5.

This is, in like manner, a derived form, from 2.

6.

Derived from 3.

7.

This form may be regarded as commencing on 5, with sharp-seven, and sharp-four.

NOTE.-It is not supposed to be necessary to give any further explanations or illustrations of these forms of the Minor Scale; the pupil who is able to sing the Chromatic Scale with tolerable accuracy will not find much difficulty in any form of the Miñor Scale.

§ 109. Every Major Scale has its relative Minor, and every Minor Scale has its relative Major.

§ 110. The relative Minor to any Major Scale is based upon its sixth, and the relative Major to any Minor Scale is based upon its third.

NOTE. The distinguishing feature of the Major and Minor Scales is the third. The Major Scale is known by its Major third, and the Minor Scale is known by its Minor third.

19

NOTE 1.-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.

NOTE 2.-The term natural, as here used, has reference to the representation of the scale, and not to the scale itself.

§ 112. 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.

See Note on the word Key, at § 21.

§ 113. In transposing the Scale, its proper relation must be preserved by the use of the intermediate-tones; 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 take such intermediate tones as may be required to constitute the new key, or to secure in it the proper order of Scale-intervals. See § 67.

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

CHAPTER XX.
MELODICS.
ics.

TRANPOSITION OF THE SCALE.

§ 111. 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.

CHAPTER XXI.

MELODICS.

TRANSPOSITION OF THE SCALE BY FIFTHS.

§ 114. 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.

§ 115. To preserve the proper order of intervals between Six and Seven, and between Seven and Eight, in this transposition, it is necessary to take the tone F-sharp as seven in the new key.

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 dif ferent intervals, as steps and half-steps. 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 take the intermediate tone, F-, for seven, and this gives the proper interval between six and seven, viz., a step. The interval between Fand G being a half-step, G is taken as eight, and the Scale is complete in the key of G, thus:

CHAPTER XXII.

MELODICS.

RELATION OF TONES.-TONE OF TRANSPOSITION.

§ 117. Tones are said to be related as follows: if C be one, D is two, E is three, and so on; or, D is two to C, or two considered in its relation to C as one; so, also, E is two to D, F is two to E, and so on; so, also, E is three to C, F is three to D, and so on.

:

Again C is sharp one, Dis sharp two, F is sharp four, G-# is sharp five, and A- is sharp six, when considered in relation to C as one. Again: D- is flat two, E- is flat three, G2 is flat five, A-b is flat six, and B-b is flat seven, when considered in relation to C as one.

§ 118. The intermediate tone required in transposition, is called THE TONE OF TRANSPOSITION, or, (in written music) THE NOTE OF TRANSPOSITION. Thus, the tone of transposition between the keys of C and G, is F.. § 119. It will be observed that, in the foregoing transposition from C to G, the pitch of the scale has been removed a fifth; and that the intermediate tone F-, or sharp-four, has been found necessary to preserve the proper order of the intervals: hence the following rule: "Sharp-four transposes the scale a fifth;" or, "The tone of transposition, between any key and its fifth, is sharp-four."

21

CHAPTER XXIII.

MELODICS.

TRANSPOSITION OF THE SCALE BY FIFTHS, CONTINUED.

§ 120. Second transposition of the Scale by fifths; from G to D. § 121. To preserve Scale relationship, or the proper order of intervals between six and seven and between seven and eight in this transposition, it is necessary to take Cas seven in the new key.

§ 122. The sign of C- is placed at the beginning of the staff, a little to the right of the previous sharp, and the two sharps are taken together as the sign of the key, or as the signature.

§ 123. Third transposition of the Scale by fifths; from D to A. Gis sharp four to D. G., therefore, is next introduced.

Elementary Exercises, 154 to 171.

§ 124. Fourth transposition of the Scale by fifths; from A to E. Dis sharp four to A. Elementary Exercises, 172 to 189.

§ 125. Fifth transposition by fifths; from E to B. A is sharp four

to E.

§ 126. Sixth transposition by fifths; from B to F# E# is sharp four

to B.

§ 127. Seventh transposition by fifths; from F# to C#. B-# is sharp four to F#.

§ 128. Eighth transposition by fifths; from C to G F DOUBLE SHARP (written thus: FX) is sharp four to C-#

§ 129. The Scale may be still further transposed by fifths; to the key of D., with nine sharps (two double sharps); to the key of A-, with ten sharps (three double sharps); to the key of E-, with eleven sharps (four double sharps); to the key of B, with twelve sharps (five double sharps), and so on.

NOTE 1-The key of B- is the same to the ear as the key of C. The difference is not in the thing itself, but merely in the sign.

