The distance between any two points in the scale, whether proximate or remote, is called an Interval. A musical interval is defined to be "a quantity of a certain kind, terminated by a graver and an acuter sound." But for the purposes of speech, it is necessary to regard that quantity as either continuous sound, or imaginary space; and to consider the effect of the transit of the voice from one degree of the scale to another as constituting an interval, whether the voice is concretely heard or discretely omitted between them. The intervals in their proximate order are measured as follows:*

The interval, or the quantity of concrete voice either heard or omitted between the first and second places, as numbered in the diagram, is called a Tone.

That between the second and third is likewise a tone.

That between the third and fourth, which appears in the diagram, as but half the space of a tone, is called a Semitone.

The interval between the fourth and fifth; fifth and sixth; sixth and seventh, is each a tone-and lastly, that between the seventh and eighth, or first of the next series, a semitone.

The intervals between the degrees of the scale, whether proximate or remote, are designated numerically; the extreme degrees being inclusively counted. Thus, from the fourth to the third, or from the sixth to the seventh, is the interval of a second; and from the second to the sixth, or

visions of quantity. Thus Magnitude is the concrete quantity; for the lines, surfaces, and solids which constitute it, have their respective parts, so to speak, concreted or united immediately with each other-whereas Number is the discrete quantity; since the succession of its constituent integers is altogether different from any kind of continuity.

The most familiar illustration of these terms, as applied to the two kinds of quantity in musical sound, is furnished by the form of a ladder, in which the side rails represent the concrete, and the rounds the discrete.

The well informed reader should regard this general view of the scale, and the manner of its illustration, with a thoughtfulness of my design. I have omitted the theoretic distinction of greater and lesser tone, of diatonic and chromatic semitone, and of the major and minor scale, together with other particulars, both melodial and harmonic, with the intention to notice only what is preparatory to the description of speech.

from the fourth to the eighth, is the interval of a fifth. And so of the rest.

Though the several discrete sounds of the scale are named according to their ordinal number, yet the first, relatively to its rising series, is generally called the Key-note: whereas the eighth, when considered in relation to the previous keynote, is called the Octave; for otherwise it may be regarded as itself the key-note of the following series.

The succession of the seven sounds of any one series, to which the octave is usually added, is called the Natural or Diatonic Scale. It consists of five tones and two semitones; the latter being the spaces between its third and fourth, and its seventh and eighth degrees. The scale then contains these several kinds of intervals,-a semitone; a second, or whole tone; a third; fourth; fifth; sixth; seventh; and octave.

By the diagram, the interval between the second and fourth degrees, is numerically a third, yet contains but one tone and a semitone: whereas, that between the first and third contains two whole tones. From this difference in extent the former is called a Minor Third and the latter a Major Third. But since the minor third is of rare occurrence in speech, the term Third will, in this work, always refer to the major interval; and the minor will be specified when meant.

Having thus far, described the construction of the Musical Scale, I here advise the reader, who may not be a musician, and who may never have heard of the nature of that scale, to ask, from some qualified master, an audible exemplification. of its upward and downward progression, and of its several intervals; the varied practical exercises on which are, in the language of vocal science, called Solfaing and Solmization. Let him studiously imitate this exemplification, and commit it to memory. If destitute of what is called a musical ear, let him not think himself unable to learn that which he now considers as a part of music. In communities where the cultivation of this art is the fashion, these things are all

learned by thousands, who, with their natural ear, would never have caught up even a fragment of the commonest tune. And I am sure there is no one, into whose hands this book will ever fall, who can possibly avoid perceiving the several differences of meaning or expression, when he is addressed in the language of narrative, surprise, complaint, authority, or interrogation. Now these various expressive effects are perceptible to him, and accurately so, only because they are concrete or discrete movements of the voice through certain appropriate intervals of the scale. His ear therefore really recognizes these slides and transitions in speech. I shall only give to his understanding and his tongue, their musical method and names.

When an instructor cannot be met with, the use of a welltuned Piano-Forte may assist the perception of those who have no acquaintance with the scale. On the key-board of this instrument there is a front row of white keys, as they are called, and a rear row of black ones: a representation of the forms and positions of which, is given in the following diagram; where a portion of the Great Scale or Compass of the instrument is shown; and the white keys numbered above in continuation as far as twenty-one; and below in repeated septenary series.

1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

1 2 3 4 5 6 7,1 2 3 4 5 6 7.1 2 3 4 5 6 7

Now any one of the septenary series of white keys,-of which there are three in the diagram, the first beginning on its extreme left,-when struck successively ascending towards the right, gives the seven discrete rising sounds of the diatonic scale. The black keys, whose effect in modifying this scale will be noticed presently, are set between the

white ones, for the purpose of dividing the whole tones into semitones. Hence we see that the black keys are wanting at the semitonic intervals of the scale, where, of course, their design cannot apply. This omission visibly separates the black keys alternately into pairs and triplets.

With the foregoing explanation, the reader can have no difficulty in finding a diatonic series on the white keys of a Piano-Forte, since the key-note or beginning of the series always lies next below the pair of black keys. Let him then, on that series which suits the pitch of his speaking voice, severally utter the vowels, and some of their syllabic combinations, in unison with the instrumental sounds, both in their proximate order, and in the wider transitions of the other intervals of the scale, till the whole is familiar to his ear, and at the call of his memory. It is true, the PianoForte can show him only the discrete movements of pitch; but when these are under his command, the concrete, which are perhaps the most important in speech, can readily be measured by them. But to return to our definitions.

The sound produced at any of the places of the discrete scale, is called a Note. This term note, which signifies the continuation of sound on one unvarying line of pitch, is to be carefully distinguished from that of Tone. The term tone, in this essay, is applied, either to the concrete transit of the voice between any two proximate degrees, except those which bound a semitone, or to the amount of space between such degrees, when the transit is discrete.

As the term tone is thus used under two conditions, so are the terms of other intervals, included between remote degrees: for the voice may move concretely through these intervals, or notes may be made at these degrees, with the omission of the concrete. Let us call the former of these conditions, Concrete Intervals, and the latter Discrete Intervals.

The first, third and fifth notes of the diatonic scale, to which the octave, as a sort of repetition of the first, is usually added, differ from the rest, in being more agreeable to

the ear when heard in combination, and in immediate succession. The degrees, in this order, are also more readily hit by an inexperienced voice, in an endeavor to execute the several discrete intervals of the scale: and that simple instrument called the Jews-harp, together with some of the Horn species, more easily yields these notes under the faltering attempts of a learner. When therefore the pupil takes his lesson on the scale, let him familiarize his ear to the succession of the first, third, fifth and octave, omitting the intermediate degrees. Frequent reference will be made hereafter, to his perceptions on this point.

Below, is a representation of the manner in which musicians set their symbols for the diatonic sounds, on that linear table called the Staff. This staff consists of five horizontal parallel lines, having four spaces between them. Each space and line represents a degree of the scale: so that from space to line, and line to space, when they adjoin, is a second: and these degrees are called conjoint or proximate. When the discrete movement is over a wider interval than a second, it is called a Skip. The succession of the scale is here marked by black points, rising from the lowest line to the highest space of the staff: the intervals of the semitones being designated by a brace.

I have thus endeavored to describe the concrete movement of sound; and its discrete progression through the diatonic scale. But the discrete form of pitch appears under further subdivisions, which are effected in the following

manner.

In any series of seven notes, as the first marked in the preceding vertical diagram of the scale, and in that of the key-board, let us assume the Fifth, as the first of a new