2. The pleasing effect of a succession of sounds, like that of a combination, arises primarily from our perception of definite relations between the several sounds; and, as all the most nearly related sounds which can be formed upon any given root or prime are included in the common chord upon that root, hence the sounds of a chord come to be a very common foundation for melodic successions. Successions derived from this source abound in music; scarcely any melody will be found without them. In their original or primary position, the sounds of a chord form a melodious succession, whether sung in ascending or descending order; and the number of transpositions of which they admit, especially when they are extended beyond the range of a single octave, is obviously great. The intervals which are included in any one common chord thus extended, and which are called the consonant intervals, are the octave, the fifth, the fourth, the major and minor third, and the major and minor sixth. This may be seen from the following illustration (Fig. 2):-\

It is obvious, then, that these intervals should be practised as parts of the chords to which they belong, and not as parts of sequences_comprising all the intervals of the same name in the scale. Yet the latter plan is the one adopted by all the books of instruction with which we are acquainted, except that of M. J. Rudolf Weber.

In a sequence of thirds, intervals that belong to the same chord are separated by the intervention of others belonging to different chords; thus the intervals do-mi and mi-sol are separated by re-fa, re—fa and fa-la by mi-sol, mi-sol and sol-si by fa-la, and so on (Fig. 3) :

FIG. 3.-SEQUENCE OF THIRDS.

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Worse than that, a sequence of fifths violates the one best established rule of musical composition, for it produces a parallelism of consecutive fifths, or of two different scales, as may be seen in the following illustration (Fig. 4) :—

FIG. 4.-SEQUENCE OF FIFTHS.

And the sequence of sevenths is yet more barbarous, for it produces a parallelism of positive dissonances (Fig. 5):

FIG. 5.-SEQUENCE OF SEVENTHS.

In both cases the parallelism is the more apparent the more rapidly the intervals are sung; and, therefore, the better the pupils can perform the exercises, the worse it is for themselves and for everybody else within hearing.

Nor is it necessary, on the plan which we propose, that the consonant intervals should be thrummed out by running up or down the intervening degrees of the vocal ladder. On the contrary, we have shown that the diatonic steps should be taught by means of the chord notes. The latter are more closely related to one another than they are to the intervening sounds, the introduction of which, therefore, can only have the effect of obscuring the perception of that more intimate relationship.

Those persons who teach consonant intervals by dissonant ones would seem to have a very inadequate confidence in the construction of other persons' ears. They seem to regard the human ear (in others, of course) and music as two heterogeneous things, which, by their management, have to be brought to tolerate each other; and really, with the kind of music to which they too often treat their pupils, this is no very incorrect view of the case. But would it not be better to bear in mind that there is an exquisite adaptation between musical sounds and the human ear, or rather the human soul, and to count upon that adaptation in our instruction? Every teacher of music knows that it is easier to sing a chord than a scale, and yet nearly every teacher persists in teaching (?) the intervals of a chord by means of the successions of the scale. We propose the following plan for teaching chord successions :Every diatonic major scale contains six triads, half of the number being major and half minor, a symmetrical feature in the structure of the scale which does not appear to have been sufficiently noticed. Taking the natural scale, for the sake of simplicity, we have the following triads (Fig. 6) :—

FIG. 6.-TRIADS IN THE MAJOR SCALE.

It will be observed that each set of triads includes all the sounds of the scale; but how different is the disposition of those sounds in the two cases-how distinct the effects produced in each-and how great the variety which is thus introduced into the system! Much of the effectiveness of musical composition arises from the skilful intermixture of these two kinds of triad.

The major triads are the more simple, natural, and easy. They have already been practised to some extent, as the foundation of the scale; and so far a preparation will have been made for the more extended practice which must now be undertaken.

At first, each triad should be taken separately. The intervals included in it should be practised, first individually, and then in combination, in successions formed out of its sounds. Such successions the teacher may construct for himself, and write off hand on the music-board. They should be as varied as possible, and for this reason they must not be restricted to the limits of the octave. We subjoin one example in each triad (Fig. 7):

FIG. 7.-SUCCESSIONS IN THE THREE MAJOR TRIADS.
Tonic Triad.

Subdominant Triad.

Dominant Triad.

When a few such exercises have been practised, the successions in the subdominant and dominant triads should then be severally united to the successions in the tonic triad, in the same manner as the triads themselves were united in our exposition of the harmonic development of the scale, under the foregoing principle. We shall thus obtain more extended successions.

The union of subdominant with tonic successions will give us melodic phrases like the following, according to the degrees in the triads on which we found the successions (Fig. 8):

FIG. 8.-UNION OF TONIC AND SUBDOMINANT SUCCESSIONS.

