HAEMONY. 576 HARMONY OF THE SPHEBES. In the above examples, only the soprano con- tains the passing and changing notes. It is possible, however, to liave more or all voices move in notes of the same value as the soprano. The different tones of the different voices then form chords. All chords containing one or more of the notes marked * would then constitute pars- ing chords. Caoences. It is important to pay attention to the closing of a piece. The two principal cadences are the aiilliciitic and the pJufiuL The authentic cadence is the resolution of the dominant chord into the tonic. When the soprano has the funda- mental tone of the tonic, and the bass the funda- mental tone of both the dominant and tonic chords, the close is called a whole cadence. It is at the same time a perfect cadence. The whole cadence is imperfect when the soprano has any other interval than the fundamental of the tonic, or the bass any other than the fundamental tone of the dominant chord. A half cadence is the resolution of the tonic into the dominant chord, the reverse of the whole cadence. Instead of the tonic chord other triads may be used, especially those of the second, fourth, or sixth degree. A half cadence that occurs very frequently and is very beautiful is the Phrygian cadence. It con- sists of the resolution of the sub-dominant into the dominant in the minor mode. The plagal Whole Perfect Cadences. Wlole Imperfect Cadences. Modulation. Although every composition is written in a certain key, wearisome monotony would result were the composer to restrict him- self only to chords properly belonging to that key. Chords belonging to other keys are intro- duced with more or less frequency. ' Every such departure from the original key is a modulation. To modulate with artistic effect the relation of the keys and the chords belonging to each must be thoroughly understood. While pursuing the study of harmony the student at the same time is trained in the science of figured bass. It is the rule followed in all modern treatises on harmony to write out the exercises in figured bass notation. This indicates the choice of chords, whereas the leading of the voices and the distribution of the tones are lelt to the student. There is no dearth of excellent works on har- mony. Among the most famous are: Fetis, Es- quisse de Vhistoire de I'harmonie (Paris, 1840) ; Traifc complet de la thcorie et de la pratique de I'harmonie (Paris, 1844) ; Dehn. Theoretiseh- praktische Harmonielehre (Berlin, 1840) ; Haupt- mann. Die Xatur der Harmonik nnd der Metrik (Leipzig, 1853, 1873) ; Marx, Die Lehre von der ■musikalischen Eomposition (Leipzig, 1847, new edition revised by Riemann, Leipzig, 1889); Richter, Lehrbuch der Harmonie (Leipzig, 1888; Half Cadences, ^ zSz i=j= Phrygian Cadences. Plagal Cadences. Deceptive Cadences. Mixed Cadences. Various Cadences. EX. 17. cadence is the resolution of the sub-dominant into the tonic chord. The cadences just mentioned are the ones most frequently used at the close of a composition. But at the end of a phrase or section a close known as the deceptive or inter- rupted cadence is frequently found. This consists of the resolution of the dominant into some chord other than the tonic. A mixed cadence is the succession of the sub-dominant, dominant, and tonic chords, thus con.stituting a mixture of the authentic and plagal cadences. Besides the ca- dences enumerated, others not specially classified also occur. Thus the chord of the diminished seventh sometimes takes the place of the domi- nant or sub-dominant (ex. 17). translated into English by Morgan, New York, 1885) ; Jadassohn, Harmonielehre (Leipzig, 1883) ; H, Riemann, Ski~:e einer neuen Methode der Harmonielehre (Leipzig, 1880); Die Natur der Harmonik (Leipzig, 1882). For detailed information of the various topics introduced in this article, compare the separate articles on Acoustics; Augmentation; Ca- dence; Chord; Figured Bass; Interval; Key; Leading Tone; Leading of Voices; Major; Minor ; Modulation ; Motion ; Passing Notes ; Progression; Scale; Suspension; Tonality; Harjionics. HARMONY or THE SPHERES, or Music OF THE Spheres. It was a common belief among,
