From a comprehensive view of this table it will be manifest to the reader, that there are several different modes in which these functions may be arranged. Any of the distinctions given above might be taken as the generic heads of the wave; and the others might be included as species. Thus we might take the five intervals for the heads of as many sections. Then under each, for instance the octave, we might consider,-first, the equal form of this interval, and its combination with other intervals into the unequal form; secondly its direct and inverted, and thirdly its single and double forms. Or we might take the distinction into single and double for the two generic heads, and under each of these, enumerate the species, as being equal or unequal, direct or inverted and so of any other assumed order of these distinctions.

I shall, according to the arrangement in the table, divide the phenomena of the wave into two great classes, the Equal and the Unequal; and subdividing each of these by the five intervals of the scale, I shall under the heads of these intervals, consider the direct and the inverted, the single and the double forms of this element.

The pains which have been taken to define the technical terms of this essay, and the many illustrations which have been given, must have rendered the nomenclature and picture of the scale quite familiar to those who really desire to learn. The description may therefore be so easily understood, that it is unnecessary to give a notation of the wave. The reader may mark it for himself, and apply it to those syllables that convey the sentiments which will be hereafter assigned to its different forms, I shall give some examples of its use in a future section on emphasis.

SECTION XXV.

Of the Equal Wave of the Octave.

By the designating term of this section is meant the continuous movement of the voice, in the succession of its upward and downward direction, through the interval here named. It may be either single, consisting of two constituents; or double, consisting of three: though this double form is scarcely used. It may also be differently constructed, by the first constituent ascending, and the second descending, which was called the direct wave; and by the reverse order of movement, which was called the inverted wave.

In order to understand the nature of the expression of the wave, let us recollect that this element is compounded of a rising and a falling interval, the respective expressions of which have already been described. Now it will be found that the wave generally partakes of the powers of its constituents; and further, that by its continuous flexure it enables the voice to carry on a long quantity without the risk of falling into the intonation of song.

It is proper to state in this place that the wave in all its forms, is modified by the application of force upon different parts of its course. I shall particularly speak hereafter of the variation of the power of the concrete by stress. I only remark at present, that it may be applied at the beginning or the end of the line of the wave, or at the place of junction of its constituents; and that the addition of force to its termination gives to the several species of the equal wave, a coloring of temper and of scorn, which they do not possess in the natural or dwindling form of the concrete.

The equal wave of the octave in its single form is not used, as far as I know, except for common colloquial mockery. In its double form it has the same expression, under a more continued quantity. If any distinction may be made between its

direct and inverted forms, the latter from its ending in an upward concrete carries the power of interrogation: whilst the former, from its downward final movement, has the positiveness which was ascribed to the falling intervals when uncompounded. If the direct and inverted wave of the octave be double, the rule on this point will be reversed; for the direct will then end with the rising movement.

On the whole, this element, in all its ways, belongs more to the mere history of speech than to its elegancies; and may rather, in point of use and expression, be classed among vulgar mouthings.

I HAVE said enough of the nature of the wave and of intervals, to make it unnecessary to define this element. Its nomenclature alone is sufficiently descriptive of its structure. Nor need I say particularly of this nor indeed of the succeeding sectional heads of the wave, in what manner their single and double, their direct and inverted forms are made.

The equal wave of the fifth in each of its modes is used as one of the means of emphatic distinction; and has therein an expression varying with its form. The equal single direct wave of the fifth consists of an ascending and descending concrete, which have in their separated state, respectively, the sentiment of interrogation and surprise. But the conjunction of the opposite movements of those concretes, takes from the ascending interval, its indication of a question, and leaves the impressiveness of surprise or admiration on the syllable to which it is applied. But there is another effect produced besides this

annulling of interrogation. We have already learned that there is some difference between the expression of the rising and the falling concrete. The former is more cheerful and animated in its cast, the latter more deliberate and grave. Now if the discourse in which an impressive intonation of the fifth is to be used, is of a dignified character, that impressive intonation is given to the emphatic syllable by a continuation of the upward into the downward flow of this interval, in the form of its direct wave. But further, this wave is used instead of the separate rise or fall of its interval, for the purpose of giving more quantity to the syllable which bears it. I alluded to the emphasis of the simple fifth, in the fourteenth section, without a special reference to time: but if the sentiment of the phrase is such as to require an unusually long quantity, this wave or continuous downward turn of the fifth, takes the place of that simple ascending interval, which, in unskilful intonation, might be liable to pass into song.

The inverted wave of the fifth has the expression of surprised interrogation, arising out of the termination of its last constituent in the upward vanish of an interrogative interval.

There is not much difference between the expression of the single and the double wave of the fifth, except in the change of structure produced by the addition of a third constituent. The double-direct here assumes an interrogative expression, from the vanishing rise of its last constituent; and the double-inverted has the meaning of surprise from its downward termination. Perhaps there is a little scorn conveyed by the double forms of the equal wave of the fifth. This is certainly the case when the last constituent receives greater stress than the others. On the whole, however, this double form is not very frequently used as a symbol of expression.