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§ 49. The characters called sharps and flats continue their significance throughout the measure in which they occur, and also from measure to measure when the same tone is to be repeated, or until canceled by a note written upon some other degree of the staff.

NOTE.-The teacher should be careful to cause his pupils to understand that C is not C raised or elevated, and that D is not D lowered or depressed, but that the tone C or Dh (by whichever name it may be called) is an independent tone, being in pitch between C and D. It is not possible to elevate or to depress the pitch of a tone. Absolute pitch is, of course, unalterable. The error here pointed out is found in most treatises on music, see "Manual of the Boston Academy of Music," the previous editions of this work, and various other books. It is equally untrue, to say that a sharp raises or elevates, or lowers or depresses a note.

§ 50. Sharps and flats are canceled, or their significance is terminated by a sign called a NATURAL (‡).

NOTE.-Practical exercises are omitted under this head, since it is generally preferable that an ability to sing chromatic passages should be acquired in connection with tunes, or melodies, in which they are found.

CHAPTER XI.

DIATONIC INTERVALS

§ 51. In addition to the scale-intervals, or to the intervals belonging to the scale in its regular progression, called steps and half-steps, there are also other intervals occasioned by a departure from the regular scale order, or by skipping: as THIRDS, FOURTHS, FIFTHS, Sixths, SevenTHS, and OCTAVES, and there may be MAJOR and MINOR, i. e., larger or smaller.

§ 52. Intervals are always reckoned from the lower tone upwards, unless otherwise expressed.

NOTE.-Tables, or descriptions of these intervals are omitted, as well as exercises in them, since they Are better learned by a concrete than by an abstract practice.

CHAPTER XII.

THE MINOR SCALE, CONTINUED.

§ 53. In addition to the natural form of the Minor Scale, as already explained, there are also others, which, being altered from the natural, may be called artificial forms.

54. The first in the present order, is that which differs from the natural

La Si Do Re Mi Fi Si La. La Sol Fa Mi Re Do Si La. NOTE.-Composers and theoretic writers present still other forms of the Minor scale, but which it can be of no practical importance to explain.

§ 56. The natural minor scale commences with A, or A is taken as its pitch, or as one; and as A is six in the major scale of C, it follows, that the minor scale is based upon six of the major scale.

NOTE. The pupil should be reminded that the word natural, as here used, has reference only to the name of the pitch of the scale, and its repreeentation to the eye.

§ 57. The minor scale based upon six of the major scale, is called its relative minor; and the major scale, based upon three of the minor scale, is called its relative major.

NOTE-Practical exercises are omitted here, but will be found in connection with the transposition of the scale.

CHAPTER XIII.

TRANSPOSITION OF THE SCALE.

§ 58. When the scale is based on C, it is said to be in its natural position, or natural; but the pitch of the scale may be changed, and, when any other pitch than C is taken as one of the scale, it is said to be TRANSposed.

Nors. The transposition of the Scale consists not in any change of the position of the notes by which it is represented on the staff, for it may be represented in different positions, while its pitch remains the same, or it may be represented in the same position while its pitch is changed; but it consists in changing the pitch, or in taking some other pitch besides C, as one, or as the basis of the scale.

§ 59. The letter which is taken as the pitch of the scale, or as one, is called the KEY LETTER, or simply the KEY. Thus, if C be taken as one, the scale is said to be in the KEY OF C; if D be taken as one, the scale is said to be in the KEY OF D, and so on. By the key of C, is meant that the scale is based on C, or that C is taken as one; by the key of D, is meant that the Scale is based on D, or that D is taken as one, and so on.

§ 60. In transposing the scale, its proper relations, or its proper intervals, must be preserved: thus, if the transposition be from C to G, or if G be taken as one, the tone which is a step higher than G, named by another letter (A), will necessarily be two; that tone which is a step higher than A, named by another letter (B), will be three; the tone which is a half step higher than B, named by another letter (C), will be four; and so on.

§ 61. This scale relationship, or the proper order of scale intervals, must be preserved by the introduction, or use, of the intermediate tones, or the tones named sharp, or flat; or, in other words, in transposing the scale, it is necessary to omit certain tones belonging to the key, from which the transposition is made, and to introduce such intermediate tones as may be required to constitute the new key.

