that is, between the third and fourth degree, and between the third is minor, that is, composed only of a tone and a semitone, seventh and eighth degree. as may be seen in the following example: fig. 142.

Now, in the scale commencing with re' we should have a full tone between re' and mi, but between mi and fa only a semitone. It will be necessary to raise fa by a semitone, and between this elevated fa and sol, that is, from the third to the fourth degree, the semitone is necessarily found re-established in its proper position. The same thing will take place between si and ut, which are separated by a semitone in the normal scale; but in raising ut by a semitone, the order from the sixth to the seventh degree, and from the seventh to the eighth degree, would be equally re-established. These modifications are effected by the aid of two signs, the sharp, # and the flat, b. The sharp raises by a semitone, the note before which it is placed; the fiat, on the contrary, lowers it by a semitone. When the note sharpened or flattened is required to return to its normal or natural intonation, we prefix to it another sign, called the natural, viz. ↳. In this manner, the necessary order of tones and semitones in any scale can be fixed, and consequently as many scales as there are ones in the whole extent of the octave can be obtained. In order not to unnecessarily load the notation with signs, we place as the beginning of any piece of music, the accidents (that is, the sharps, the flats and the naturais), which ought to affect the modified notes throughout, and we give to each scale thus fixed the name of the note with which it commences. For example, when we say that a piece of mean that re' is the first low note, of the scale in which it is

music is in re', we or the fundamental written.

note

Modes. Our preceding observations relating to the structure of the scale have reference to the scale of ut as the model; we shall add here, of ut major, and we employ this phrase of transition in order to explain what is meant by mode. The word mode is applied to two different arrangements of the same scale-modifications which are very slight at bottom, but which communicate to it a character and properties entirely different. The language of music possesses two modes: the major and the minor. The former is especially applied to the exprcssion of joy, happiness and expanded sentiments; the other expresses sadness, grief, and dark, close, and contracted scutiments. These two modes, which are so different in their effects, differ from each other only by a slight alteration in the ystem of the scale. We have said that in the mode major, the semitones are situated between the third and the fourth, and between the seventh and the eighth degrees; in the mode minor, they are situated between the second and third, and between the seventh and eighth. Consequently, the difference consists simply in this, that in the mode minor, the first semitone is situated between the second and third degree, instead of between the third and fourth.

Fig. 112.

Mode mejor. Mode minor. Mode major.

Mode minor.

natural reciprocal relations, which exist either between the These two modes are connected with each other by very tones which bear on the clef the same accidents, or between the scale major and the scale minor of the same fundamental note. Thus the tone of at major has for its relative minor that of la minor, because neither bears any accident on the clef. The tone of re major (with two sharps) has for its relative si minor; the tone of re' minor (with a flat), is the relative of the tone of fa major, etc. Every scale can pass from the mode major to the mode minor, and reciprocally, without changing the fandamental note. For this purpose, it is sufficient to modify the signs of the clef so as to re-establish the required intervals by and the flats as negative signs, we pass from the mode minor to either mode. The sharps being considered as positive signs the mode major, by adding to the clef three positive signs; and in order to convert the mode major into that of minor, we add to the clef three negative signs. Moreover, it is evident that effacing the flats is equivalent to adding the sharps, and effacing the sharps is equivalent to adding the fiats. Examples: fig. 143.

From this arises an important point in the reading of music, namely, the determination of the tone of the fundamental note of the scale in which the piece is written. By the inere inspection of the signs placed on the clef, every musician must know what is the scale which is used as the foundation of the piece which he is about to perform. These signs are subject in their arrangement to rules so symmetrical that they are easily fixed in the memory as soon as they are studied with attention. The following is a summary of the preceding details in a few words :

The first sharp placed on a clef is always a fa. The following sharps are placed from fifth to fifth in the ascending scale: ut, sol, re, la, mi, si.

is

clef.

In the sharpened tones the fundamental note or tonic major always a semitone below the last sharp placed on the In the flattened tones the first flat is placed on the si. The following flats are placed from fifth to fif on the descending scale; si, mi, la, rẻ, sol, ut, fa.

In the flattened tones the fundamental note is always five degrees below the last flat; if there be several flats, the fundamental note rests on the last but one.

degrees above the fundamental note major, and inversely.
The fundamental note of a relative minor is always two

The normal scale of the mode minor is that of la. In com-fe, mencing with this note, we find a semitone between si and ut, that is, between the second and third degree. In following the ascending scale, we meet a semitone between mi and fa, and a full tone betwcen sol and la final. This has been the source of many disputes among musicians. Some have raised the fa as well as the sol by means of a sharp; others have preserved the fa in its natural state, and only raised the sol; a third set have inade no alteration, so that the semitone remained in its natural place between the sixth and seventh degree. Thus, there are three ways of terminating the ascending scale minor, and three ways of employing them at pleasure, but with very different effects; but it is to be especially observed that the principal character of this scale consists in the interval from the second to the third degree, which is always a semitone. All this proves, however, that the termination of the ascending scale minor is not an essential characteristic; but in descending this scale we can alter it as well as in ascending; and what is more remarkable is, that the interval between the seventh and eighth degree, which is called the sensible note, and which is almost forced to be a semitone in ascending, is more grateful to the ear in the descending scale when it is a full tone.

The fundamental difference between the mode major and the mode minor is expressed by saying that, in the former the third (the interval between the first and third degree) is major, that is, composed of two full tones; and that in the latter, the

Transition is made from a fundamental note major to the same fundamental note minor, by adding to the clef three negative signs, cr their equivalent.

