Just why the intervals of the fifth and fourth should have been chosen for this parallel music, which is excruciating to our modern ears, is not positively known. The simple obvious answer to the riddle is that Hucbald and his contemporaries based their theories on the theories of the Greeks, who regarded the fifth and fourth as consonances nearest the perfect consonance of the octave and unison. But in that case we have to ask ourselves why Hucbald and his followers regarded the diaphony of the fourth as pleasanter than that of the fifth which they none the less acknowledged was more nearly perfect. Dr. Hugo Riemann has suggested a solution to this difficulty which is in substance that organum was an attempt to assimilate elements of an ancient art of singing practised by the Welsh and other Celtic singers. The Welsh scale is a pentatonic scale, that is, a scale of five steps in which half steps are skipped. In terms of the keyboard, it can be represented by a scale starting upon E-flat and proceeding to the E-flat above or below only by way of the black keys between or by a similar progression between any other two black keys an octave apart. In such a scale parallel fourths are impossible, as indeed they are in the Greek scales of eight notes upon which the church music was based; but whereas the progression of the fourths in the Greek scales is broken by the imperfect and very unpleasant interval of the tritone, in the pentatonic scale it is interrupted by the pleasing major third. Such a progression of fourths and thirds seems to spring almost naturally from the pentatonic scales and was very likely much practised by the ancient Welsh singers.[65] A comparison of two examples will make the difference obvious.
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.
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.
II
However, before considering the new diaphony, we have still to trace the further progress of the organum of Hucbald and Odo. The next theorist of importance was Guido of Arezzo. To Guido have been attributed at various times most of the important inventions and reforms of early polyphonic music, among them descant, organum and diaphony, the hexachordal system, the staff for notation, and even the spinet; but the wealth of tradition which clothed him so gloriously has, as in the case of many others, been gradually stripped from him, till we find him disclosed as a brilliantly learned monk and a famous teacher, author of but few of the works which possibly his teaching inspired. He has recently been identified with a French monk of the Benedictine monastery of St. Maur des Fosses.[66] He was born at or near Arezzo about 990, and in due time became a Benedictine monk. He must have had remarkable talent for music, for about 1022 Pope Benedict VIII, hearing that he had invented a new method for teaching singing, invited him to Rome to question him about it. He visited Rome again a few years later on the express invitation of Pope John XIX, and this time brought with him a copy of the Antiphonarium, written according to his own method of notation. The story goes that the pope was so impressed by the new method that he refused to allow Guido to leave the audience chamber until he had himself learned to sing from it. After this he tried to persuade Guido to remain in Rome, but Guido, on the plea of ill-health, left Rome, promising to return the following year. However, he accepted an invitation from the abbot of a monastery near Ferrara to go there and teach singing to the monks and choir-boys; and he stayed there several years, during which he wrote one of the most important of his works, the Micrologus, dedicated to the bishop of Arezzo. Later he became abbot of the Monastery of Santa Croce near Arezzo, and he died there about the year 1050. During the time of his second visit to Rome he wrote the famous letter to Michael, a monk at Pomposa, which has led historians to believe that he was actually the inventor of a new division of the scales into groups of six notes, called hexachorda, and a new system of teaching based on this division.
The case of Guido is typical of the period in which he lived. Very evidently an unusually gifted teacher, as Hucbald was a hundred years before him, his influence was strong over the communities with which he came into contact, and spread abroad after his death, so that many innovations which were probably the results of slow growth were attributed to his inventiveness. The Micrologus contains many rules for the construction of organum below a cantus firmus, which are not very much advanced beyond those of Hucbald and Odo. The old strict diaphony is still held by him in respect, though the free is much preferred. To those intervals which result from the ‘free’ treatment of the organizing voice, however, he gives names, and he is conscious of their effect; so that, where Hucbald and Odo confined themselves to giving rules for the movement of the organizing voice in such a way as to avoid the harsh tritone even at the cost of other dissonances, Guido gives rules to direct singers in the use of these dissonances for themselves, which, as we have seen, in the earlier treatises were considered accidental. This marks a real advance. But there is in Guido’s works the same attempt merely to make rules, to harness music to logical theory, that we found in Hucbald’s and Odo’s; and it is again hard to believe that his method of organizing was in common practice, or that it represents the style of church singing of his day. From the accounts of the early Christians, from the elaborate ornamentation of the plain-song in mediæval manuscripts in which it is first found written down, and from later accounts of the ‘descanters’ we are influenced to believe that music was sung in the church with a warmth of feeling, sometimes exalted, sometimes hysterical even to the point of stamping with the feet and gesticulating, from which the standardized bald ornamentation of Guido is far removed. Furthermore, the next important treatises after Guido’s, one by Johannes Cotto, and an anonymous one called Ad Organum Faciendum, deal with the subject of organum in a wholly new way and show an advance which can hardly be explained unless we admit that a freer kind of organum was much in use in Guido’s day than that which he describes and for which he makes his rules.