ORIGINS OF CONCORD AND DISCORD The diatonic major scale (or something very like it) may be found by playing eight successive white notes from C to C on the pianoforte. It would be better to accept this as a scientific defi nition than to begin the study of harmony with questions like that as to whether the first hen preceded or followed the first egg. The interesting fact is that the ancient Greeks showed a latent harmonic sense by developing the diatonic scale that has proved itself capable of bearing our classical system of harmony. In the article Music the origin of scales is touched upon ; in the mean time we may assume that eggs are eggs without waiting for the latest researches of bio-chemistry.
The one ostensible effort the Greeks made at organizing simul taneous notes of different pitch was the practice of magadizing. The magadis was a stringed instrument with a bridge that divided the strings at two-thirds of their length. The shorter portion of the string then sounded an octave higher than the longer. To magadize, therefore, was to get the voices of children or women to sing in octaves above the voices of men.
Now we may begin our survey of harmonic combinations with two propositions. First, any two notes an octave apart are har monically identical. From this we may draw two useful inferences —first, that doubling in octaves never was and never will be a process of harmonization ; and, secondly, that a combination does not change its meaning by the addition or subtraction of an octave.
The second fundamental proposition is that harmonies are built upwards from the bass. This will be denied by some theo rists; but the present line of thought is not an a priori theory, but the observation of facts. By "low" notes we mean sounds pro duced by slow vibrations, and by "high" notes sounds produced by rapid vibrations.
The harmonic identity of notes an octave apart was a matter of physical sensation before the dawn of history. In 1862 Helm holtz explained it and a great many other facts in musical aesthet ics. He solemnly warned musical theorists against hastily apply ing his scientific results to the art of music, and warned them in vain. But we may safely draw some inferences from his discovery that the timbre of a note depends upon the selection and propor tion of a series of overtones in the vibration-ratios of aliquot parts of the fundamental note. Thus, a note adds nothing to a lower note if it is at the distance of an overtone; except in that if the distance is not exactly one or more octaves the combination will assume the harmonic sense of its difference from an octave; thus, a 12th is equivalent to a 5th.
Distances of pitch, it may here be explained, are called inter vals. They are reckoned (numerically and inclusive of both notes) up a diatonic scale. From the fundamental (or tonic) note of a major scale (as from C on the white notes of the pianoforte) all intervals within that scale are major, and the 4th, 5th and octave are called perfect. Intervals a semitone less than major are called minor, except in the case of perfect intervals, which become im perfect or diminished when reduced by a semitone. Otherwise a diminished interval is a semitone less than minor. An augmented interval is a semitone greater than major. The terms "augmented" and "diminished" should be applied only to chromatic intervals, that is to say, to intervals of which one note is foreign to the scale of reference. There is in every scale one 4th that is greater than perfect (F to B in the scale of C) and one imperfect 5th (B to F). This diatonic enlarged 4th is called the tritone. Intervals are "in verted" by raising the lower note to a higher octave ; thus the imperfect 5th is the inversion of the tritone 4th.
Helmholtz's discovery of the nature of timbre proves that cer• tain aspects of harmony are latent in nature. Conversely, the art of harmony constantly produces effects of timbre apart from those of the particular instruments in use. But musical elements interact in ways that quickly carry musical aesthetics into regions far removed from any simple relation between harmony and timbre. What acoustics can tell us of concord and discord is not only inadequate for our musical experience, but contrary to it. Acoustics tell us that the rapid "beats" that distress the ear in harsh combinations are due to the periodic reinforcements and weaknesses that occur as the waves,get in and out of phase with each other. When these beats are so rapid as to produce a note of their own, this resultant tone may or may not be pleasant ; the painful stage of beats is that in which they are noticeable, as a flickering light is noticeable. Combinations that are out of beating distance may set up beats between the upper note and the octave harmonic of the other. On this criterion, 3rds and 6ths, especially the minor 6th, are rougher than many combinations that rank as discords, or than some that have never been digested in classical harmony, such as the 7th overtone.
The art of music had not attained to the simplest scheme for dealing with discords before it traversed the acoustic criterion in every direction. It became a language in which sense dictated what should be accepted in sound. The minor 6th, as the inver sion of the major 3rd, occurs in many positions of what has come to be the most fixed chord in music, the major triad. On the other hand, a discord beyond beating-distance will have no beats if it is produced in a timbre that has no octave overtones; but if its sense has come to be that of a discord, its timbre will not make it a concord.
The theorists of the 16th century shrewdly regarded the major triad as really a chord of six notes, in the ratios of which they called the Sestina: Long before this natural phenomenon had been recognized music had organized many other elements into its language, and harmony had become (what it has ever since remained, apart from experiments) counterpoint. This arose, slowly and painfully, out of devices diametrically opposed to it. The organum or diaphonia Its intention was that of a glorified unison and it survives, unheard except as artificial timbre, in the guise of a shrill aura above the notes of the full organ when that instrument is using the most ancient of its registers, the mixture stops. (Some ob servers have reported the present practice of something like diaphonia in remote parts of Japan.) The problem of counterpoint was attacked in two ways. First there was a slow evolution through experiments in ornamenting one or more voices of an organum. This gradually took shape as the art of discant, and was slow to move far from the founda tion of parallel perfect concords. On the other hand, a violent frontal attack was made by the "motets" of the 13th and i4th centuries, which had no connection with the sublime motet-form of i 6th century church music, but consisted in the simultaneous singing of several melodies, independent and perhaps pre-existing; the combination being rough-hewn into a harmony justified by the rule of marche, ou je t'assomme. The rough-hewing consisted in contriving that the perfect concords should be conspicuous at the strong accents, on which condition the rest of the harmony could take care of itself. We are apt to misread our documents by forgetting that the note which is now double the length of the longest note in normal use originally deserved its name of "breve." A Hungarian band produces a general harmonic effect more like that of Brahms's Hungarian dances than like any less classical music ; but if the details of the Hungarian ornamentation and part-writing were written in breves, semibreves and minims we should find them remarkablyjike mediaeval counterpoint.