A further illustration of the relations of chords is afforded by those of the Dominant and Tonic. They are connected by their roots being a fifth apart, which is the simplest interval, except the octave, in music; but their other components are entirely distinct, as is the compound tone of the roots, since none of their lower and more characteristic harmonics are coincident. They thus represent the strongest contrast in the diatonic series of a key, and when taken together define the tonality more clearly than any other pair of chords in its range.
The relations of keys are traced in a similar manner; as, for instance, by the tonic and perfect fifth of one being in the diatonic series of another, or by the number of notes which are common to both. The relations of the keys of the minor third and minor sixth to the major mode (as of E♭ and A♭ with reference to C) are rendered intelligible through the minor mode; but the converse does not hold good, for the relations of keys of the major mediant or submediant to the minor mode (as of E minor and A minor with reference to C minor) are decidedly remote, and direct transition to them is not easy to follow. In fact the modulatory tendency of the minor mode is towards the connections of its relative major rather than to those of its actual major, while the outlook of the major mode is free on both sides. The relation of the key of the Dominant to an original Tonic is explicable on much the same grounds as that of the chords of those notes. The Dominant key is generally held to be a very satisfactory complementary or contrast in the construction of a piece of music of any sort, but it is not of universal cogency. For instance, at the very outset of any movement it is almost inevitable that the Dominant harmony should early and emphatically present itself; hence when a fresh section is reached it is sometimes desirable to find another contrast to avoid tautology. With some such purpose the keys of the mediant or submediant have at times been chosen, both of which afford interesting phases of contrast and connection; the connection being mainly the characteristic major third of the original tonic, and the contrast being emphasised by the sharpening of the Dominant in the first case, and of the Tonic in the second. The key of the subdominant is avoided in such cases because the contrast afforded by it is not sufficiently strong to have force in the total impression of the movement.
The relations of the parts of any artistic work in a similar manner those of contrast within its of proportion and tonality. For instance, those of the first and second section in what is called 'first movement' or 'sonata' form are based on the contrast of complementary tonalities as part of the musical structure, on the one hand; and on contrast of character and style in the idea on the other; which between them establish the balance of proportion. The relation of the second main division—the 'working-out' section—to the first part of the movement is that of greater complexity and freedom in contrast to regularity and definiteness of musical structure, and fanciful discussion of characteristic portions of the main subjects in contrast to formal exposition of complete ideas; and the final section completes the cycle by returning to regularity in the recapitulation.
The relations of the various movements of a large work to one another are of similar nature. The earliest masters who wrote Suites and Sonate di Camera or di Chiesa had but a rudimentary and undeveloped sense of the relative contrasts of keys; consequently they contented themselves with connecting the movements by putting them all in the same key, and obtained their contrasts by alternating quick and slow movements or dances, and by varying the degrees of their seriousness or liveliness: but the main outlines of the distribution of contrasts are in these respects curiously similar to the order adopted in the average modern Sonata or Symphony. Thus they placed an allegro of a serious or solid character at or near the beginning of the work, as typified by the Allemande; the slow or solemn movement came in the middle, as typified by the Sarabande; and the conclusion was a light and gay quick movement, as typified by the Gigue. And further, the manner in which a Courante usually followed the Allemande, and a Gavotte or Bourrée or Passepied, or some such dance, preceded the final Gigue, has its counterpart in the Minuet or Scherzo of a modern work, which occupies an analogous position with respect either to the slow or last movement. In modern works the force of additional contrast is obtained by putting central movements in different but allied keys to that of the first and last movements; the slow movement most frequently being in the key of the Subdominant. At the same time additional bonds of connection are sometimes obtained, both by making the movements pass without complete break from one to another, and in some cases (illustrated by Beethoven and Schumann especially) by using the same characteristic features or figures in different movements.
The more subtle relations of proportion, both in the matter of the actual length of the various movements and their several sections, and in the breadth of their style; in the congruity of their forms of expression and of the quality of the emotions they appeal to; in the distribution of the qualities of tone, and even of the groups of harmony and rhythm, are all of equal importance, though less easy either to appreciate or to effect, as they demand higher degrees of artistic power and perception; and the proper adjustment of such relations are as vital to operas, oratorios, cantatas, and all other forms of vocal music, as to the purely instrumental forms.
The same order of relations appears in all parts of the art; for instance, the alternation of discord and concord is the same relation, implying contrast and connection, analogous to the relation between suspense or expectation and its relief; and to speak generally, the art of the composer is in a sense the discovery and exposition of intelligible relations in the mutifarious material at his command, and a complete explanation of
