sings normally above the _cantus firmus_, though the whole style is so relatively free that the parts frequently cross each other, sometimes coming to end with the organizing voice below. In the second place, contrary movement in the voice parts is preferred to parallel or oblique movement; that is, if the melody ascends, the accompanying voice, if possible, descends, and _vice versa_. Thus the two melodies have each an individual free movement and the science of polyphony is really under way. Moreover, they proceed now through a series of consonances. There are no haphazard dissonances as in the earlier free organum of both Hucbald and Guido. The organizing voice is no longer directed only in such a way as is easiest to avoid the hated tritone, but is planned to sing _always_ in consonance with the _cantus firmus_. The following example illustrates the movement of the parts in this new system: [Illustration: Music] 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