NOTE.-The difficulty in transposing the scale consists in the transfer of absolute to relative pitch.

CHAPTER XIV.

TRANSPOSITION OF THE SCALE BY FIFTHS.

§ 62. First transposition of the scale by fifths, from C to G. All the tones which constitute the key of C will be found to belong also to the key of G, with the exception of F.

§ 63. To preserve the proper order of intervals between six and seven, and between seven and eight in this transposition, it is necessary to omit F, and to take F sharp as seven in the new key.

864. The sign of F sharp (#) is placed at the beginning of the staff, immediately after the clef, and is called the SIGNATURE (sign) of the key. Thus, the signature of the key of G, and also of its relative minor E, is one sharp, or F

sharp. The signature of the key of C, and also of its relative minor A, is said to be natural.

NOTE. The true idea of transposition cannot be acquired from verbal explanations, or descriptions, or from signs, diagrams, or ocular illustrations; the subject can only be fully appreciated by the presenta tion of the reality through the ear. The words used to define transposition, or the signs of transposition, are often mistaken for the reality, and pupils are supposed to understand the thing itself, when they have only been made acquainted with its nomenclature, or with the manner of its representation. But while transposition is one thing, and a visual illustration of it quite another, insufficient, of itself, yet, since illustrations of the kind may be of some aid to the learner, we present the following:

step,

half

half

seven, eight, two, three,

sharpfour. five.

half

step, step. step, step, step,

half

step.

One, two, three, four, five, six, seven, eight.

EXPLANATION. On the upper staff, in the above diagram, the Scale is represented in the Key of C The distances of the notes, one from another, represent the intervals. On the lower staff. G is taken as one, A as two, B as three, C as four, D as five, E as six; and thus far the intervals are right. But as the interval between six and seven must be a step, it is seen at once that F will not do for seven, because the interval between E and F is but a half-step; it becomes necessary, therefore, to omit F, and to take the intermediate tone, F, for seven. and this secures the proper interval between six and seven, viz., a step. The interval between F and G being a half-step, G is taken as eight, and the Scale is complete in the key of G; so that the tones which constitute the Scale in the key of G, are, G, A, B, C, D, E, FL, and G.

10

§ 49. The characters called sharps and flats continue their significance throughout the measure in which they occur, and also from measure to measure when the same tone is to be repeated, or until canceled by a note written upon some other degree of the staff.

NOTE.-The teacher should be careful to cause his pupils to understand that C is not C raised or elevated, and that D is not D lowered or depressed, but that the tone C or Dh (by whichever name it may be called) is an independent tone, being in pitch between C and D. It is not possible to elevate or to depress the pitch of a tone. Absolute pitch is, of course, unalterable. The error here pointed out is found in most treatises on music, see "Manual of the Boston Academy of Music," the previous editions of this work, and various other books. It is equally untrue, to say that a sharp raises or elevates, or lowers or depresses a note.

§ 50. Sharps and flats are canceled, or their significance is terminated by a sign called a NATURAL ().

NOTE.-Practical exercises are omitted under this head, since it is generally preferable that an ability to sing chromatic passages should be acquired in connection with tunes, or melodies, in which they are found.

CHAPTER XI.

DIATONIC INTERVALS

§ 51. In addition to the scale-intervals, or to the intervals belonging to the scale in its regular progression, called steps and half-steps, there are also other intervals occasioned by a departure from the regular scale order, or by skipping: as THIRDS, FOURTHS, FIFTHS, SIXTHS, SEVENTHS, and OCTAVES, and there may be MAJOR and MINOR, i. e., larger or smaller.

52. Intervals are always reckoned from the lower tone upwards, unless otherwise expressed.

NOTE.-Tables, or descriptions of these intervals are omitted, as well as exercises in them, since they are better learned by a concrete than by an abstract practice.

CHAPTER XII.

THE MINOR SCALE, CONTINUED.

§ 53. In addition to the natural form of the Minor Scale, as already explained, there are also others, which, being altered from the natural, may be called artificial forms.

§ 54. The first in the present order, is that which differs from the natural

La Si Do Re Mi Fi Si La. La Sol Fa Mi Re Do Si La. NOTE.-Composers and theoretic writers present still other forms of the Minor scale, but which it can be of no practical importance to explain.

