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shurely i missed some concept but why b7 -> CH -> B7 is not valid/ mentioned at page 25 of lesson book volume 1 ??
I assume that you meant b7-ch-b7 (the B7 threw me off). The reason this is not valid or mentioned is because there is no “ch” available as a lower neighboring tone in the mixolydian. It is in turn a “6” which is diatonic and instead mentioned here.
On the other hand, if you are asking why it isn’t used as an upper chromatic NT, that is due to the modal ambiguity that chromatic upper NTs create and therefore are avoided for the most part(see p.46 Lesson Book). In this case it would sound like a major 7 and creates some rather nasty dissonance (at least at slow to medium tempos) with the b7 which is a primary guide tone of this chord/scale.
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