An "octave" is not eight intervals... it's twelve. A KEY, however, is eight notes OUT of that octave.
A sharp and B flat are the same note... referred to in two entirely different ways. WHY? If there's only one note, shouldn't you pick one notation and stick with it? If you're going to refer to both A sharp and B flat, shouldn't they each be the same distance away from B and from A, but not quite all the way to the midpoint in between A and B?
These are relatively minor gripes though... here's the one that REALLY kills me. So there are twelve intervals in an octave - six full steps, each with a half step in between, for a total of twelve. Okay. And we notate this using a letter for the full step, and a sharp or a flat to modify that full step to produce the proper half step, so that you have A, A sharp, B... all relatively logical, right?
Well, sort of. Except that, randomly, instead of being noted A B C D E F, with a sharp or a flat in between each full note interval... there randomly isn't such a thing as B# or E#. You don't actually skip the FREQUENCY, mind you - the frequency shift between one note and the next is the same no matter what - but you don't have a B# or an E# in much the same way that you don't have a 13th floor on a lot of skyscrapers. You do, but somebody just shifted the damn numbers around and put a 14 on it instead of a 13.
So what should be a simple task - picking out the notes in a key - turns into a fucking nightmare. In a major key, you pick out the notes by full step intervals, except for a half step at the third and seventh notes. For a minor key, it's the same thing, except the half steps are at the second and fifth intervals. Now, if things were noted sensibly - from A to F with sharps for each half step - the key of E major would look like this:
E F A A# B# C# D# E
Simple, right? But no, the notes run from A to G with B# and E# missing, so it looks like this:
E F# G# A B C# D# E
Yeah, it took me five minutes of screwing up and going back to get that right, because you have to not only deal with where you move forward a half step and where you move forward a full step, but where the notation LOOKS like you went forth a full step, but you really only went forward a half step. Or where you have to move what looks like a step and a half to go one.
IN. FREAKING. SANE.
And music majors? By and large, they don't even know/notice this is weird. And may require significant amounts of explanation to understand why this is weird. B# and E# "just aren't."