Sixths. A minor sixth is equal to three steps and two half steps, or eight half steps, represented thus:

A major sixth is equal to four steps and one half step, or nine half steps, represented thus:

An augmented sixth is equal to five steps, or ten half steps, represented thus:

150. Introducing Sixths.

In the seventh measure the key is changed though the signature remains the same.

Sevenths. A diminished seventh is equal to three steps and three half steps, or nine half steps, thus:

A minor seventh is equal to four steps and two half steps, or ten half steps, thus:

bo

A major seventh is equal to five steps and one half step, or eleven half steps, thus:

151. Introducing Sevenths.

Consonances and Dissonances. All the perfect intervals, the major and minor thirds, and the major and minor sixths, are called consonances, as the effect of any of them upon the ear is that of completeness.

The perfect consonances are the perfect prime, perfect fourth, perfect fifth, and perfect octave.

The imperfect consonances are the major and minor thirds and the major and minor sixths.

All the diminished and augmented intervals, and the major and minor seconds and major and minor sevenths are dissonances.

Inversion of Intervals. Intervals are inverted when the order of their tones is reversed and the first tone is taken an octave higher. Intervals may also be inverted by simply taking the second tone an octave lower.

LAW OF INVERSION

I. All perfect intervals when inverted remain perfect.

2. All major intervals when inverted become minor.

3.

All minor intervals when inverted become major.

4. All diminished intervals when inverted become augmented.

5.

All augmented intervals when inverted become diminished. 6. A prime when inverted becomes an octave thus:

8. A third when inverted becomes a sixth thus: