The practice of adding extra parts to a Canto fermo at the distance of a fourth or fifth, with an octave to make it complete, seems to have been common for some time, and was expressed by such terms as 'diatessaronare,' or in French 'quintoier.' This however was not the only style of combination known to Hucbald, for in another example which consists chiefly of successions of fifths and octaves the parallelism is interrupted at the close, and the last chord but one contains a major sixth. Further than this, Burney gives an example in which the influence of a drone bass or holding note is apparent, whereby the origin of passing notes is indicated, as will be observed in the use of a ninth transitionally between the combinations of the octave and the tenth in the following example at *.
The use of tenths in this example is remarkable, and evidently unusual, for Guido of Arezzo, who lived full a century later, speaks of the 'symphonia vocum' in his Antiphonarium, and mentions only fourths, fifths, and octaves. This might be through Hucbald's notions of combination being more vague than those of Guido, and his attempts at harmony more experimental; for, as far as can be gathered from the documents, the time which elapsed between them was a period of gradual realisation of the qualities of intervals, and not of progress towards the use of fresh ones. Guide's description of the Organum is essentially the same as the succession of fourths and fifths given by Hucbald; he does not however consider it very satisfactory, and gives an example of what was more musical according to his notions; but as this is not in any degree superior to the second example quoted from Hucbald above, it is clear that Guido's views on the subject of Harmony do not demand lengthy consideration here. It is only necessary to point out that he seems to have more defined notions as to what is desirable and what not, and he is remarkable also for having proposed a definition of Harmony in his Antiphonarium in the following terms—'Armonia est diversarum vocum apta coadunatio.'
The Diaphony or Organum above described was succeeded, perhaps about Guido's time, by the more elaborate system called Discantus. This consisted at first of manipulation of two different tunes so as to make them tolerably endurable when sung together. Helmholtz suggests that 'such examples could scarcely have been intended for more than musical tricks to amuse social meetings. It was a new and amusing discovery that two totally independent melodies might be sung together and yet sound well.' The principle was however, early adopted for ecclesiastical purposes, and is described under the name Discantus by Franco of Cologne, who lived but little after Guido in the eleventh century. From this Discantus sprang counterpoint and that whole genus of polyphonic music, which was developed to such a high pitch of perfection between the 14th and the 17th centuries; a period in which the minds of successive generations of musicians were becoming unconsciously habituated to harmonic combinations of greater and greater complexity, ready for the final realisation of harmony in and for itself, which, as will be seen presently, appears to have been achieved about the year 1600. Franco of Cologne, who as above stated describes the first forms of this Descant, is also somewhat in advance of Guido in his views of harmony. He classifies concords into perfect, middle, and imperfect consonances, the first being the octaves, the second the fourths and fifths, and the third the major and minor thirds. He puts the sixths among the discords, but admits of their use in Descant as less disagreeable than flat seconds or sharp fourths, fifths, and sevenths. He is also remarkable for giving the first indication of a revulsion of feeling against the system of 'Organising' in fifths and fourths, and a tendency towards the modern dogma against consecutive fifths and octaves, as he says that it is best to mix imperfect concords with perfect concords instead of having successions of imperfect or perfect.
It is unfortunate that there is a deficiency of examples of the secular music of these early times, as it must inevitably have been among the unsophisticated geniuses of the laity that the most daring experiments at innovation were made; and it would be very interesting to trace the process of selection which must have unconsciously played an important part in the survival of what was fit in these experiments, and the non-survival of what was unfit. An indication of this progress is given in a work by Marchetto of Padua, who lived in the 13th century, in which it appears that secular music was much cultivated in Italy in his time, and examples of the chromatic progressions which were used are given; as for instance—
Marchetto speaks also of the resolutions of Discords, among which he classes fourths, and explains that the part which offends the ear by one of these discords must make amends by passing to a concord, while the other part stands still. This classification of the fourth among discords, which here appears for the first time, marks a decided advance in refinement of feeling for harmony, and a boldness in accepting that feeling as a guide in preference to theory. As far as the ratios of the vibrational numbers of the limiting sounds are concerned, the fourth stands next to the fifth in excellence, and above the third; and theoretically this was all that the mediæval musicians had to guide them. But they were instinctively choosing those consonances which are represented in the compound
