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I’m working through a Barrons AP Music Theory book and was very confused by one of the diagrams. The diagram begins with a major second created by a G to an A, or a M2 due to it being a whole step. It then adds a sharp to the G, making the interval a half step smaller. They then label this an augmented 2nd, despite it being a smaller interval than before. Wouldn’t a G sharp to an A be a m2? Could someone explain why or why not this is true? Or is it a printing error in the book?

Edit: here is the diagram in question. enter image description here Everything except the leftmost example makes sense to me.

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    I answered straight away, because I think I know what the confusion is about. If I'm wrong, can you post a picture of the diagram? – Michael Curtis Apr 17 '19 at 17:16
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    I’ve added the diagram in question if you wouldn’t mind taking a second look. – Tim Anderson Apr 17 '19 at 17:41
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EDIT

In the image of the chart, the left most pair M2 -> A2, the sharp is on the A not the G. So G to A is an M2, but G to A# is indeed an A2.

I'll leave my original answer below, it has some application genrally.

I suspect the example is for an A minor scale in which case we would want to look at the segment F G A.

If we add the sharp to make the harmonic minor scale the segment becomes... F G# A ...and we see that the augmented second is not between the G# and A, but between the F and G#.

This example from the harmonic minor is probably the most common textbook example of an augmented second.

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    Michael, I had obviously 20 minutes to write my answer ;) as when I started the question was 7 min. old and no comment. So I was looking ab at first for Barrons Music Theory Book and studied the downloadable Pdfs. (And I wondered whether OP’s question might be just a hidden advertisement for Barron’s books.) So my conclusions about the F-G# was the same like yours. – Albrecht Hügli Apr 17 '19 at 17:45
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    My apologies, such a simple thing! Thank you for the additional wisdom on the harmonic scales however, I’ll make sure to remember that for the future. – Tim Anderson Apr 17 '19 at 17:52
  • @TimAnderson, no problem (up vote please) – Michael Curtis Apr 17 '19 at 18:08
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You are misreading the diagram. The leftmost example adds a sharp to the A, not the G. The actual interval is G-A♯, a genuine augmented second. Note the placement of the sharp on the space of the A instead of the line of the G. Pay special attention to the placement of the sharp on the "dim6" diagram in comparison, where the sharp is placed on the line of the G.

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G - A is a whole step (major second)

G#- A is a half step (minor second)

G# is the VII of a minor scale

by augmenting the seventh degree of a minor scale we get a step of 1+1/2 tone between F - G#: so F -G# is an augmented second

I assume they describe how the harmonic minor scale is derived from natural minor. But as you don’t post the passage you’re referring or in which chapter you are reading we can only assume ...

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