doubled a melody in 5ths and octaves they believed themselves
to be doing no more than extending and diversifying the means
by which a melody might be sung in unison by different voices.
How they came to prefer for this purpose the 4th to the 5th
seems puzzling when we consider that the 4th does not appear
as a fundamental interval in the harmonic series until that series
has passed beyond that part of it that maintains any relation
to our musical ideas. But it was of course certain that they
obtained the 4th as the inversion of the 5th; and it is at least
possible that the singers of lower voices found a peculiar pleasure
in singing below higher voices in a position which they felt
harmonically as that of a top part. That is to say, a bass, in
singing a fourth below a tenor, would take pleasure in doubling
in the octave an alto singing normally a 5th above the tenor.[1]
This should also, perhaps, be taken in connexion with the fact
that the interval of the downward 4th is in melody the earliest
that became settled. And it is worth noticing that, in any
singing-class where polyphonic music is sung, there is a marked
tendency among the more timid members to find their way into
their part by a gentle humming which is generally a 4th below
the nearest steady singers.
The limited compass of voices soon caused modifications in the medieval parallelisms of 4ths and 5ths, and the introduction of independent ornaments into one or more of the voices increased to an extent which drew attention to other intervals. It was long, however, before the true criterion of concord and discord was attained; and at first the notion of concord was purely acoustic, that is to say, the ear was sensitive only to the difference in roughness and smoothness between combinations in themselves. And even the modern researches of Helmholtz fail to represent classical and modern harmony, in so far as the phenomena of beats are quite independent of the contrapuntal nature of concord and discord which depends upon the melodic intelligibility of the motion of the parts. Beats give rise to a strong physical sense of discord akin to the painfulness of a flickering light (see Sound). Accordingly, in the earliest experiments in harmony, the ear, in the absence of other criteria, attached much more importance to the purely acoustic roughness of beats than our ears under the experience of modern music. This, and the circumstance that the imperfect concords[2] (the 3rds and 6ths) long remained out of tune owing to the incompleteness of the Pythagorean system of harmonic ratios, sufficiently explain the medieval treatment of these combinations as discords differing only in degree from the harshness of 2nds and 7ths. In the earliest attempts at really contrapuntal writing (the astonishing 13th and 14th-century motets, in which voices are made to sing different melodies at once, with what seems to modern ears a total disregard of sound and sense) we find that the method consists in a kind of rough-hewing by which the concords of the octave, 5th and 4th are provided at most of the strong accents, while the rest of the harmony is left to take care of itself. As the art advanced the imperfect concords began to be felt as different from the discords; but as their true nature appeared it brought with it such an increased sense of the harmonic poverty of octaves, 5ths and 4ths, as ended in a complete inversion of the earliest rules of harmony.
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The harmonic system of the later 15th century, which culminated in the “golden age” of the 16th-century polyphony, may be described as follows: Imagine a flux of simultaneous independent melodies, so ordered as to form an artistic texture based not only on the variety of the melodies themselves, but also upon gradations between points of repose and points in which the roughness of sound is rendered interesting and beautiful by means of the clearness with which the melodic sense in each part indicates the convergence of all towards the next point of repose. The typical point of repose owes its effect not only to the acoustic smoothness of the combination, but to the fact that it actually consists of the essential elements present in the first five notes of the harmonic series. The major 3rd has thus in this scheme asserted itself as a concord, and the fundamental principle of the identity of octaves produces the result that any combination of a bass note with a major 3rd and a perfect 5th above it, at any distance, and with any amount of doubling, may constitute a concord available even as the final point of repose in the whole composition. And by degrees the major triad, with its major 3rd, became so familiar that a chord consisting of a bare 5th, with or without an octave, was regarded rather as a skeleton triad without the 3rd than as a concord free from elements of imperfection. Again, the identity of the octave secured for the combination of a note with its minor 3rd and minor 6th a place among concords; because, whether so recognized by early theorists or not, it was certainly felt as an inversion of the major triad. The fact that its bass note is not the fundamental note (and therefore has a series of upper partials not compatible with the higher notes) deprives it of the finality and perfection of the major triad, to which, however, its relationship is too near for it to be felt otherwise than as a concord. This sufficiently explains why the minor 6th ranks as a concord in music, though it is acoustically nearly as rough as the discord of the minor 7th, and considerably rougher than that of the 7th note of the harmonic series, which has not become accepted in our musical system at all.
But the major triad and its inversion are not the only concords that will be produced by our flux of melodies. From time to time this flux will arrest attention by producing a combination which, while it does not appeal to the ear as being a part of the harmonic chord of nature, yet contains in itself no elements not already present in the major triad. Theorists have in vain tried to find in “nature” a combination of a note with its minor 3rd and perfect 5th; and so long as harmony was treated unhistorically and unscientifically as an a priori theory in which every chord must needs have a “root,” the minor triad, together with nearly every other harmonic principle of any complexity, remained a mystery. But the minor triad, as an artistic and not purely acoustic phenomenon, is an inevitable thing. It has the character of a concord because of our intellectual perception that it contains the same elements as the major triad; but its absence of connexion with the natural harmonic series deprives it of complete finality in the simple system of 16th-century harmony, and at the same time gives it a permanent contrast with the major triad; a contrast which is acoustically intensified by the fact that, though its intervals are in themselves as concordant as those of the major triad, their relative position produces decidedly rough combinations of “resultant tones.”
By the time our flux of melodies had come to include the major and minor triads as concords, the notion of the independence of parts had become of such paramount importance as totally to revolutionize the medieval conception of the perfect concords. Fifths and octaves no longer formed an oasis in a desert of cacophony, but they assumed the character of concord so nearly approaching to unison that a pair of consecutive 5ths or octaves began to be increasingly felt as violating the independence of the parts. And thus it came about that in pure 16th-century counterpoint (as indeed at the present day whenever harmony and counterpoint are employed in their purest significance) consecutive 5ths and octaves are strictly forbidden. When we compare our laws of counterpoint with those of medieval discant (in which consecutive 5ths and octaves are the rule, while consecutive 3rds and 6ths are strictly forbidden) we are sometimes tempted to think that the very nature of the human ear has changed. But it is now generally recognized that the process was throughout natural and inevitable, and the above account aims at showing that consecutive 5ths are forbidden by our harmonic system for the very reason which inculcated them in the system of the 12th century.
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II. Tonality.—As soon as the major and minor triad and their first inversions were well-defined entities, it became evident that
- ↑ It is at least probable that this is one of the several rather obscure reasons for the peculiar instability of the 4th in modern harmony, which is not yet satisfactorily explained.
- ↑ The perfect concords are the octave, unison, 5th and 4th. Other diatonic combinations, whether concords or discords, are called imperfect.
