# Diminished Intervals - does a double diminished interval exist?

I'm doing practise questions for an upcoming test, and I have to name an interval from E to G double flat. Would that be a double diminished third? I'm not sure what to call it. Also if I invert it will it be a double augmented sixth?

You're exactly right on all fronts!

Since G♯ is in the E-major scale, E–G♯ is a major third. From there, we just make the necessary alterations until we reach E–G♭♭. If E–G♯ is a major third, then E–G♮ is a minor third, E–G♭ is a diminished third, and thus E–G♭♭ is a doubly diminished third.

In any event, it's definitely not a minor second (or even an augmented unison). These intervals are enharmonically equivalent to a doubly diminished third, but if the pitches are spelled as some type of E to some type of G, it must be measured as a third.

We can walk through the same process when we invert the interval, as well: G♯–E is a minor sixth, G♮–E a major sixth, G♭–E an augmented sixth, and thus G♭♭–E a doubly augmented sixth.

Intervals like this are really more "theoretical" in nature as opposed to "practical," but the logic in determining their size is sound (...excuse the pun).

• Thanks for the thorough explanation Richard! I understand better now – saf Nov 21 '18 at 22:58
• Makes me wonder why questions like this are posed in exam papers. Pretty sure I've never come across E>Gbb, and these days, most writers would write it as E>F, wrongly, maybe, but far easier to read... – Tim Nov 22 '18 at 8:34
• Probably just to ensure that the students are learning the language correctly. – ggcg Nov 25 '18 at 15:54