The Mixionian scale, also known as the bebop dominant scale, is an eight-tone scale (octatonic scale) that can be built using the following steps between notes: 1, 1, ½, 1, 1, ½, ½, ½.
One example of the Mixionian scale is: G, A, B, C, D, E, F, F#. This scale is shown below in traditional notation and in guitar tablature notation.
This scale carries the name "Mixionian" as it is a mixture of the Ionian scale (the standard major scale, G, A, B, C, D, E, F# in the example above) and the Mixolydian scale (G, A, B, C, D, E, F in the example above).
This scale is the first mode of the bebop dominant scale (the bebop dominant scale itself) and the fifth mode of the bebop Dorian scale (or the fourth mode if we ignore the passing tone F#; the mode of the bebop dominant scale starting on F# is sometimes called the seventh mode whereas the mode starting on F is the flat seventh mode and so sometimes the bebop dominant scale is described as having seven modes even though it is an eight-tone scale).