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Why is chord labelled as IVb7?

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In Hooktheory II, there is an example where you are in the minor mode, but borrowing the dominant 7th IV chord from the dorian mode. This chord is labelled as IVᵇ⁷ in the hookpad example (picture attached), but in the text it’s labelled as IV⁷.
image

I’m not sure about a couple of things:

  1. Which of IVᵇ⁷ and IV⁷ is correct? Or are both correct and referring to different things?
  2. If IVᵇ⁷ is correct, why is that the case?
    2.1. Is it because the b7 in IVᵇ⁷ refers to the b7 relative to the major scale? This doesn’t make much sense to me because both minor and dorian have a b7 relative to major.
    2.2. Is it because the dominant 7th IV chord has degrees 4, #6, 1, 3 relative to the minor scale, and the #6 is converted to b7 to make it more obvious that it’s a type of 7 chord? But then that’s still weird because usually the 7 in IV⁷ refers to the fact that we’re adding the 7th note from the bass (which is 3 in this case), not to the 7th degree from the root.

If anyone could clarify this, I’d be very grateful!

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