NOTE 2. The keys beyond F- (six sharps) are but seldom used, as the same variety may be more easily obtained in the transposition by fourths. The keys beyond E (four sharps) are seldom used in church music,

Five, six, seven, one, two, three, four, five, six, seven, eight.

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

NOTE.-An explanation of the above diagram is supposed to be unnecessary, as it would be similar Tthat at 6116 Elementary Exercises, 136 to 153.

CHAPTER XXIV.

MELODICS.

TRANSPOSITION OF THE SCALE BY FOURTHS.

NOTE. The reason why the Scale is transposed by fifths or by fourths, is this: those keys which are based on five or four of any given key are its most nearly related keys. Any key, and the key which is based upon its fifth, have all their tones but one in common. Thus to the key of C belong all the tones which belong to the key of G. with the exception of F sharp; and to the key of G belong all the tones which belong to the key of C, with the exception of F; hence the near relation between the two keys. Again, the same is true of any key, and the key which is based on its

fourth. The key of C and F, for example, have all their tones in common, with a single exception. Hence the near relation

§ 130. First transposition of the Scale by fourths; from C to F.

§ 131. To preserve the identity of the Scale, or the proper order of intervals between three and four, and between four and five, in this transposition, it is necessary to take B-b as four in the new key. B- is, therefore, the signature to the key of F.

§ 133. Second transposition of the Scale by fourths; from F to B-b. § 134. To preserve the proper order of intervals between three and four. and between four and five in this transposition, it is necessary to take Eb as four in the new key.

§ 135. The sign of E- is placed a little to the right of the previous flat, and the two flats are taken as the signature.

Elementary Exercises, 210 to 227. § 136. Third transposition of the Scale by fourths; from B-b to E-b. A-b is flat seven to B-b. A-b, therefore, is the next flat introduced. Elementary Exercises, 228 to 245. § 137. Fourth transposition of the Scale by fourths; from E- to A-b. D- is flat seven to E-b. D, therefore, is the next flat introduced. Elementary Exercises, 246 to 263. § 138. Fifth transposition by fourths; from A- to Db. Gb is flat sever to A-b.

§ 139. Sixth transposition by fourths; from D-b to G-b. C-b is flat seven to D-b.

§ 140. Seventh transposition by fourths; from G-b to C-b. Fb is flat seven to G-p.

§ 141. Eighth transposition by fourths; from C to F. B DOUBLE FLAT (written B-b) is flat seven to C-b.

142. The Scale may be still further transposed by fourths: to the key of Bbb, with nine flats (two double flats); to the key of E bb, with ten flats (three double flats); to the key of A-bb, with eleven flats (four double flats); to the key of D.bb, with twelve flats (five double flats); and so on.

NOTE 1.-The key of D- is the same to the ear as the key of C. The difference is not in the thing itself, but merely in the sign. NOTE 2.-The keys beyond G (six flats) are but seldom used, as the same variety may be more easily obtained in transpositions by sharps. The keys beyond A- (four flats) are seldom used in church music.

Diagram furnishing an illustration of the transposition by fifths or by fourths through the whole circle of keys.

B, Five sharps

E, Four harps.

23 NOTE.-Passing tones, considered with respect to harmony, do not belong to the chord in which they occur.

§ 144. Appoggiatura. When a passing tone precedes an essential tone on an accented part of a measure, it is called an APPOGGIATURA.

NOTE. From Appoggiare, an Italian word, which signifies to lean, or to rest upon. An appoggiatura is a tone on which the voice leans or rests in its passage of intervals, or from one tone to another. The appoggiatura is generally considered a tone of einbellishment, but it should rather be regarded as a tone of expression, since it is designed to give tenderness or pathos to a performance.

C.

EXPLANATION-Commencing with the key of C, we pass to the right by fifths, as follows: G, D, A, E, B, F-, D-, A-, E-, B-, F, back again to C; or, commencing with C, we pass to the left by fourths, thus F, B-, E, A, D, G-5, B, E, A, D, G, back again to C. It will be understood that the key of F- is the same as the key of G; as represented, and also as named, there appear to be two keys, but this view is confined to the mere names and signs; in reality there is but one key.

§ 146. The Shake or Trill. A rapid alternation of a tone with the conjoint tone above it, at an interval of either a step or a half-step, is called a SHAKE OF TRIll.

NOTE.-The shake is a very brilliant musical embellishment. Its proper practice gives flexibility to the voice.

CHAPTER XXV.

MELODICS.

APPOGGIATURA-TURN-SHAKE OR TRILL-PORTAMENTO.

§ 143. Passing Tones. Tones not essentially belonging to a melody are often introduced into music, called PASSING TONES. They are sometimes represented by notes of smaller size than those in which the music is mostly written, though this distinction is not generally observed.