The presence in the octatonic scale of the disagreeable tritone, marked with a star in the example, forced even Hucbald and Odo to make some provision for avoiding it. This consisted in limiting the movement of the 'organizing’ voice. It was not allowed to descend below a certain point in the scale. In those cases, therefore, in which the _cantus firmus_ began in such a way that the organizing voice could not accompany it at the start without sinking below its prescribed limit the organizing voice must start with the same note as the _cantus firmus_ and hold that note until the _cantus firmus_ had risen so that it was possible for the organizing voice to follow it at the interval of the fourth. In the same way the parts were forced to close at the unison if the movement of the _cantus firmus_ did not permit the organizing voice to follow it at the interval of a fourth without going below its limit. The following example will make this clear:

In this case it will be noted that the movement of the parts is no longer continuously parallel, but that there are passages in which it is oblique. Indeed it is hardly conceivable that strict parallel movement was ever adhered to in anything but theory. It is interesting to observe how even in theory it had to give way, and how by the presence of the tritone in the scale the theorists were practically forced into a genuine polyphonic style. The strict style, as we have already remarked, was hardly more polyphonic than the magadizing of the Greeks; for, though the voice parts are actually different, still each is closely bound to the other and has no independent movement of its own; but in the freer style there is a difference if not an independence of movement.

The Art of Music - Vol. 1 — Part 136

In connection with this example it is also well to note that through the oblique movement the parts are made to sound other intervals than the fourth or fifth or unison, which with the octave were regarded for centuries as the only consonances. At the first star they are singing the harsh interval of a second; immediately after they sing a major third. By the earliest theorists these dissonances were disregarded or accepted as necessary evils, the unavoidable results of the restrictions under which the organizing voice was laid. But if the free diaphony was practised at all it was to lead musicians inevitably to a recognition of these intervals, and of the effect of contrasting one kind with another. In the works of Hucbald and Odo and their contemporaries, however, the ideal is theoretically the parallel progression of the only consonances they would admit, the fourth, fifth, and octave. Oblique movement was first of all a way to escape the tritone, and the unnamed dissonances were haphazard. Thus we find only the mere germ of the science of polyphony. The dry stiffness of the music and the inadequacy of the cumbersome rules must lead one to believe that learned men, true to their time, were doing what they could to define a popular free practice within the limits of theory. The sudden untraceable advent of a new free style some hundred years or more later goes to prove that the free descant of a genuinely musical people was never actually suppressed or discontinued by the influence of the theorists.

The Art of Music - Vol. 1 — Part 136