6.

Two notes separated by four degrees of the staff represent a

sixth, thus:

7.

Two notes separated by five degrees of the staff represent a seventh, thus:

8. Two notes separated by six degrees of the staff represent an octave, thus:

Qualities of Intervals. Except of the prime, of which there are two kinds, perfect and augmented, there are three kinds or qualities of each of the above-named intervals; and these three kinds vary in the different intervals to be considered.

Resolutions of Intervals. In playing intervals for students to discern by ear, those intervals which are identical in sound as played on the pianoforte, but which differ in representation and in name, should always be played with their natural resolution.

Intervals Seemingly Identical. Intervals which are identical on the keyboard, such as the augmented prime and the minor second, or the augmented sixth and the minor seventh, should not be considered as the same interval. They are represented differently upon the staff, have different resolutions, bear different relations to other tones, and when harmonized have a different mental effect.

Primes. A perfect prime is two tones in unison; hence, it is generally called an unison. Its tones are represented by the same degree, thus:

In the following illustrations the small notes indicate the resolution. An augmented prime is equal to a half step; it is represented by one degree, and but one letter is employed in naming the tones, thus:

Seconds. A minor second is equal to a half step, and is represented by consecutive degrees, thus:

A major second is equal to a step or to two half steps, and is represented by consecutive degrees, thus:

An augmented second is equal to a step and a half step, or to three half steps, and is represented by consecutive degrees, thus:

Thirds. A diminished third is equal to two half steps, and is represented thus:

A minor third is equal to a step and a half step, and is represented thus:

A major third is equal to two steps or to four half steps, and is represented thus:

Fourths. A diminished fourth is equal to a step and two half steps, or four half steps, represented thus:

A perfect fourth is equal to two steps and one half step, or five half steps, represented thus:

An augmented fourth is equal to three steps, or six half steps, called the tritone, represented thus:

Fifths. A diminished fifth is equal to two steps and two half steps, or six half steps, represented thus:

A perfect fifth is equal to three steps and one half step, or seven half steps, represented thus:

An augmented fifth is equal to four steps, or eight half steps, represented thus: