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I was looking at their official songbook. The key of the song is C minor. The progression goes Ab∆ (VI) C-7(I) Fsus4 (IV major???) F7 (IV dominant??) Ab∆.

The F in C minor is F-7, and F7 is neither secondary dominant of Ab∆ nor it's tritone sub. Where is this F7 coming from then?

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The F7 is a secondary dominant for Eb. It gives the feeling that it's about to do an F7 -> Bb7 -> Eb motion, but after giving you those feelings the plan is cancelled and it goes to IV of Eb i.e. Abmaj7 instead. "Gotcha! You though we were going to F7 - Bb or something, didn't you!"

In order for something to work as a dominant or secondary dominant for something, the dominant-tonic motion doesn't actually have to happen. If you press pause at the F7, you can analyze its meaning in the context, before knowing what's going to happen next. If your mind anticipates something, the anticipation is true and valid at that moment, regardless of if the anticipated thing actually occurs or not.

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The F7 arises from modal mixture. It adds a slight Dorian flavor to the song. It fits because of a chromatic inner-voice motion (Bb -> A -> Ab).

Note that Fsus4 in the key of C minor would ordinarily resolve to Fm, so resolving it instead to the major instead adds an element of surprise, without ruining the identity of the Fsus4 as a suspension over a triad. This was a favorite technique for Bach and Faure, among many composers.

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