The section on chrominicism really blew my mind! Imagine the natural notes not being equally natural but gradually sharpening or flattening depending on the direction in the series of fifths. If chords (and harmony) are built in the series of fifths would it not be preferable to call a "descending" progression a flattening progression (since it goes to a flatter chord) and to call an "ascending" progression a sharpening progression (since it goes to a sharper chord)?

Perfectly right! We stand corrected. Changes will follow. Thanks.

Can someone please explain how chrominicism works with equal tempered tuning? for example, doesn't B# have the same chrominic position as C? Thank you.

Chrominicismexists in equi-tempered tuning, pythagorean tuning, "functional tuning," and any of the forms ofjust intonation, although the calculations vary minutely from one to the other. Chrominicism should not be confused with proximity in absolute pitch. Chrominicism is a relative indication of where a note is found within the fundamental generative structure of the series of perfect fifths. For instance, B is five "notches" sharper than C, because it is located five perfect fifths away in the series. B# is seven notches sharper than B, and twelve notches sharper than C. Since a note (for example C) and its chromatic version (for example C#) differ by a semi-tone, and because they are seven notches apart in the series, we can say that the size of each "notch" is one-seventh of a semi-tone. Now, this semi-tone, and therefore the notch, will be micro-tonally different depending on which tuning is used.
So you see, a C and a B# have different chrominic positions, even though they happen to be tuned the same in equi-tempered tuning. The context makes all the difference. For example, in a Dominant/Tonic swing in the key of A major, a B# would be a sharpeningchromaticization(by 7 notches) of the B, the fifth of the E7 chord, and would have an extremely strong tendency to resolve upward to the C#, the third of the Tonic chord. A C-natural, on the other hand, would be a flattening chromaticization (by 7 notches) of the C#, the third of the Tonic chord, and would have a very strong tendency to resolve downward to the B of the Dominant chord. This illustrates why it is so important to label our notes correctly and not use enharmonic spellings in a haphazard way. A chordal tone that has been chromaticized retains its same letter name (along with a chromatic designation), whereas anon-chordal tone, whether diatonic or chromatic, will have a different letter name than the note it is embellishing. (The non-chordal tone is, in fact, a chord tone of a neighboring chord).