A few standard examples are to be found in the Supplement. These should be played over and studied until they are thoroughly familiar—not only for the pleasure to be derived, but for the indispensable training afforded in polyphonic listening.
Ex. No. 9 Canon by Thomas Tallys (1510-1585).
Ex. No. 10 Canonic Variation by Schumann from the Études Symphoniques.
Ex. No. 11 of Bach's Goldberg Variations.
Ex. No. 12 Canon in B-flat minor, op. 38, Grieg.
Ex. No. 13 Canon in F-sharp major, op. 35, Jadassohn.
One of the most simple and direct types of polyphonic composition is the form known as the Invention in which, as the term implies, the composer—through his inventive genius and by means of the polyphonic devices of imitation and transposition—develops to a logical conclusion some short and characteristic motive. We are fortunate in having from Bach himself, that consummate master of polyphony, two sets of such Inventions: fifteen for two voices, and fifteen for three. These flights of fancy—in which art so subtly conceals art—though originally composed for the clavichord and harpsichord (the precursors of the pianoforte), are very effective on our modern instrument and should be in the possession of every music-student.[36] A brief analysis is now given of the first one in the set for two voices, and Nos. 4, 8 and 10 in this set are particularly recommended for study; also Nos. 2, 6 and 14 among those for three voices. The opening motive
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is the foundation of the entire composition and is at once imitated, canonically, in the lower voice. Then the two voices play about, with figures clearly derived from the motive, until we reach, in measures three and four, a systematic downward transposition of the material. Such transpositions or shiftings up or down in pitch are called Sequences. They are very frequent in all polyphonic composition, give a strong sense of unity to melodic progression and are generally carried out in groups of three, i.e., the original figure and two repetitions. After the sequence the music naturally works toward the most nearly related key (the dominant) and in the seventh measure reaches in that key its first objective. These Inventions of Bach, as well as the Dance forms soon to be studied, are almost invariably in what is known as Two-part form, i.e., the music consists of two main divisions, clearly marked off by cadences[37]; the first of which modulates to the dominant or some related key while the second part, starting in this key, works back to a final close in the home key. In Inventions it early became customary in the second part to begin with the same motive as the first—but in the opposite voice. Thus we see, in the Invention now being discussed, that the seventh measure begins with the original motive in the bass which, in turn, is imitated by the Soprano—a process just the reverse of that in the opening measures.