The foregoing examples may show how a melody may pass from one key to another. By harmonising them, we see how the chords of one key pass to those of another. It will be observed that the chord of the new key is always preceded by the chord of its dominant

The above are the keys into which we can pass most easily from the key of C major. If the original key A minor, the keys into which we can pass most easily are, C major, E minor, G major, D minor, and F majorFrom A minor to C major.

From A minor to F major.

is very rarely used. This note, besides having a minor | may be made to D and C major, and to A, B, and E third, has an imperfect fifth, F natural; and, to make minor; and, taking E as the original minor key, tranit the fundamental note of a key, whether major or sitions may be made to G major, B minor, D major, minor, its fifths must be made perfect, by changing FA minor, and C major. The learner should exercise to F sharp-which is not in the scale. himself in writing similar modulations in all the diffe rent keys.

In the above examples of transitions from C major, or A minor, to other keys, these notes must be understood as standing for any major or minor key, from which transitions may be made in the same manner. Thus, taking G as the original major key, transitions

1 བ༔ ་

e

The smoothest and most gradual modulation is effected by means of a chord which is, common to both keys; that is, which belongs both to the original key and to the new key

wod anna vont echymazo majonezol ati" g

In the first of these examples, the first triad of G belongs both to the original key of C and to the new key of G. In the second example, the triad of F (of which A is the bass) belongs both to the original key of C and to the new key of F.

Modulation is less gradual (though it may be perfectly admissible), although the chord which immediately precedes the new key is not common to both keys

In the first example, the triad of F belongs to the original key of C, but not to the new key of G. In the second example, the triad of G belongs to the original key of C, but not to the new key of F. This kind of modulation generally produces a chromatic melody, or a melody containing an accidental semitone in one of the parts; as from F to F sharp, or from B to B flat, as above.

When a chord is succeeded by another, in such a manner that one of the notes of the first chord appears in the second chord, altered by a sharp or a flat, the note must be followed by its alteration in the same part, so as to make a chromatic melody, as in the preceding examples. When the note of the first chord appears in one part, and the altered note of the second chord appears in another part, this produces a fault, called a false relation; as, for example

To be avoided thus

8

The following example is a chain of modulations, in which every key is relative to that which precedes it. All the modulations are effected by an intermediate chord, which is the dominant seventh, generally employed in one of its inversions

E minor. What is good in the one case, might be bad | ing examples of this rule, similar to those given above. in another; and all the above-mentioned modulations -from the second note of the scale to the third, from the third to the fourth, &c.-can only be used under the above condition.

When the primitive key is minor, in like manner, we may modulate from the fourth note of the scale to the fifth, from the fifth to the sixth, from the sixth to the seventh, from the fourth to the seventh, and vice versa. The learner may exercise himself in findFrom C major to D major.

In the above modulations into the keys of different notes of the scale, the keys are major or minor according as their thirds, as they stand in the scale, are major or minor, as already shown; as we modulate from C to D minor, E minor, &c. We may also, though more seldom, modulate from C to D major, F major, &c.; but this must be done by a longer chain of intermediate chords, so as to prepare the ear gradually for the transition. For example

Or

We may likewise modulate from a given key to notes which are not in the scale of that key; as, for example, from C to E flat, B flat, A flat, &c. These modulations ought to be gradually effected, by passing into some intermediate key, which is relative to the keys which precede and follow it. Thus, in order to modulate from C to B flat, we may pass first from C to F, and then from F to B flat

It may be laid down as a general rule, that, as we may pass from a major key to a minor key on the same note (as from C major to C minor), or from a major key to the minor key of its subdominant (as from C major to F minor), we may pass from a major key to all the keys which are relative to these two other keys. Thus, from C major we may pass to all the relative keys of C minor, or to all the relative keys of F minor.

Modulations from C major to the relative keys of C minor

From C to E flat.

From C to F minor.