From a comprehensive view of this table it is manifest, there might be other methods of arranging its details. Each 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 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; Second, its direct and inverted; and Third, 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 Unequal; and subdividing each of these by the five intervals of the scale, shall under the heads of these intervals, consider the direct and inverted, the single and double forms.

The pains taken to define the technical terms of this essay, together with the exemplification by diagrams, in the second section must have rendered all the movements through the scale, quite familiar to those who really desire to learn. The description of the wave may therefore be so easily understood, that without a further notation, the reader can readily imagine its various forms, in applying them to syllables.

In order to understand the purpose, and expression of the wave, let us recollect that it is compounded of a rising and a falling interval, the several characteristics of which have already been described. Now it will be found, that the wave generally partakes of the respective powers of its constituents; and further, that a continuous line of contrary flexures, enables the voice to carry on a long quantity, without the risk of falling into the linear intonation of song.

The expression of the wave in all its forms, is modified by the application of stress to different parts of its course: at the beginning, or at the end, or at the place of junction of its constituents.

SECTION XXVI.

Of the Equal Wave of the Octave.

THE Equal Wave of the Octave, is made by a movement of the voice, through its upward, and continuously into its downward interval. 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, forming the direct; and by a reversed succession, forming the inverted wave.

The equal wave of the octave in its single form is rarely employed in serious discourse. If used in the lower range of pitch, to avoid the sharpness of the falsettte, it gives an appropriate expression to the strongest sentiment of astonishment and of admiration. When it assumes the higher range, as it is apt to do, it loses its dignity as an impressive sign. Children sometimes employ it for mockery in their contentions and jests. Its double form has the same expression, under a more continued quantity. The reverse order of its constituents, gives a different character, respectively to its single-direct, and its single-inverted forms; for the latter by ending in an upward concrete, has the intonation of a question, through what we called the Interrogative Wave while the former by a downward final movement, has the positiveness and surprise of the simple falling intervals. When the direct and the inverted wave of the octave is respectively double, the rule of final expression will be reversed; for the doubledirect will then end with the rising or interrogative movement.

On the whole, the double form of the wave claims attention rather as a part of our physiological history, than as a subject of oratorical propriety and taste; and may, in point of use and expression, be rather classed among vulgar mouthings.

SECTION XXVII.

Of the Equal Wave of the Fifth.

ENOUGH has been said of intervals, to explain the nature of the Equal Wave of the Fifth. Its nomenclature is descriptive of its structure. Nor need it be shown particularly of this, nor indeed of the succeeding sectional heads of the wave, in what manner the single and double, the direct and inverted forms are made.

The equal wave of the fifth, 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, each having in its separate state, respectively, the sentiment of interrogation and of positiveness and surprise. But a junction of these opposite constituents takes in a great degree, from the rising, its indication of a question, while it leaves to the falling, the full character of positiveness and surprise. There is however, another effect of this junction, besides the overruling of interrogation. When' a sentiment requiring the downward fifth, is grave or dignified, that character is expressed by pre-joining the rising fifth, and thus forming the direct wave. And further, the direct wave is used instead of the simple fall, merely to give time to the syllable that bears it; for should the sentiment of the emphatic syllable require a prolonged quantity, this wave takes the place. of the simple interval, which under unskillful intonation might, in the effort to extend it, be liable to pass into the linear intonation of song.

The inverted wave of the fifth has the compound expression of surprised interrogation, produced by the termination of its last constituent in the upward vanish. And thus it appears, the direct wave of this, as well as of other wider intervals, retains a degree of interrogation; and the inverted, a degree of its positiveness and surprise.

There is not much difference between the expression of the single, and the double wave of the fifth, except what arises from a change of structure 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 doubleinverted has the meaning of surprise from its downward termination. Perhaps there is a little scorn conveyed by the double form 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 sign of expression.

SECTION XXVIII.

Of the Equal Wave of the Third.

THE Equal Wave of the Third, in the degree of its expression, bears such a relation to the equal wave of the fifth, as the simple rise of the third bears to the simple rise of that interval.

In all its forms, whether single or double, direct or inverted, the expression resembles respectively, but in a more moderate degree, that of the different species of the equal wave of the fifth. From its less impressive character, it is more frequently employed for emphasis in plain and dignified discourse, than the fifth and the octave, which are especially appropriate to colloquial dialogue, and to the wider intonation of the drama. It also serves, like the other waves, to extend the quantity of syllables in deliberate and dignified discourse; and to preserve, at the same time, the characteristic concrete of speech.

The equal wave of the minor third is used in song, but is not admissible into speech. The expression of the inverted wave of this interval, does not differ much from that of its direct form.

SECTION XXIX.

Of the Equal Wave of the Second.

WE have now to consider the equal wave of the second, which if ever the time for a Natural, and thereupon a Scientific System of Elocution shall come to pass, will be regarded as a very important and interesting part of intonation.

The difficulty of arranging perspicuously the details of a subject, altogether as new to the author himself, as to his reader; and of giving a full description of parts that are elementary and closely related, but that must be successively explained, has obliged me to proceed in the way of gradual and partial development; of subsequent addition; of anticipation; and of frequent reconsideration, which distinguishes the proposed method of this essay. For the complete arrangement of a science, which in the progress of years or centuries, has gradually grown to the fulness and accuracy of its definitions and order, method after method has been tried and rejected; and the studious inquirer, knowing the attempts and failures of his predecessors, is taught the deficiencies and requisites of classification. But for this offered system of intonation, there was no preceding outline of truth; no instructive sketches of corrected errors, to save me from my own; and as yet, even no friendly-enmity of criticism to 'pluck' them from my pages and 'throw them in my face.' I was therefore at first, and even in preparing this fourth edition, obliged to ask the poor assistance of my own endeavors, to supply my oversights, and correct my faults. A hard, and too often a vain and fruitless labor. Consistently with the manner of Dividing and Instructing here employed, our account of the diatonic melody, regarded only the radical and concrete pitch of the second, and its successions; in order thereby to avoid confusing the reader. Other functions and uses of the concrete were therefore kept out of view. It