HARMONY. Harmony is the branch of musical theory which treats of the simultaneous combination of tones into chords and the suc cessive interlinking of chords. It may appro priately be styled the grammar of music.
The traditional presentation of the subject begins with an explanation of intervals. An interval is formed whenever two tones are simultaneously combined. Thus C and the adjoining D make an interval of a second, C and E of a third. When three tones are combined we have a triad. Normally a triad consists of the fundamental tone together with its third and fifth. C E G is an example. Every tone in the scale has its triad, as is shown in the whole notes of the illustration (which is here confined to the major scale).
The most important triads are those on the first, fourth and fifth degrees. They are designated respectively as the tonic, subdominant and dom inant triads. At the end of the example there are three different forms of the same chord, the difference depending on the tone which occupies the lowest position. The third last is the chord in its fundamental form, the next is the chord of the the last the chord of the "sixth and fourth? The upper voices, too, like the lowest, may be shifted about, as well as spread apart (open position), but there are no special names for the resulting chord-forma tions. By adding another third above the high est tone of the normal triad (quarter notes of the example), we obtain a chord of the seventh. Every triad in the scale has its corresponding diord of the seventh, but the most important is that which is built on the dominant, and which is consequently styled the dominant chord of the seventh. The addition of still further notes gives rise to chords of the 9th, llth and 13th. These, however, are not recognized by all theorists as independent formations.
The fundamental chords adduced may be subjected to numerous alterations and modifica tions. One or more tones may be raised or low ered chromatically, thus giving rise to chords. Foreign elements may be introduced into the chords or interspersed between them. There may be suspensions and anticipations, passing and changing notes, pedal points and stationary voices. A suspension is a tone which hangs over, or is from a previous chord. An anticipation is one which reaches forward into the next chord. Changing notes are foreign notes entering abruptly into a har mony, like unprepared suspensions; passing notes fill in the spaces between successive har monic tones. Pedal points are sustained or re curring tones in the bass accompanying decided changes of harmony above, stationary voices are the same thing when the sustained tones are in the upper parts. Modulation, finally, refers to the transition from one key to another, and completes the basic operations on which har monic progressions depend.
As to the particular rules governing har monic progressions, it is of course impossible i to go into their details, involving — as it would —a great number of illustrative examples. Suf fice it to have pointed out the nature of the material involved. The system in which this material comes to view, and which we have just sketched, is admirably neat and clear, and has served its purpose well. It must not be sup posed, however, that it is the only conceivable system, or that others have not been proposed. Riemann, for example, has worked out one which is certainly original, even though it may not win our complete assent. In the ordinary system harmonies are conceived as built up from below, the lowest tone serving as gener ator of the others. This seems to be in agree ment with natural laws. For according to acoustics, the two upper tones of the major triad and the three upper tones of the dominant seventh chord are contained in the lowest tone as partials. Riemann follows the ordinary prac tice with reference to major chords, but when i he comes to the minor he reverses it, i. e., he builds them downward from above. Acoustic ally he bases his procedure on the supposed ex istence of "undertones)" With reference to his classification of harmonies, likewise, he deviates widely from the ordinary view. Thus he re gards the triad on the seventh degree of the scale (B in our example), as an abbreviated dominant seventh chord, with the lowest tone (G) missing. And he considers the chord of the sixth and fourth as a fundamenal or first position triad, with a suspension in the two upper voices. Alfred Day likewise admits ellip tical chords, e. g., in the case of the seventh chord on the second degree of the scale (I) in our example). He conceives this as a chord of the llth, with the lower B and G omitted. Another interesting idea of his is that accord ing to which some chords have double roots, which is tantamount to saying that they are composed of fragments of two chords. A valu able suggestion, indeed, of which — strange to say — little use has been made. The combina tion of parts into new wholes is a phenomenon to be observed everywhere. Thus the centaur combines the head and chest of a man with the lower parts of a horse; the word ((shan't)) is composed of portions of the words "shall' and anot.n What more natural, accordingly, than that music, with its wealth of material, should make use of similar abbreviations and combina tions? It would be out of place, however, to follow up this suggestion, as the function of the present review is to give a summary of ex isting opinions, rather than to develop new ones.