Lydian Augmented and the Mark Levine book criticisim

[Aquatist]

Please excuse my ignorance, but I have a quick question:

Relating to the Lydian Augmented scale, I understand from a modal approach it is the 3rd mode of the Melodic Minor scale ascending. For a case study, let's use the "C Melodic Minor ascending" (Eb Major Lydian Augmented).

I understand it can also be notated as, Eb Major #4, #5, Eb Major #5 for shorthand notation, and G/Eb as a slash chord. So my question is, is the #4, #5 a universal term? Meaning, if I was thinking Bb Lydian Augmented will it pop up on a chord chart as #4, #5? Because technically the 4th would be natural, right?

I'm also curious to know what kind of criticism has people held against The Jazz Theory Book? So far, the only thing that bothers me is having to transpose all of the theory to a written approach in different keys (like the previous example above), and little or no help finding good, flexible fingering from a technical view.

[motherlode]

All things Lydian are found here:

http://www.lydianchromaticconcept.com/forum/