affords a full musical enjoyment, sensuous as well as aesthetic and intellectual. Further, when the ear is able to recognize the exact shade of melodic quality in an interval, as that of the fifth, fourth, etc., it discovers numberless points of likeness in the successive steps of a movement, and in this way various sequences of notes become united under another pleasing aspect of artistic unity.

The simplest form of such Melodic Uniformity is supplied by the recurrence of a melodic interval or series in precisely the same order, and in the same octave, an element of variety being supplied by the introduction of subordinate and ornamental notes. Thus, for example, the two parts of the following series :

exhibit the same melody, slightly disguised in the second bar by the addition of the figurative notes. This mode of melodic resemblance is very conspicuous in the works of Haydn and Mozart, and forms the basis of Musical Variations.

A different form of melodic similarity presents itself when a given movement is transported into another region of tone, by the selection of a new initial note related to the first. The most obvious illustration of this mode of melodic variation is afforded by the repetition of a sequence of tones in a higher octave. The octave of a note is not only its closest melodic correlate, but also, in a sense, the same note in another locality. Hence to repeat a form of movement in different octaves is to preserve the greatest amount of melodic uniformity. When the timbre of the notes, as well as their height, is different, such a parallelism affords a very distinct pleasure, as may be seen in choral song and in orchestral music. The presence of melodic unity in diversity is, however, scarcely distinct till the initial notes of the parallel passages are qualitatively different. The simplest example of this melodic correspondence is an unbroken succession of fifths, fourths, etc. Such a series sounds, no doubt, very monotonous to a trained ear, and yet one may find in the classical writings of Mozart and Beethoven brief passages of just this simple character. A melodic parallelism becomes more pleasing when it connects, not pairs of tones, but longer series. A natural melodic order of tones is that of the common chord, namely, the third, fifth and octave; and a melodious combination which moves through this simple order may be reproduced in a slightly

altered form, by simply changing the initial tone. For example, in the opening Allegro of Mozart's sixth Sonata, one finds the following parallelism among many others:

&c.

Every student of music is aware how frequently a simple melodic phrase is repeated with a slightly different starting-point, as for example, the fifth or fourth of the first note. Indeed, the developments of melody display conspicuously the aesthetic value of such discoverable resemblances. A common change of movement in all the simpler forms of song is from a melodic series in the order of the common chord of the tonic, to a corresponding series in that of the fifth of the tonic. For example, a German Volkslied which begins with the following simple melody,

goes on to repeat a part of this melodic movement in the key of the dominant (G).

Another example of such simple melodic parallelism, disguised, however, by a happy admixture of variety, may be found in a wellwell known song of Mozart, which begins as follows :

In the higher styles of composition the same thing is observable. In the picturesque windings of an aria or of a sonata-melody, the recurrence of similar melodic phrases in related keys is a source of a distinct æsthetic gratification. In polyphonic music, again, one may see the influence of this æsthetic principle in the laws of fuguestructure, according to which the leading theme has to be resumed by another part, either in the same key or in a related key, namely, that of the fifth or dominant.

These melodic variations and symmetrical combinations, however influential in the total effect of music, do not constitute the whole charm of melodic form. As I have already remarked, a chief element of beauty in sequent groups of æsthetic impressions is the presence of a point of final repose, towards which all the steps of the movement may be seen to lead up. We discovered an imperfect form of this progressive side of musical unity in the arrangement of tones with respect to a final and restful level of tonic height. A far more potent influence in uniting the successive parts of melodic structure is supplied by our system of Tonality, which erects a certain note, namely, the tonic or key-note, into the ruling member of the series, the point of departure and of final repose in melodic

movement.

Our modern Key-system, major and minor, appears to owe its æsthetic value to three circumstances. First of all, it supplies a central point to melodic movement, about which it may wander, and towards which it may tend as its resting-place; secondly, it affords as the framework of melody, a series of tones closely united to one another by natural affinity; while, finally, it furnishes an ample range of movement of fairly equal gradations.

