tone of the lower note, that is in the series of harmonics of which it is the prime tone, or 'generator,' and among these the fourth does not occur; and they had not yet learnt to feel the significance of inversions of given intervals; and therefore the development of their perception of harmonies, dealing as yet only with combinations of two different notes at a time, would lead them to reject the fourth, and put it in the category of discordant intervals, in which it has ever since remained as far as contrapuntal music is concerned, while even in harmonic music it canno be said to be at all on an equality with other consonances.
The next writer on music of any prominent importance after Marchetto was Jean de Muris who lived in the 14th century. In his 'Ars Contrapuncti' he systematises concords, as the previous writers had done, into perfect and imperfect; but his distribution is different from Franco's, and indicates advance. He calls the octave and the fifth the perfect, and the major and minor thirds and major sixths the imperfect concords. The minor sixth he still excludes. Similarly to Franco he gives directions for intermingling the perfect and imperfect concords, and further states that parts should not ascend or descend in perfect concords, but that they may in imperfect. It is clear that individual caprice was playing a considerable part in the development of musical resources in de Muris's time, as he speaks with great bitterness of extempore descanters. He says of this new mode of descanting, in which they professed to use new consonances, 'O magnus abusus, magna ruditas, magna bestialitas, ut asinus sumatur pro homine, capra pro leone,' and so on, concluding, 'sic enim concordiæ confunduntur cum discordiis ut nullatenus una distinguatur ab aliâ.' Such wildness may be aggravating to a theorist, but in early stages of art it must be looked upon with satisfaction by the student who sees therein the elements of progress. Fortunately, after de Muris's time, original examples begin to multiply, and it becomes less necessary to refer to reporters for evidence, as the facts remain to speak for themselves. Kiesewetter gives an example of four-part counterpoint by Dufay, a Netherlander, who was born about 1360. This is supposed to be the earliest example of its kind extant, and is a very considerable advance on anything of which there is any previous account or existing examples, as there appears in it a frequent use of what we call the complete common chord with the third in it, and also its first inversion; and in technical construction especially it shows great advance in comparison with previous examples, and approaches much nearer to what we should call real music. It requires to be noted moreover that this improvement in technical construction is the most striking feature of the progress of music in the next two centuries, rather than any large extension of the actual harmonic combinations.
The works of Ockeghem, who lived in the next century to Dufay, do not seem to present much that is worthy of remark as compared with him. He occasionally uses suspended discords in chords of more than two parts, as—
from a canon quoted by Burney; but discords are of rare occurrence in his works, as they are also in those of his great pupil Josquin de Prés. For instance, in the first part of the Stabat Mater by the latter (in the Raccolta Generale delle Opere Classiche, edited by Choron), there are only ten examples of such discords in the whole eighty-eight bars, and it is probable that this was a liberal supply for the time when it was written.
Ambros says that Josquin was the first to use accidentals to indicate the modifications of notes, which we are tolerably certain must have been modified according to fixed rules before his time without actual indication in the copies. Josquin certainly made use of them also to obtain effects which could not have been derived from the ordinary principles of rendering the music, and thus took an important step in the direction of assimilating the ecclesiastical scales in the manner which gradually resulted in the musical system we now use. A remarkable instance of this is his use more than once of a concluding chord with a major third in it, the major third being indicated by an accidental. Prior to him the concluding chord had contained only a bare fifth at most, and of this there are examples in his works also, as—
from the Benedictus of the Mass 'Faysans regrets' quoted by Burney (ii. 500)—in which progression the use of the E♭ is worthy of notice; but his use of the major third shows a remarkable advance, especially in the direction of feeling for tonality, which is one of the essential features of modern music.
This use of the major third in the final chord of a piece in a minor key became at a latter time almost universal, the only alternative being bare fifth, as in the last example; and the practice was continued far on into modern music; as by Bach and Handel, in the former of whose works it is very common even in instrumental music. And still later we find it in Mozart, at the end of the 'Quam olim Abrahæ' in the Requiem Mass. On the other hand, at the conlusion of the Chorus 'Dies Iræ' of the same mass the final chord appears, as far as the voices are concerned, with only a fifth in it, as in the example from Josquin above. However with composers of the harmonic period such as these t has not been at all a recognized rule to avoid be minor third in the final chord, its employment avoidance being rather the result of charac-
