Wouldn’t the reason B is incorrect as minor sixth in an Eb key, versus Cb, be that they function differently — Cb implying a lead downward (diminution) and B a lead upward (augmentation)?
I think you're mistaking the intervals with the note names. The flat 6, i.e. b6, or B/Cb in this case, is just an interval a minor sixth from the root, Eb.
The name of the note does not in any way indicate its function. C natural is the flat 3rd in the key of A minor, for example. F natural is the b6 in that same key.
B/Cb are called enharmonic equivalents in modern Western theory, even though it wasn't always the case.
Not really, it's the flat 3. Which is the same note, but I don't think anyone uses #2. #9, sure, but #2 I haven't seen or heard of. In any case, it's not the interval that determines which enharmonic equivalent to use. And Cb and B# are very rarely used in any case, just like E#, Fb, F##, etc. Yeah, I don't like playing in C#.
Wouldn’t the reason B is incorrect as minor sixth in an Eb key, versus Cb, be that they function differently — Cb implying a lead downward (diminution) and B a lead upward (augmentation)?
I think you're mistaking the intervals with the note names. The flat 6, i.e. b6, or B/Cb in this case, is just an interval a minor sixth from the root, Eb.
The name of the note does not in any way indicate its function. C natural is the flat 3rd in the key of A minor, for example. F natural is the b6 in that same key.
B/Cb are called enharmonic equivalents in modern Western theory, even though it wasn't always the case.
Is C the sharp two in A though? I think most would specify that as B#, C’s enharmonic equivalent.
Not really, it's the flat 3. Which is the same note, but I don't think anyone uses #2. #9, sure, but #2 I haven't seen or heard of. In any case, it's not the interval that determines which enharmonic equivalent to use. And Cb and B# are very rarely used in any case, just like E#, Fb, F##, etc. Yeah, I don't like playing in C#.