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

How to recognize a doubly diminished fourth?
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 C / F♭♭:
Let's take the C major scale to have C as the tonic:

From the rule stated above, the interval C / F is a perfect fourth, so the interval C / F♭ is a diminished fourth, and so the interval C / F♭♭ is a doubly diminished fourth.
Inversion of the doubly diminished fourth
The inversion of the doubly diminished fourth is the doubly augmented fifth.
Here is an example of a doubly augmented fifth:

Musical examples of doubly diminished fourth
No examples yet, but feel free to send me some examples!
Interval identification game
You will find this interval in my Intervals identification game: