This is the form of the great majority of polkas and waltzes, except that the song forms standing for A and B respectively are very often of three periods instead of two. This form also lies at the foundation of the great majority of salon pieces for the piano.
The only difference between the rondo form and the form last described—the proper designation of which is "song form with trio"—is that the rondo introduces passage work between the subject and the second subject. Should it be desired to develop the rondo to a greater length, the second subject can be repeated after the repetition of the first, and the first subject brought in still again. A third subject can be introduced, and in the longest rondo form the schedule is like this, C standing for the third subject:
A-B-A-C-A-B-A-Coda.
A form of this sort might extend to a very considerable length, as happens in the case of Chopin's Rondo in E-flat major, opus 18, which reaches to ten or twelve pages and occupies about ten minutes to perform.
The essential principle of musical form—form in music—is quite analogous to form in literature. As in a poem or article the first consideration is Unity, or the preponderance of a leading idea, and the second Variety, or the occurrence of interesting illustrative matter, and the third Symmetry, or the just relation between the different parts in order that the leading idea may not be obscured by the prolixity of the subordinate ideas, so the same principles prevail in music. Unity also is attained by peculiarly similar means in both cases. As in the article the leading idea is repeated a number of times in order to impress it upon the hearer, but frequently in different language, so in music the principal idea is repeated more times than any other in the course of the piece; and in the small forms, or rather in the molecular construction of a piece of music, the repetitions are in a great variety of speech, exactly as they are in a well-made article. The same idea can be presented in different aspects, and different words may express it. In music this takes place through the appearance of the motive in different chords from those in which it first appeared, giving rise to variations in the melodic intervals and the like.
Symmetry in music is much more exactly observed than in literary composition, even in verse, since music itself is a matter of time and vibration, and the proportionate and mathematical relation of parts belongs to the very essence of the art. Every musical form, therefore, whether large or small, consists essentially of one leading idea and of two or more subordinate ideas, brought in with whatever cleverness of treatment the composer may find convenient, and the whole turned over and diversified according to his fancy.
In certain aspects the musical forms bear a good deal of resemblance to the quasi-geometric figures called arabesques, in which a certain line or form is many times repeated; or to the arrangement of crystals which the frost forms upon the glass of the window, when the simple crystalline form of water is repeated in a great diversity of ways, and larger figures and curious symmetries and suggestions are brought out. In music of a serious construction the leading motives are diversified in a great variety of ways by being made to appear in different chords and intervals from the original form, and by being carried into other keys, whereby the impression upon the ear is very materially modified, at the same time without destroying the unity of the idea.
Musical forms in general may be divided into elementary and complete. The elementary forms are those which are used as structural elements in the larger or complete forms. Thus, a motive repeated becomes a phrase; a phrase repeated or answered by counter-theme becomes a section; a section repeated becomes a period; the period repeated or modified becomes a two-period form or a period group, which may extend to a considerable number of periods. Out of these elementary forms the large forms are constructed. Beginning with the song form as the principal subject, the rondo goes on with a second song form as second subject, and so on to any extent desirable, according to the plan given above. In analyzing a large piece of music to find these leading subjects, the student should begin by first finding the great divisions in the piece, such as, for instance, those where an entirely new melody comes in a change of key, and the like. Having found the larger points of joining, he should then proceed to find the dividing lines in the smaller parts, which, in music, is rendered somewhat more difficult in consequence of the entire absence of punctuation bringing out relations of this kind. Not only are the marks wanting, but the bars confuse the eye and make it more difficult to find the real point where the ideas begin and end. The student, however, accustomed to memorizing his music, and consequently to thinking about it, will soon be able to find it by his intuition, in the same way that the reader knows when the sentence has been completed by the sense and not necessarily by the period which is placed after the last word.
There are a few leading types of form to which all others more or less conform. The first of these, and perhaps, on the whole, the most important, are those which are called unitary forms. A unitary form is a musical form with only one leading melodic idea, out of which the entire piece is developed. This can only be done in one or the other of three ways. Taking the simplest way first, it will be to develop this leading idea into a song form according to the pattern given above, in the beginning of this discussion. This, being sufficiently obvious on the face of it, requires no further attention here. Forms of this kind belong essentially to popular music, although they are not uncommon by way of relief in the more elevated art music.
There are two types of unitary form, however, which enter into and color all instrumental music to a degree, making it indispensable that the pupil thoroughly understand them. The first of these is the fugue. In the fugue a melodic subject of two measures or four, rarely more, is taken by a single voice and is answered by another voice in the dominant, and this again by the third voice in the original key, and so on according to the number of voices performing the fugue. The voice which has completed the subject goes on with the counter-subject or the counterpoint while the second voice is singing the subject. When all the voices have had their turn at the phrase there is an interlude of modulating material, after which the subject comes again and is answered one or more times in the properly related keys, for which the artificer of fugues has his rules already prepared, following the principles laid down by Bach. After this second appearance of the theme in these new keys, another interlude, and then an additional strophe in still a different key and with finer treatment; and thus, according to the fancy of the composer and his skill, the piece is extended to one, two, or even six or eight pages. But during the whole of it the principal subject has reappeared at very short intervals and in a great variety of keys, while the interlude matter has always been of a lighter and less significant character. In order to arrive at an appreciation of fugues, the student perhaps can not do better than to begin with some of the two-part inventions of Bach, which, while not following the fugue form strictly, approximate it very nearly. The first invention and the eighth are perhaps the best for this purpose. After these, an easy fugue in the "Well-tempered Clavier," such as the one in D major or that in C minor; more difficult examples are those in C-sharp major and in G major. In the development of fugues the old masters made use of a great variety of artifices, including all the devices of double counterpoint at the tenth and twelfth, canon and inversion, the latter applied not alone to the relation of the voices but also to the melodic material constituting a voice. "The fugue," Cherubini says, "contains everything which a good composer ought to know," and it is, in fact, the underlying element in all serious moments of modern music except those which are purely lyric. The fugue underlies the elaboration in the middle of a sonata-piece, and, in fact, is the original source, as said before, of nearly all the serious moments in the higher departments of art.