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

How to recognize a doubly augmented third?
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 / E♯♯:
Let's take the C major scale to have C as the tonic:

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

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