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

How to recognize a doubly augmented fifth?
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♭ / G#:
Let's take the C major scale to have C as the tonic:

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

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