Coincidentally there are no commonly used scales or modes with two consecutive semitones. The semitone gaps are always spaced out. With 11 notes (excluding the octave), that only leaves 4 possibilities for a 7 note scale if you remove rotations. These correspond to major, harmonic minor, melodic minor and harmonic major. It’s easy to prove with pencil and paper concentrating on c to c
> That’s true but in those cases they are passing tones.
That may well be their main function, especially in bebop (it's not so certain in blues), but they're still considered as part of the scale.
> For examples in a bebop scale you don’t tend to arpeggiate using both the consecutive tones.
That's true for any non-chord tones. The intervals are still very common (in bebop you commonly simply walk the whole scale up and/or down in straight 8ths or 16ths, playing adding the passing tone for the chord tones to end up on the downbeats).
As a kid I dismissed the piano because nobody explained to me why the keyboard was so stupid looking, laid out so irregularly. WbWbWWbWbWW. Wot?
Only some self-education (much later) revealed that 12 tones per octave deliver some excellent harmonies, not 11 or 13 or 20 or 36 or whatever. Twelve. But the harmonies come only on odd steps. So we have 5 semitones to a perfect fourth (4:3 harmony), then two semitones to a perfect fifth (3:2 harmony), then 5 semitones to the octave.
And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW.
If only someone had explained all this in grade school.
I didn't really understand your explanation so I might be restating your ideas, but just in case:
> And then - just to keep it confusing - we have to split both of those groups of five semitones, so... we arbitrarily split them as 2-2-1 (i.e. WbWbWW keys). Thus the white/black keyboard pattern, starting at C, of WbWbWWbWbWW. If only someone had explained all this in grade school.
We don't arbitrarily split them! It was very much made on purpose to match the diatonic scales, which are very natural due to being a chain of fifths. E.g. from F ascending 5ths: F-C-G-D-A-E-B-¡F!
It's not arbitrary that we based modern keyboards around heptatonic scales! Then we added some black notes so we can transpose, which is pretty convenient on 12-TET.
Mmmm yes, and that’s also a bit confusing because it dodges around why the scale was and is 7 notes to begin with.