In music theory, a diminished sixth is an interval that has seven half steps
The diminished sixth requires that:
- The interval must be a sixth interval (six note names between the first and the last).
- The interval must have seven half steps.
What does a diminished sixth look like?
Here is an example of a melodic diminished sixth (two music notes in a melody) and a harmonic diminished sixth (in a chord):

How to recognize a diminished sixth?
Rule of music theory: All intervals in a major scale starting with the tonic (degree I) are either major or perfect, and only unison, octave, fourth and fifth are perfect (the others are major).
Example with the interval G / E♭♭:
Let's take the G major scale to have G as the tonic:

From the rule stated above, the interval G / E♮ is a major sixth, so the interval G / E♭ is a minor sixth, and so the interval G / E♭♭ is a diminished sixth.
Inversion of the diminished sixth
The inversion of the diminished sixth is the augmented third.
Here is an example of an augmented third:

Musical examples of diminished sixth
Interval identification game
You will find this interval in my Intervals identification game: