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The dash through the 6 thus 7, and the 4 thus 41, operates as a #.

Another set of combinations called discords, are procured from the chord of the dominant 7th, termed the chord of the 7th.

When the bass steps into the place of the 3d as before mentioned, it is termed the first derivative of the 7th, and takes the figures , being the chord of sixth and fifth. When the bass steps to the 5th or dominant, it is termed the second derivative of the 7th, and takes the figures 3, being the chord of the fourth and third. When the bass steps still a degree farther into the place of the 7th, it is termed the third derivative of the 7th, and takes the figures , and is called the chord of the fourth and second, or simply the second.

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Thus far the figures shew what harmony is built upon the bass; and when the bass ascends from its foundation place into those of the derivatives, the harmony is then said to be inverted, as the key-note, which ought to be at the bottom, is then above the bass.

In considering the numerous chords still to be explained, as the figures become so very complex, it is doubtful whether they tend to simplify our notions further than pointing out the root or foundation note of the chord. The discord of the diminished 7th is produced by raising the bass note of the dominant 7th a semitone, which forms a compound of three minor 3ds,

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naturally resolving into the harmony of a semitone above the bass note,

and having the same derivatives as the dominant 7th. The effects of this chord in modulation are strikingly powerful; and it readily admits of a transition to any chord in which one of its notes may form a part.

There is still a higher class of discords to be mentioned, which are produced by placing the chord of the dominant 7th upon the common chord, forming the chord of the 11th, resolving into the common chord thus :

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By adding the 3d above the dominant 7th, we obtain the chord of the 13th, which involves every

note in the diatonic scale, and resolves into the common chord.

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These discords are in fact a compound of appogiatura notes, forming suspended harmonies, which ultimately melt into the common chord.*

CHAPTER XXXIX.

MODULATION.

There is no branch of musical science more necessary to a composer than modulation. It may be said to be the key which opens to the admiring ear

* I have noticed this effect in the clanging or clashing of St. Margaret's bells at Leicester, when on a visit at Birstal House. At this distance the discordancies die away, and you hear nothing but the pure harmony of the common chord.

all the treasures of harmony.'* As melody signifies a progression of single sounds, so in the science of harmony does modulation signify a progression of chords, or mixed sounds. To conduct the harmony with ease and grace, is a distinguishing quality in a first-rate composer. When we modulate upon an organ or piano-forte, in passing from one chord to another, it may be laid down as a general rule, that one of the fingers should remain upon that key which is to form a part of the succeeding chord. This gives a smoothness to the transitions, readily perceived by the ear. For bold and sudden effects, these connecting 'links of harmony' are dispensed with, and the changes are produced by dashing into chords at distances more remote. The following is a progression of common, or fundamental chords..

Adagio.

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This slow shifting scenery in the theatre of harmony constitutes the sublime part of devotional music. The following are ordinary modulations in major keys, with their relative minors.

* Taylor, of Norwich

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