The erection of a particular tone into a unique prominence and supremacy appears to a modern ear an essential element of all melody; and one finds, as a matter of history, that even in the rudimentary scales of the Greeks, a special honour was given to the middle tone (μéon). In our modern system of major and minor keys, the relation of the successive steps of a melody to the tonic is made more distinct by the addition of harmony and determining chords. In simple movements it is the presence of one key-note which defines the steps of the melody. In by far the largest number of cases melody sets out and returns to the same note. By the same note I mean, of course, a given note, such as C or G, in any octave. I have already remarked that the octave of a note holds a unique melodic relation to it, by reason of which it is called by the same name. Hence, there is a number of notes, as C1, C2, C3, etc., which

* As I remarked in the previous essay, Helmholtz seeks to construct both the major and minor modes of scale by means of two degrees of natural affinity. In the minor key the successive notes have less melodic affinity with the tonic, and to this fact seems to be owing the characteristic obscurity and elegiac sadness of this scale.

† Aristotle has some curious speculations on the reasons of this supremacy. See Problemata XX. and XXXVI., quoted by Helmholtz.

may alike serve as resting-points, though the range of these is limited by the demands of a familiar level of tone already referred to.* In the smaller number of cases in which the initial and final tone of a melody does not coincide with the key-note, it falls on some closely related note, namely, the third or fifth, which by its constant presence in the chord of the tonic acquires a representative character in respect of the key-note. Further, our tonic system allows of transitory changes of key, through which a melody gains, not only greater variety, but also new points of departure and repose. In this way a movement may make, so to speak, a temporary halt, lingering in some related major or minor key, and so fall into distinct passages, each of which has its own circular route to and from its key-note. In other words, in addition to the larger and permanent controlling point of rest, modulation in other keys supplies subordinate and temporary controlling points.

There is little space here for illustrations either of the progressive unity or of the symmetry thus given to melody by the dominance of a key-note. A very simple sequence of tones becomes pleasing when thus confined in one progressive order, as may be seen in the Swiss Ranz des Vaches:

The melody becomes more picturesquely varied and symmetrical when it falls into two parts, of which the first has its own temporary repose. The most common case of such division is when the intermediate point of rest coincides with the dominant, as in the following series.

Here the whole movement falls into two melodic phrases, of which the first is a departure from the tonic (G), in the direction of the dominant (D); and the second, a return from this point of momentary sojourn to the primal resting-place. Thus it possesses a simple progressive unity while it presents the hearer with distinct

Owing to this fact of the perfect resemblance of a note to its octave, the progress of the tonic scale is alternately towards and from the point of repose. Accordingly, it has been represented by one German writer as a spiral curva winding about a vertical cylinder.

and well-balanced parts. And the same holds good of all the more complex groupings of melodic phase.

I may conclude this account of the aspects of melodic form, by referring to the effect of culture on the perceptions of these characters. Just as familiarity with the whole series of scales supplies the mind of a hearer with definite ideal standards of height, etc., so a knowledge of the tonic system supplies it with a new standard of melodic form. In attending to a new composition an amateur instinctively seeks to discover the ruling key-note, and, retaining this in memory, he views all successive phases of melody in relation to it. Every clang in the melodic series is faintly estimated as a correlate of the tonic, or of some new note which temporarily fills the place of the tonic, and thus clearer intuitions of melodic character are obtained. Further, through the retention of this dominant element, the hearer instinctively anticipates a final return to the same point; and to this fact are due such effects as the ear's dissatisfaction at too long a sojourn in a foreign key, the slightly teasing yet pleasantly stimulative impression of a partial but illusive conclusion, and the deep content it experiences at the realization of the final repose.

The nature of Harmony, as a form of immediate sensuous pleasure, has been sufficiently discussed in the preceding essay. We have now to consider it as an element of musical form.

In

The intellectual ingredient in the perception of harmony begins with the discrimination and recognition of definite shades of this quality. When this capability is acquired, music presents new aspects of clearness and simplicity, and of obscurity and mystery. this way, for example, the bright clear chords of the major are distinguished from the gloomy and troubled combinations of the minor. And thus music gains, with the addition of harmony, a new element of variety and of unity. A change from pure harmony to disturbing discord constitutes the strongest form of musical contrast. Passages from the perfect harmonies of the major common chord (C—E—G) to less perfect accords afford elements of variety and artistic relief. On the other hand, sequences of chords of similar harmonic character manifest a certain aesthetic unity. Finally, a movement which passes from imperfect to perfect harmony, or through the three phases of initial clear harmony, mediate temporary discord or clouded harmony, and final perfect harmony, presents a pleasing mode of progressive unity. All students of music know how the introduction of obscure chords at the commencement of a piece stimulates expectation, while the addition of them to a con