In What is the interval between Db and D# some of the comments indicate that the interval Db->Eb can be considered as a diminished third. I would think that Fbb (double-flatted F) is a diminished third above Db.
Is there more than one (name for the) note that is a diminished 3rd above Db?
If so, wouldn't this ambiguity exist for all of the other intervals?
Note: I'm aware that in a world of equal temperament, this is kind of moot, but that formally there is a difference between Eb and Fbb.
Is there more than one (name for the) note that is a diminished 3rd above Db?
Nope, only one correct answer. D to F is a minor third. Db to Fb is also a minor third. A Diminished interval is one semitone below the minor interval, (in this case) while still being a third away from the root note i.e. F double flat.
If so, wouldn't this ambiguity exist for all of the other intervals?
No ambiguity, only one correct answer.
Notes may be played in the same place and have different names. D to E is a second. It cannot be a third even if the notes are played on the same key as some third interval. To determine what a second is, you start on the bottom (bottom being 1) and count until you get to the number 2: D(1) - E(2).
If you start on a D, both an Augmented Unison and a Minor Second will both be played at the same place on the piano, but that does not make an Augmented Unison or a Minor Second the same interval.
This confusion often arises from teachers who try and cut corners when teaching intervals by just making it an exercise in counting semitones. This is absolutely the wrong way to teach it, as D# and Eb are both three semitones from the note C but are in no way the same interval.
