Bebop scales...

[borrowed from a post from squid

Ok, so i wanted to chime in here since it seems appropriate to mention the major bebop scale as traditionally accepted. that is:
scale degrees (from the root of the scale) 1 2 3 4 5 #5 6 7.

In other words, a major scale with a passing tone between the 5th and 6th scale degrees.

To anyone unfamiliar with bebop scales, the general idea is to strategically place a passing tone in a 7 note scale in order to form an 8 note scale which, when played in a continuous eighth note rhythm with a chord tone on the downbeat, causes the chord tones to continue to fall on the downbeat. Essentially, this can be done using a passing tone wherever it works to this effect.

There are, however, some commonly accepted versions of the bebop scale mentioned such as the major i just mentioned and the bebop dominant as described by jonasfixe and mr. beaumont.

The other common one is the bebop dorian, but this is a point of contention in the literature of jazz theory...

the bebop dorian scale is alternately described as

1) 1 2 b3 3 4 5 6 b7 (dorian with both the major and minor 3rd)
and
2) 1 2 b3 4 5 b6 6 b7 (dorian with both the major and minor 6th)

In the first case, if we were to play the corresponding dominant bebop and dorian bebop scale in a ii-V situation, we'd find that both contain the same notes.
Specifically, in a ii-V to Cmaj:

Dorian bebop(1) = D E F [F#] G A B C
Dominant bebop = G A B C D E F [F#] (mixolydian with both 7ths)

One consideration here is that it is common to simply play the dominant tonality over the entire ii-V in bebop, and these tones are gleaned from an analysis of that type of approach. However, if these scales are thought of as separate entities and played as such, different chord tones are in fact emphasized.

Dorian bebop(2) = D E F G A [Bb] B C

As for the 2nd bebop dorian, i personally don't get it in the case of a ii-V since that "B" is emphasized and sounds to me like an arrival to the V chord. That's fine if you're going for an anticipation, but as for a type of scale designed to facilitate movement within a chord, it doesn't really seem to fit the bill IMO. In a "modal" situation, though, it sounds real cool to my ears.
But yeah, it's the concept of forming that 8 note, rhythmically symmetrical scale that is the real meat of all this, and it can be applied to just about any scale that has an odd number of scale tones to begin with from phrygian dominant to melodic minor to your basic pentatonics...