In George Russell's The Lydian Chromatic Concept of Tonal Organization, he introduces the notion of "horizontal scales":
They are horizontal because they include the fourth degree in their structure (B♭ in the F Lydian Chromatic Scale). (p. 17)
This is in contrast to vertical scales, which include the Lydian B♮.
But my question is how he derives the four horizontal scales, which are:
- F major: F G A B♭ C D E
- F major flat seventh: F G A B♭ C D E♭
- F major augmented fifth: F G A B♭ C♮ C♯ D E
- F Lydian flat seventh: F (G) A♭ A♮ B♭ B♮ C D E♭ (E)
As far as I can tell, there is no explanation for how these scales are formed, which seems really odd for someone basing his entire theory on the acoustical properties of the harmonic series.
How are these scales formed? Frankly, it almost seems as if (especially in the final scale) he just threw some darts at a board until he decided he was done creating his scale.