HARMONY. HARMONY. below the original cantus. This crude experiment v.as the beginning of harmony. In the sixteenth century Zarlino, in his great work Istitiizioiii hunnoiiichc, established the consonance of the third, and also discovered the polarity of major and minor. That this discovery did not bear fruit innncdiately is due to the invention of figured bass, which determines all intervals from the bass tone instead of the fundamental. Tar- tini. in the eighteenth century, tried to develop Zarlino's ideas, but failed because he could not get awaj' from the theories of figured bass. Thus the idea of the polarity of major and minor fell into oblivion, until in 18.53 Moritz Hauptmann (q.v.) established this relation on a firm .scientific basis. But after the third was once recognized as a consonance, the basis for the construction of chords was given. Still, music could not free itself from the fetters of the church modes (q.v.). Hence the development of music took place along the lines of polyphony (q.v.) or contrapuntal writing. Only after the establishment of the major and minor modes in place of the church modes, and the subsequent introduction of equal temperament (q.v.), which rendered modulation into all keys possible, could music develop har- monically. Thus Bach, while marking the high- est development of the polyphonic contrapuntal style, at the same time marks the beginning of homophonic harmonic writing. Since then the progress of harmony has been very rapid. Pro- gi-essions that startled one generation by their dis- sonance and boldness were accepted as pleasing and natural by the next, until, in the works of the great masters of the nineteenth century, we have a wealth and variety of harmonies that their predecessors never dreamed of. To-day all music is conceived as resting upon a harmonic basis. All tones are regarded on the basis of consonant chords, so that dissonant chords are conceived not as independent formations, but as modifications of a fundamental consonant chord. That this view is the only rational one, and rests upon a natural basis, is conclusively proved by the fact that the works of the greatest writers of the polyphonic style can all be reduced to a sim- ple harmonic basis. The importance of harmony in modern music cannot possibly be overestimated. Emotional ex- pression depends almost entirely upon the choice of harmonies. The same melody harmonized dif- ferently is capable of expressing widely diflferent moods and emotions. This is strongly illustrated by the leading motives in the works of Wagner. The same melodic phrase occurs frequently in a different harmonic garb in accordance with the varying demands of the dramatic situation. The development sections of Beethoven's symphonies and sonatas afford innumerable examples of won- derful and surprising effects produced by different harmonization of the original themes. Simple folksongs can be invested with a transcendent beauty by a judicious, refined harmonization. For example : The simple German folksong, Es ist bestimmt in Gottes Rath, appeals to every one through its tender melody sustained only by the simplest harmonic chords. Mendelssohn has taken this simple melody, and, without altering even a note, has harmonized it so exquisitely that his version appears like a high-art song. Upon closer examinatiim, we will find that the tender sadness of the original melody has been intensified by Mendelssohn's rich harmonies into sorrowful resignation. It is highly interesting to compare the many harmonic settings of Luther's famous hymn. Eln fc.ste Burg ist un.ter Gott. Bach's wonderful setting cannot be surpassed (ex. I) ; and yet what a different character does ,^h{^= Fd-^ — rr^ ■■^l 1 '^ ^^1 1
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-1 L^ L^ - -^ 1 ^— EX. 1. Wagner impart to this simple melody when he introduces it in his Kaisermarsch (ex. 2). The P .<=. -sfS- ^^^ J- » --^ ^^£^^P -| — r -| — r i E^ 1 1 »)<«<. 1°- — *— [^ 1 ^^ a j — , ?3i?n s=«- 1 ^ ■ EX. 3. EX. 2. three notes constituting the melodic outline of the motive of Fate in the Nibelungen are surely in- significant enough in themselves. This motive derives its solemn and majestic character solely from the rich underlying harmony (ex. 3). One more example to prove the im- portance of har- mony. The prin- cipal theme of the allegretto in Beethoven's A major Sympho- ny is almost ap- palling in its meagre monotonous melody. Yet, by means of the mast marvelous harmimic com- binations, the master has transformed it into one of the most impressive and deeply emotional phrases to be found in the whole range of music (ex. 4). In the great masters the gift of harmony is in- born. Wagner expressly declares that no melody ever occurred to him apart from its harmonic basis. Yet a talent for harmony can be culti- vated to a certain extent. Every thorough mu- sician is capable of harmonizing a given melody in several ways. Besides the choice of the chords there is another important factor, namely, the proper distribution to the different voices of the different tones composing a chord. This has to do with the leading of the voices and the rules to be observed in correct -writing. It cannot be the object or purpose of an article like the present to attempt a technical exposition of so broad a subject as harmony. The following is, there- fore, intended to give the general reader some idea of the scope and function of the varioxis subjects comprised under the collective title of harmony. Intervals. Under this heading the tones are treated in respect to the distance or difference in the degree of the scale that separates them one from the other. If two tones are soimded simul- taneously they form harmonic intervals; if sounded successively, melodic intervals. All in- tei-%'als are reckoned from the fundamental tone
