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This is a pretty odd question, since you say you can easily identify intervals but not their tonality. All I can say is that you have to put those notes in context of the key signature - I think that when I look at scores, I constantly have the key-signature in my head, and when I come across an interval, my brain follows these steps:
1. Identify the bottom note
2. Identify the interval
3. Look for accidentals.
So if I was in C, I would come across an E with a third on top and no accidentals. Then I would know that because E natural to G natural is minor, it's a minor interval. But I guess the problem you are talking about is that you wouldn't immediately know that particular intervals are major or minor. I would have to say that the reason I can instantly tell whether or not an interval is minor or major is because I'm a pianist, and it's fairly easy to see how many notes there are in between intervals on the piano, and that gets ingrained in your head after you play the piano for a while. I've never played guitar, but I would imagine that playing the guitar would have the same interval-ingraining effect (because guitar players have frets.) I guess what I'm saying is that the way to learn the tonality of an interval is just memorization.
Now of course, if there is a sharp on top of the interval, or a natural where there was before a flat, it's likely that the interval is major or augmented. If there is a flat on the bottom of the interval or natural where there was a sharp, then it's likely the interval is major or augmented. But if there is a flat on top of an interval or natural where there was a sharp, or there is a sharp on the bottom of a interval or a natural where there was a flat, then it's likely the interval is minor or diminished.
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