I read this from Arnold Schoenberg's Preliminary Exercises in Counterpoint. The original part is: Later, intermediary regions are likewise introduced (Simple Counterpoint in Three Voices, Chapter VIII); "Their purpose is usually that of emphasizing a contrast through their harmonic differences. This is achieved by using the characteristics of these regions more or less as if they themselves were basic tonalities."

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From what I can tell, Schoenberg's term here is ambiguous and, honestly, unimportant.

Imagine we're in C major. Now, imagine we modulate to E major. There's occasionally a gray area between the "obviously C major" part and the "obviously E major" part where it's unclear exactly what tonic is. In many cases, composers will hint at keys other than either C or E. These hinted-at keys are the "intermediary regions," so named because they occur between the more important tonalities of (in this case) C and E.

"Intermediary regions" are apparently not related to Schoenberg's Chart of Regions that I discuss in my answer to Old Books with chord progression charts or matrices?

(This answer is based off of p. 103 of Dudeque's Music Theory and Analysis in the Writings of Arnold Schoenberg.)

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