Intervals within Scales

Seconds

All unmarked seconds on this page are Ma2 intervals

The following second intervals are found in the major scale.

The following second intervals are found in the natural minor scale.

The following second intervals are found in the harmonic minor scale.

The following second intervals are found in the melodic minor scale.

Thirds

The following third intervals are found in the major scale.

The following third intervals are found in the natural minor scale.

The following third intervals are found in the harmonic minor scale.

The following third intervals are found in the melodic minor scale.

Fourths

The following fourth intervals are found in the major scale.

The following fourth intervals are found in the natural minor scale.

The following fourth intervals are found in the harmonic minor scale.

The following fourth intervals are found in the melodic minor scale.

Fifths

The following fifth intervals are found in the major scale.

The following fifth intervals are found in the natural minor scale.

The following fifth intervals are found in the harmonic minor scale.

The following fifth intervals are found in the melodic minor scale.

Sixths

The following sixth intervals are found in the major scale.

The following sixth intervals are found in the natural minor scale.

The following sixth intervals are found in the harmonic minor scale.

The following sixth intervals are found in the melodic minor scale.

Sevenths

The following seventh intervals are found in the major scale.

The following seventh intervals are found in the natural minor scale.

The following seventh intervals are found in the harmonic minor scale.

The following seventh intervals are found in the melodic minor scale.

Octaves

All of the octave intervals within the scales discussed so far have been Perfect octaves.

Inverting intervals (harmonic inversion)

Intervals can be inverted by placing the lower note one octave higher. As an example, the interval of a major 3rd from C to E can be inverted by placing the C one octave higher so that it is above the E note. The resulting interval is a Minor 6th.

A simple mathematical formula is used to calculate interval inversions. Simply subtract the interval number in question from the number nine to get the inverted interval number.

Formula: 9 - (Interval number) = (inverted interval number)

example 9 - 3 = 6

The prefix will often change when an interval is inverted. The following prefix changes should be made when inverting intervals.

Interval prefixes and inversions

All Major intervals when inverted will become Minor

All Minor intervals when inverted will become Major

All Perfect intervals when inverted remain Perfect

All Augmented intervals when inverted will become Diminished

All Diminished intervals when inverted will become Augmented

Intervals and their inversion usually have a similar dissonant or consonant effect on the ear. The harmonic interval of a second and its inversion, a seventh, both frequently have a dissonant effect (clashing, tension producing). The interval of a third and its inversion, a sixth, both usually have a consonant effect (harmonious, pleasing effect). The interval of a fourth and its inversion, a fifth, both usually have an open sonorous effect somewhere between consonance and dissonance depending on the musical situation.

Melodic Inversion of Tone Rows

Interval inversion is used in a different way in a style of composition that uses a series of tones called a tone row. As an example, consider the 3 note tone row; A, C, B. When a tone row is inverted, the interval from one note to the next is not changed, simply the direction is reversed.

To create an inversion of the tone row one must change the direction of the interval from one tone to the next when compared to the original tone row. In the original 3 note tone row, the interval from the first two notes (A to C) is up a minor third , the interval from C to B is down a minor second. The inversion of the 3 note tone row would begin on A then go down a minor third to the note F# then up a minor second to the note G. This type of melodic inversion is used frequently in a compositional style known as serialism.

(insert example)

Compound intervals

Compound intervals are intervals greater than an octave. So far the discussion of intervals has been limited to distances up to an octave. Obviously intervals larger than an octave do exist and are quite common in music. The intervals of 9th, 10th, 11th, 12th, 13th, 14th, and 15th are related to intervals that have been previously discussed. As an example, the interval of a major 9th is simply a Major 2nd plus a perfect octave; likewise, an interval of an augmented 11th is simply an augmented 4th plus a perfect octave. Usually it is more convenient to discuss compound intervals as if they were simple intervals (one octave or less), however, it is helpful to use the terms 9th, 11th and 13th when discussing complex chord structures (particularly common in the Jazz style).

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