§ 56. The natural minor scale commences with A, or A is taken as its pitch, or as one; and as A is six in the major scale of C, it follows, that the minor scale is based upon six of the major scale.

NOTE. The pupil should be reminded that the word natural, as here used, has reference only to the name of the pitch of the scale, and its repreeentation to the eye.

§ 57. The minor scale based upon six of the major scale, is called its relative minor; and the major scale, based upon three of the minor scale, is called its relative major.

NOTE-Practical exercises are omitted here, but will be found in connection with the transposition of the scale.

CHAPTER XIII.

TRANSPOSITION OF THE SCALE.

§ 58. When the scale is based on C, it is said to be in its natural position, or natural; but the pitch of the scale may be changed, and, when any other pitch than C is taken as one of the scale, it is said to be TRANSPOsed.

Nor. The transposition of the Scale consists not in any change of the position of the notes by which it is represented on the staff, for it may be represented in different positions, while its pitch remains the same, or it may be represented in the same position while its pitch is changed; but it consists in changing the pitch, or in taking some other pitch besides C, as one, or as the basis of the scale.

§ 59. The letter which is taken as the pitch of the scale, or as one, is called the KEY LETTER, or simply the KEY. Thus, if C be taken as one, the scale is said to be in the KEY OF C; if D be taken as one, the scale is said to be in the KEY OF D, and so on. By the key of C, is meant that the scale is based on C, or that C is taken as one; by the key of D, is meant that the Scale is based on D, or that D is taken as one, and so on.

§ 60. In transposing the scale, its proper relations, or its proper intervals, must be preserved: thus, if the transposition be from C to G, or if G be taken as one, the tone which is a step higher than G, named by another letter (A), will necessarily be two; that tone which is a step higher than A, named by another letter (B), will be three; the tone which is a half step higher than B, named by another letter (C), will be four; and so on.

§ 61. This scale relationship, or the proper order of scale intervals, must be preserved by the introduction, or use, of the intermediate tones, or the tones named sharp, or flat; or, in other words, in transposing the scale, it is necessary to omit certain tones belonging to the key, from which the transposition is made, and to introduce such intermediate tones as may be required to constitute the new key.

NOTE.-The difficulty in transposing the scale consists in the transfer of absolute to relative pitch.

CHAPTER XIV.

TRANSPOSITION OF THE SCALE BY FIFTHS.

§ 62. First transposition of the scale by fifths, from C to G. All the tones which constitute the key of C will be found to belong also to the key of G, with the exception of F.

§ 63. To preserve the proper order of intervals between six and seven, and between seven and eight in this transposition, it is necessary to omit F, and to take F sharp as seven in the new key.

864. The sign of F sharp (#) is placed at the beginning of the staff, immediately after the clef, and is called the SIGNATURE (sign) of the key. Thus, the signature of the key of G, and also of its relative minor E, is one sharp, or F

sharp. The signature of the key of C, and also of its relative minor A, is said to be natural.

NOTE. The true idea of transposition cannot be acquired from verbal explanations, or descriptions, or from signs, diagrams, or ocular illustrations; the subject can only be fully appreciated by the presenta tion of the reality through the ear. The words used to define transposition, or the signs of transposition, are often mistaken for the reality, and pupils are supposed to understand the thing itself, when they have only been made acquainted with its nomenclature, or with the manner of its representation. But while transposition is one thing, and a visual illustration of it quite another, insufficient, of itself, yet, since illustrations of the kind may be of some aid to the learner, we present the following:

EXPLANATION. On the upper staff, in the above diagram, the Scale is represented in the Key of C The distances of the notes, one from another, represent the intervals. On the lower staff, G is taken as one, A as two, B as three, C as four, D as five, E as six; and thus far the intervals are right. But as the interval between six and seven must be a step, it is seen at once that F will not do for seven, because the interval between E and F is but a half-step; it becomes necessary, therefore, to omit F, and to take the intermediate tone, F, for seven. and this secures the proper interval between six and seven, viz., a step. The interval between F and G being a half-step, G is taken as eight, and the Scale is complete in the key of G; so that the tones which constitute the Scale in the key of G, are, G, A, B, C, D, E, FL, and G.