(A.S.: Assuming that "non-compound" means "contains eight or less degrees.")
TL;DR: How to invert doubly augmented seventh?
I've ran into inversion problem with greater-than-octave intervals (not only compound ones).
Simple inversion is to invert something like major sixth (i.e.
C4 to A4), – obviously, we will get minor third (
A4 to C5).
A bit more complicated inversion is to invert compound intervals: you should first bring it to non-compound view; so, major third over octave
E♮4 to G♯5 becomes minor sixth –
G♯5 to E♮6 (or
G♯4 to E♮5, or
G♯3 to E♮4).
Other weird thing is to invert augmented octave: it considered as compound interval and becomes diminished octave (not diminished unison, as one might think, since diminished unison is incorrect interval).
So, if there is a doubly augmented seventh (
C♭4 to B♯4), what interval will we got if invert it? Doubly diminished second (
B♯4 to C♭5)? Is this correct? Is it OK that lower pitch is higher than upper one?