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

How to recognize a a diminished seventh?
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 B♭ / A♭♭:
Let's take the B flat major scale to have B♭ as the tonic:

From the rule stated above, the interval B♭ / A is major seventh, so the interval B♭ / A♭ is minor seventh, and so the interval B♭ / A♭♭ is diminished seventh.
Inversion of the a diminished seventh
The inversion of the a diminished seventh is the augmented second.
Here is an example of a augmented second:

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