Augmented and Diminished Intervals

Question

I am going through a huge theoretical "reboot" with Laitz's Complete Musician on my own, and I'm having trouble counting the intervals here:

This is in treble clef. The first highlighted interval in the lower part (d5/A4) makes sense; the second (A2/d7) I don't get it. Where did that seventh come from? isn't it just a second between A and B? What am I missing?

Answer 1

Ab to B natural is an Augmented second (A2), but if you inverse that interval, i.e. B natural to Ab it is a 7th diminished (d7).

You can also see that in the first example where you have D to Ab (d5/A4). Where the interval between D and Ab is a diminished fifth (d5) and the inverted interval is Ab to D which is an augmented fourth (A4).

Answer 2

1. Note there is Ab in the key signature at the beginning of the measure. This means any A is Ab, lowered by half-tone.
2. It's difficult to guess without context, but it seems the notation refers to regular and inverted intervals. So (assuming it's in treble clef)
   • D4-Ab4 is diminished 5th
   • Ab4-D5 is augmented 4th
   • Ab4-B4 is augmented 2nd
   • B4-Ab5 is diminished 7th