Bebop Scales From The Diatonic Major Scale :
The interval formula is 1 - 2 - 3 - 4 - 5 - #5 - 6 - 7. This is the major scale including a passing tone (#5) between the fifth and the sixth.
The formula is 1 - 2 - b3 - 3 - 4 - 5 - 6 - b7. Compared to the Dorian mode this scale has an additional note, a major third, between the minor third (b3) and the fourth (4).
Notice that there is a second version of the Dorian bebop scale with a major 7 between the b7 and the tonic (1).
The formula is 1 - 2 - 3 - 4 - 5 - 6 - b7 - 7. This is the Mixolydian mode including a major seventh.
The formula is 1 - b2 - b3 - 4 - b5 - 5 - b6 - b7. It has an additional fifth between the flat fifth (b5) and the minor sixth (b6).
The interval formula is 1 - b2 - 3 - 4 - 5 - b6 - b7 - 7. This scale is also referred to as Altered Bebop and is derived from the fifth mode of the harmonic scale, the Phrygian dominant mode.
The interval formula is 1 - 2 - b3 - 4 - 5 - 6 - b7 - 7. This is a variation of the Dorian mode, often used in jazz improvisation. This scale incorporates a chromatic passing tone between the b7 and the tonic (1)
Other Bebop Scales
Formula is : 1 - 2 - b3 - 4 - 5 - b6 - b7 - 7 . This scale has a chromatic passing tone (b7) between the minor sixth (b6) and the major seventh (7).
The double Dorian bebop scale is actually the dorian mode with a passing tone (b2) between the tonic (1) and the major second (2).
The formula is : 1 - 2 - b3 - 4 - 5 - #5 - 6 - 7. The melodic minor bebop scale is derived from the ascending form of the melodic minor scale. It has a chromatic passing tone between the 5th and 6th notes.