It is a number 2 interval, but being 4 semitones, it is beyond an augmented second. So, what it is?
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The interval from any G (flat / sharp / neutral) to any A (flat / sharp / neutral) (in the same octave) is always a second. In your case, since the G is flat and the A is sharp, you have a doubly augmented second.
Of course, this interval is sonically equivalent to a major third.
Matt L.
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@fferri: In practice it occurs very rarely, and I haven't yet seen a symbol for it. – Matt L. Apr 17 '18 at 10:09
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2@fferri: On [this site](https://harmonia.illiacsoftware.com/support?article=206) I've found `++2` but I don't know how common and universally accepted it is. – Matt L. Apr 17 '18 at 10:11
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3Has anyone ever personally seen this used? I have not. I'd be curious to see an example. I cannot think of a theoretical justification for using it, either. I'd be interested in an explanation for that as well. – Heather S. Apr 17 '18 at 11:09
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1@HeatherS. See the question that Tim H posted as a comment to the original post: https://music.stackexchange.com/questions/15430/are-doubly-augmented-and-doubly-diminished-intervals-practical – Richard Apr 17 '18 at 13:21
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@HeatherS. In less tonal (or maybe bi-tonal) music voice leading may provide a reasonable explanation. However, I agree it is contrived. – 11684 Apr 17 '18 at 13:38
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4“Of course, this interval is sonically equivalent to a major third.” This is only true in equal temperament. – 11684 Apr 17 '18 at 13:39
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@MattL. The guys at that site may have riffed on the standard "+" symbol for augmented interval :-) . I'll note that Dolmetsch does not list any double-anything symbol. – Carl Witthoft Apr 17 '18 at 14:39
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@HeatherS. I found a surprising example of this kind of enharmonic relations in surprisingly early music: have a look at bar 75 and 102 of violin sonata K 481 (Mozart). – 11684 Apr 30 '18 at 08:39