MUSIC 85 ceases, for the effect of such unity supersedes harmony for the moment. There are certain keys which have a close alliance to others. Given a certain key or tonic, for example, on which it is proposed to write a piece, say C : the keys having the closest alliance to this are G major, the fourth below ; A minor, the third below ;. F major, the fourth above ; and E minor, the third above. Next in order of alli- ance to are E major, E flat major, A major, and A flat major. The key of B major is widely dissociated from C ; so too B flat ma- jor; and F sharp major is a distant musical shore only to be approached in a long musical voyage. D minor and D major in their rela- tions to C can be used but transiently. D flat major can be reached readily through minor. The passing to a new key without an inter- mediate chord is called a transition ; when one or more chords are used, it is called a modu- lation. Transitions are among the brilliant effects of modern dramatic music. A great surprise, sudden and violent emotion, warrants a transition, and the change may be further enforced by an explosion of all the orchestral instruments. The transition is marked in pro- portion as the notes of the scale are changed. A transition from to G for the purpose named would be timid and feeble ; but one from C to A flat or D flat would be effective. In the one case all the notes of the chord of G are found in the scale of C ; in the others, two notes are changed ; hence the shock. "We close this portion of the article with a few observations on the relations existing between the physical theory of consonance and disso- nance and the aesthetics of music. Helmholtz founds his theory of consonance and dissonance on the fact that whenever a dissonance is per- ceived beats are produced by the constituent sounds of the chord, and that in consonance these beats are few or entirely wanting. On this physical basis the intervals are placed in the following order, according to their degree of freedom from dissonance. The octave stands first, then follow the fifth, the fourth, the major third, the major sixth, the minor third, the minor sixth. This classification, as stated, is based on the decreasing number of beating harmonics in the successive intervals; but it does not necessarily follow that the smoothest chords will always be those which are musi- cally the most pleasing ; for may there not be some other property which gives us greater satisfaction than mere consonance ? "^Esthetic considerations come in here, with the same right to be heard as mechanical considerations within their own domain. Now unquestion- ably the ear's order of merit is not the same as the mechanical order. It places thirds and sixths first, then the fourth and fifth, and the octave last of all. The constant appearance of thirds and sixths in two-part music, com- pared with the infrequent employment of the remaining concords, leaves no doubt on this point. In fact these intervals have a peculiar richness and permanent charm about them, not possessed by the fourth or fifth to anything like the same extent, and by the octave not at all. The thin effect of the octave undoubtedly depends on the fact that every harmonic of the higher of two musical sounds forming that interval, coincides exactly with a harmonic of the lower sound. Thus no new sound is intro- duced by the higher note ; the quality of that previously heard is merely modified by the alteration of relative intensity among the con- stituent harmonics. Major and minor thirds bring in a greater variety of pitch in the re- sultant mass of sound than does the fifth ; but this can hardly be said of the major and mi- nor sixths compared with the fourth. On the whole, we are inclined to attribute the predi- lection of the ear for thirds and sixths, over the other concords, to circumstances connected with its perception of key relations, though we are not able to give a satisfactory account of them. The ear enjoys, in alternation with consonant chords, dissonances of so harsh a description as to be barely endurable when sustained by themselves. This constitutes a marked distinction between it and the other organs of sense. As instances of the kind of discords in which the ear can find delight, take the following. The chord marked * should in each case be played first by itself, and then in the place assigned to it by the composer. The effect of this isolated discord is so intensely harsh that it is at first difficult to understand how any preceding and succeeding concords can make it at all tolerable ; yet the sequence, in both phases cited, is beautiful. Last Chorus, BACH'S Passion." (St. Matthew.) Considerations such as those just alleged tend to show that, while physical science is ab- solutely authoritative in all that relates to the constitution of musical sounds, and the smoothness of their combinations, the com- poser's direct perception of what is musi-
