would not have had it been

This sounds just fine to my ear, but I wonder:

1. Is this proper?
2. Is this all a conjugation of "to be", as it seems to me?
   
3. What is the formal grammatical term for this?

This is a combination of modals, conditionals, and past participles that I am able to understand but unable to describe or name.

Thank you!

I may be able to construct a sentence that uses that sequence of words correctly, but that doesn't mean that you have done so.

CJ

"[A soul song sung by a white woman was] played on rock radio.  I believe rock radio would not have played it if the song had been performed by a heavy-set black woman."

In deference to the anonymous respondent, I will remove the which.

"[A soul song sung by a white woman was] played on rock radio.  It probably would not have had it been a soul song performed by a heavy-set black woman."

I'm not writing for composition advice, but I do appreciate it.  I am asking whether  (strictly formally, and strictly the "would not have had it been" portion in an otherwise-unflawed sentence) the construction is syntactically flawed, and, if not, can you give this native speaker the name of the conjugation/mood being used?  The answer would sound something like "conditional past perfect", but that (of course) is not the right answer.

A thank you in advance, and if formal grammar questions are beyond the scope of this board, no problem there, and I will thank you and move back to lurking. 

joshuamcgee

“ What I was asking is would it be possible for the construction to be correct, but yes, a whole sentence is better.”

... it probably would not have, had it been ...

It is a "third conditional", if you want the technical name.  And the underlying if clause if it had been is rephrased with subject-verb inversion as had it been.

CJ