Havin' Fun With Some Intervals!

[zedrein]

In my spare time I enjoy printing out exercise sheets that list two musical intervals inverted so that I can keep aware of their names and relationship to one another eg A-F is a minor 6th while F-A is a major 3rd and C-G# is a augmented 5th while G#-C is a diminished 4th...get the idea? Well anyway I was writing out some enharmonic equivalents of these intervals and got some very interesting note and interval names. Help me determine if my logic is sound in their unconventional naming:

A-Cb diminished 3rd? Cb-A augmented 6th?

A-Gbb double diminished 7th? Gbb-A double augmented 2nd?

C-Cb diminished unison? Cb-C augmented unison?

D-Abb double diminished 5th? Abb-D double augmented 4th?

And yes, this is what you might call "theory for theorys sake" but dammit I enjoy such trivialities!

[walternewton]

From a nomenclature standpoint they look sound...in practice I think only one or two (e.g. Augmented Sixth) might be applicable in any but the very rarest of situations, if ever.