The other objection to the classification is its vagueness when formulated in such an empirical way; but in order to understand fully both this objection and the former it will be necessary to go somewhat deeper into the matter.
In every artistic whole there must be balance and proportion. In musical works this is chiefly obtained by the grouping of harmonies. An artistic whole may be obtained in one key by throwing stress first upon one harmonic centre, passing from that to one which represents an opposite phase, and then passing back to the original again. In the article Harmony it has been pointed out that the harmonies of the Tonic and the Dominant represent the most complete opposition of phase in the diatonic series of any key; the most perfect simple balance is therefore to be found in their alternation. For example, the first fifteen bars of the Trio in the Scherzo of Beethoven's Symphony in A form a complete artistic whole of themselves. There are six bars of Tonic harmony and one of Dominant forming the first group, and then six of Dominant harmony followed by one of Tonic harmony forming the second group. The balance is perfect, and the form the simplest in all music; and it might reasonably be called the 'simple primary form.' It is to be found in the most diverse quarters, such as single chants of the Anglican Church, sailor's hornpipes, German popular waltzes and Ländler, and the trivial snatches of tunes in a French opera-bouffe. The manner of obtaining the balance is however not necessarily restricted to the above order; for it is quite equally common to find each of the two groups containing a balance in themselves of Tonic and Dominant harmony. In that case the balance is obtained thus C G C C G C, instead of C G G C as in the former instance; but the principle which underlies them is the same, and justifies their being classed together. The subsidiary harmonies which are associated with these main groups are independent, but are most effective when they converge so as to direct attention to them. When greater extension is required, the balance is found between key and key; each key being severally distinguished by an alternation of harmonic roots, so as to be severally complete when they are to be a prominent part of the form. Subsidiary transitions occur much as the subsidiary harmonies in the preceding class, and must be regarded in the same light. The identity of principle in these two classes is obvious, since in both alike it consists of taking a definite point to start from, and marking it clearly; then passing to another point, which will afford the needed contrast, and returning to the original to conclude. But as in the latter class the process is complicated by the changes of key, it may best be distinguished from the former as 'complex primary form.'
It is not necessary to enter into details on the subject of the extent, treatment, and distribution of the keys; neither is it possible, since the principle when put upon this broad basis admits of very great variety, as indeed it is desirable that it should. But to guard against misapprehension, it may be as well to point out a few of the broadest facts.
In the first place, the several sections which serve to mark the elements of form need not be distinct and independent pieces, though they most frequently are so in the older opeta and oratorio songs, and in the minuets and trios, or marches and trios, of instrumental music. In many examples, especially such as are on a small scale, there is no marked break in the continuity of the whole, the division at most amounting to nothing more than a cadence or half-close and a double bar, and often to not even so much as that. With regard to the distribution of ideas, it may be said that the several sections are often characterised by totally independent subjects, especially when the piece is on a large scale; but there are many examples, especially in the form of themes for variations, when, notwithstanding a certain freedom of modulation, the predominance of one main idea is unbroken.
Professor Marx has called attention to the fact that this form is sometimes amplified by repetition; that is to say, when the return to the original key has been made to follow the contrasting section or Trio, a fresh departure is made, and another contrasting section or Trio is given, after which follows the final return to the original key and idea. Examples of this occur in the Symphonies of Beethoven and Schumann, as well as in less important works; and it is well to take note of the fact that in this case the form under consideration shows its close relationship to the Rondo form; for that form in the hands of early instrumental composers such as Rameau and Couperin was little else than the frequent repetition of a main idea in a principal key, interspersed with contrasting episodes, which in the present case answer to the Trios.
The occurrence of Codas with this form is very common, but for the discussion of that point reference must be made to the article under that head and to the article Form.
Finally, it will be well to return shortly to the consideration of the distinctive name of 'Lied' which has been given to this form. In the choice of it, its author was probably guided by a well-grounded opinion of the superior antiquity of song to other kinds of music, which led him to infer that the instrumental forms which he put under the same category were imitated from the 'Lieder.' But this is not by any means inevitable. It will have been seen from the above discussion that in this form the simplest means of arriving at artistic balance and proportion are made use of; and these would have been chosen by the instinct of the earliest composers of instrumental music without any necessary knowledge that vocal music was cast in the same mould. And there is more than this. In songs and other vocal music the hearer is so far guided by the sense of the words that a total impression of