Augmented and Diminished Intervals

In order to maintain function within a chord, it is sometimes necessary to expand or shrink our naturally occurring intervals. When we expand a Major or Perfect interval by a half step, the resulting distance between notes is called an Augmented interval, and is commonly notated with the abbreviation “Aug” and followed by the interval:

 intervalsmajorminorperfect.aiff

When we shrink a minor interval by a half step (or shrink a Major interval by two half steps), the result is a diminished interval. Diminished intervals are commonly labeled with the abbreviation “dim”, followed by the interval:

 7 intervals.aiff

Perfect intervals are exceptions to the rule. There are no minor 4ths or 5ths; when you shrink a Perfect 4th or 5th by a half step, the result is a diminished interval:

 8 intervals.aiff

The Tritone

A tritone is an Augmented 4th or diminished 5th. It happens naturally between the 4th and 7th scale degree, and is the only interval within the harmonic series that cannot be classified as Perfect, Major, or minor:

 9 intervals.aiff

The Tritone has been considered unstable and dissonant in Western Music, and was seldom used until the nineteenth century.  Today it is commonly accepted and used.

Why do we use Augmented and Diminished intervals?

Looking at Augmented and Diminished intervals, it seems like there are easier ways to write the same intervals enharmonically. For instance, isn’t a diminished 6th really a Perfect 5th? Isn’t an Augmented 2nd really a minor 3rd?

 10 intervals.aiff

When it comes to distance between notes, it is often easier to express a diminished or Augmented interval as a Perfect, Major, or minor interval. However, the number of the interval, i.e. 2nd, 3rd, 5th, 6th, etc, would be different, so it would not be the same interval:

Augmented and diminished intervals are used to describe alterations in advanced harmonies that would necessitate giving the harmony an entirely different name, and therefore making the analysis much more confusing.

Defining intervals by half steps

Intervals can be defined by counting the half steps between the two notes. A minor 2nd is one half step, a Major 2nd is two half steps (one whole step), and so on:

Half steps                    Interval

0                                   P1

1                                   m2

2                                   M2

3                                   m3

4                                   M3

5                                   P4

6                                   Aug4/dim5

7                                   P5

8                                   m6

9                                   M6

10                                 m7

11                                 M7

12                                 P8

While counting half steps is easier at the outset, finding the interval by key becomes much faster with practice.  Once learned, it is to your advantage when performing music.