We have placed under each succession the triad from which it springs. It will facilitate the singing of the passages, if the harmonic progression be heard at the same time. The class may be divided into four divisions, one to sing the melody, while the other three sustain the triads. The change from one triad to another may be made at a signal from the hand of the teacher.

Similarly, the union of dominant with tonic successions will give passages like the following (Fig. 9):—

FIG. 9.-UNION OF TONIC AND DOMINANT SUCCESSIONS.

At this stage, the teacher should explain to his pupils that to the third and fifth on the dominant the seventh (fa) may be added, whereby what is called the chord of the dominant seventh is produced. The progression of the tonic and dominant harmonies, and the melodic successions arising therefrom, should then be practised over again with this more extended form of the latter harmony. The progression of the chords in the three positions will be as follows (Fig. 10):

FIG. 10.-PROGRESSION OF CHORDS OF TONIC AND SEVENTH.

And the melodic successions arising from that progression will be such as these (Fig. 11):

FIG. 11.-SUCCESSIONS IN CHORDS OF TONIC AND SEVENTH.

In these two melodic progressions, which we may call the subdominant and dominant progressions, we have the materials of a very large quantity of simple melody.

The sub-dominant progression cannot singly form the basis of a complete melody.

It is obvious that a piece of music, to have a complete effect, must give a decided impression of one key. Now, next to those of the fundamental or tonic chord, the sounds which are most characteristic of any one key are clearly the two which, with the first and second sounds of that chord, form the two semitones; for it is the position of these which distinguishes one major key from another. These sounds are, in any key, the seventh and the fourth (Si and Fa). The seventh is the more distinctive of the two, because it fixes the leading semitone, which is, of course, that of the principal or key-note. Hence it is, that the seventh of the scale is called by the French the "ton sensible," and by us the leading note."* It is indispensable, according to our modern ideas,† that this sound should be heard in any musical composition, however short, if not in the melody, at least in the harmony. Therefore, a complete composition cannot be formed from the subdominant progression, which does not include the seventh.

But the dominant progression does include the seventh, and accordingly it may of itself form the foundation of a musical composition; and the effect of such a composition is rendered fully complete and satisfactory when the chord of the dominant is employed in its extended shape, for then both the characteristic notes are present, the fourth sound of the scale being the one that forms the minor seventh on the dominant.

Compositions of this kind are the most simple and easy that exist in music, and they are therefore the first that should be practised by beginners in the art. That this is the natural course to pursue in teaching music, is further evidenced by the fact that it is precisely little ditties belonging to this class that are most readily caught up by the popular ear, and become most widely known. Each of the three national airs which we subjoin springs solely out of the harmonic movement in question by the melodic dispersion of the sounds of the two chords, and the introduction of passing notes connecting these sounds into scale passages. This common feature in their structure; their accidental correspondence in form of measure, length of phrase, and arrangement and number of phrases; and the further accidental and curious circumstance, that they are respectively founded for the most part on the three levels in the two chords (lowest, middle, and uppermost)-these several circumstances combined cause the three melodies to admit of being sung together by three different registers of voice, and to produce full harmony when so sung. We copy the idea, and the exact form of the melodies, which have undergone a few necessary alterations, from the first number of "Davidson's Handbook of Part-Music for Singing

* The explanation, so often given by teachers of singing, that the seventh is called the leading-note because it appears to lead into the key-note, is nonsense.

+ The Scotch Highlanders appear to have done without the seventh of the key in former times; but then these braw Hielandmen" have managed to do without many things which we consider indispensable.

Classes, Schools, and Families," in which they will be found, accompanied by suitable words, written by R. Crowe, Esq., Professor of Music in the Liverpool Collegiate Institution, with whom this clever idea appears to have originated (Fig. 12):—

FIG. 12.-THREE MELODIES FORMED FROM TWO CHORDS.

The union of the subdominant with the dominant progression gives rise to compositions one degree more complex, and therefore one degree more difficult, than the last. These compositions form a still larger class, including, besides waltzes and other easy dance-tunes, with which we have at present nothing to do, a considerable number of popular airs. Among these we may perhaps be allowed to mention the Scotch songs, "Auld Lang Syne," "Bonnie Dundee," ‚” “Bonnie Prince Charlie," "Ye Banks and Braes," "“Annie Laurie," "March, march over the Border," and "The Boatie rows;" the Irish air, My lodging is on the cold ground;" the Negro melodies, "Carry me back to Old Virginny," Lucy Neal," "Uncle Ned," " Buffalo Gals," "Sing, sing, ye Darkies,

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* London: G. H. Davidson, Peter's Hill, Doctors' Commons, price 6d.