Let me add one point: Frankly, I hadn't been aware of the fact that the naming of intervals simply derives from counting staff positions (or white keys, or EC middle row buttons). Prior to taking part in this current discussion I had been of the opinion that the difference of, for instance, an augmented unisone and a minor second would be one regarding the diatonic function, i.e.: that F# to G would have to be regarded as minor second just as part of a Gmaj scale (or one of the relatives). Now I have learned, that the basic concept is not just diatonic based, but more specific upon the single "world" of Cmaj/Amin/Ddor/Gmix a.s.f. and not be transferred to other keys.
I'm not sure I understand what you're saying here. Are they not both true? What meaning does counting letters have if not in a diatonic context? F#-G and Gb-G sound the same out of context. The intervals have different names because of how they are used (and the expectations that they create in the listener) in the context of the diatonic scale.
David, thank you for the reply! I seem to have learned from it that even the somehow distracting use of bb and ## ensures just the portability of the basic white-key concept into any given key. The same is pretty obvious regarding the - functional - minor second.
But just to ensure that I've got it right now I'd like to come back to the - non-functional - augmented unisone as well. Talking, for instance, about Schubert and his frequent "shadowing" from Major to Minor, regarded as one first step of, say, weakening the diatonic funktionality: F#-F (in the key of D) equals E-Eb (in the key of C); no (minor) second in any event.
This leads me back to my attempt to refine the formula regarding Don's chart one more time: The step from sharp to natural equals the step from natural to flat as every three notes share the same staff position.
After all, I find that diatonic issue (which I have always been into) all the more fascinating! Very productive thread for me as well...
I hesitate to add that notorious ceterum censeo of mine, but... anyway! I am regarding Piano and EC (and the German 20b concertina, as contrasted with the 30b-onwards Anglo due to its kind of irregular row of accidentals) as basically diatonic instruments because all the tones are strictly organised around the naturals (which might fit the Crane as well, apart from its recently discussed irregularity).
Might well be that I'll fall on at least one pair of sympathetic ears in this context...