Transition is made from a fundamental note minor to the same fundamental note major, by adding to the clef three positive signs, or their equivalent.

One point often embarrasses the student, respecting the determination of the tone; and this is the choice between the mode major or the mode minor represented by the same signs on the clef. One simple method of determining it is this: when the fundamental note is not clearly fixed by the first or the last concords of the piece, we search for what would be the sensible note (the 7th degree) of the tune if it be minor. In this case, the sensible note would be necessarily affected with an accident (positive or negative) in the course of the first

Points may be added to the rest-signs, and they serve also to increase them by half their value. It is plain, as this table shows, that the values of the notes and the values of the rests are the same in point of duration, and are employed to complete the measure in the same proportions. Their difference consists in their expression being negative instead of being positive.

Signs of Measure.-The measure of a piece of music is indicated on the clef by the following signs. The measure of two times, that is the binary measure, is expressed by a C, or by the figures; that of four times, by a C crossed vertically by a bar, thus ; the measure of three times, that is the ternary measure, is expressed by, or only 3, which signifies that it is composed of the value of three crotchets. An important variety of the measure of two times, or binary, is that which is marked, and of which each time is divided into three quavers. In the measure of four times, or quarternary, marked 13, each time is divided into three quavers, which is called a triplet. The measure is one of three times, each being represented by a quaver. General rule:-In every measure expressed by two figures of which one is placed above the other, the upper figure indicates how many times this measure must contain the division of the measure of four times expressed by the lower figure considered as unity. Thus indicates that the measure contains three times the fourth part of the measure of four times, or three crotchets; indicates that it contains nine times the eighth part of the same measure, that is, nine quavers; and so on. We must now determine the proper duration of this division of the measure taken as unity. There are two methods, the one approximate the other very exact. The former, which is the most common, consists in placing at the commencement of a piece of music a word generally taken from the Italian language, which indicates the movement of the composition. The words of this kind, although many, can be reduced to some standards which are modified by augmentative or diminutive expressions. Thus, a very slow movement is indicated by the words lento, largo, larghetto; when it is somewhat less slow, it is indicated by the terms grave, adagio, cantabile, moderato; a more firm and animated movement is indicated by the words andante and andantino; a gay and lively movement, by the terms allegro and allegretto; lastly, a quick and rapid movement, by the words presto, prestissimo, vivace, etc. All these words, of which the value is well known to musicians, have been long employed to express the movement of a musical piece. Nevertheless, it is evident that in order to express these different rates of movement exactly, mechanical means must be employed. After a great number of trials, the metronome of M.

Maëlzel has generally been adopted. This instrument is composed of a pendulum which is put in notion by a clock, and which divides a unit of time, the minute, for instance, into a greater or less number of parts, according to the length given to the rod. This length has a certain ratio to the duration which the division of the measure taken as unity must represent, and it is regulated by means of a bob which is made to rise or fall on the rod, which is graduated accordingly.

Signs of Expression-The signs of musical expression have for their object the indication of those varied shades of feelings, such as the sweetness, force, etc., of the notes, which give to music, so to speak, its physiognomy, and enable it to represent all the different emotions of the soul. The following signs are employed in the regulation of such expressions; some are applied to the intensity of the sounds; others to the association of the notes; others to the modification of the general movement. The first set vary between the limits of pianissimo (the softest or sweetest), expressed by PP., and fortissimo (the strongest or loudest), expressed by FF. A single P indicates piano (soft or sweet), as forte, denoted by a single F, indicates strong or loud. P and F themselves are also modified by the signs sf or rf (that is, sforzando or rinforzando), or by dim. (diminuendo), eres. (crescendo), cal. (calendo), etc. The signs or express the increase or decrease of the force of a single note or of a member of a passage in music. The lozenge <> indicates a crescendo of small extent, or a note merely strengthened. Two signs are sufficient to denote whether the notes are connected or detached. The curve indicates that the notes which they unite must be run together or connected in their utterance, and the points placed above each note signifies that these notes must be detached. When the points thus separated are surmounted by a curve, the notes besides being connected must be articulated in a sensible manner. Lastly, the momentary acceleration of the general movement is indicated by the letters accel. (accelerando); or they are moderated by these, ritard. (ritardando). When a rest greater than its normal value is to be made on a note, it is surmounted with the sign which is called a point of

rest.

Clefs. The clefs or keys are chiefly required in order to supply the want of extent in the staff. Every voice and every instrument has its diapason, that is, its own proper extent or compass of sound. The limits of each must be marked accordingly. The clef is employed to show the extent of the staff, to determine its position in the long series of sounds appreciable by the ear, and to represent in short compass the range of the pianoforte. By help of this artifice, a piece written for a given voice or instrument can be performed by a different voice or an instrument of a different diapason. The whole of a piece may be thus transposed into the medium staff which better suits every instrument or every voice.

There are three principal clefs: the clef of sol, which is that of the tenor voice, of violins, flutes, clarinettes, hautboys, horns, and the right hand of pianists; the clef of fa, which is commonly used for the bass; it determines the place of fa on the fourth line; when applied to the voice, its position may be varied. As to the clef of ut or do, it gives its name to the note on which it is placed. The alto of the clef of ut is written on the third line; its place can also be changed when applied to the voice. These three clefs seem placed at the ascending fifth from each other; yet the medium ut of the clef of fa is at the lower octave of that of the clef of ut, and at the double octave of the medium ut of the clef of sol. The following table shows the form, the relative position of the clefs in use, and the place of the medium ut on their respective staves.

CONSPECTUS OF THE THREE VOICES-INDICATIVE MOOD, FIRST PERSON SINGULAR.