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Hi, sorry if its a dumb question but I was wondering what the correct inversion of an augmented 7th interval would be. Based on what I understand an inversion is just putting the lowest note an octave up. An augmented 7th has 12 semitones, similar to an octave/ perfect 8th, which would lead me to think that inverting it would basically be just raising the whole interval up an octave(for example if I were playing G3 and G4 on a piano, I would invert it to G4 and G5). But from what else I have learned is that Augmented and Diminished intervals always invert into each other(as well as major to minor, perfect to perfect, and vice versa for both), and the numerical values of certain intervals always invert into each other(2nds invert to 7ths, 3rds invert to 6ths, 4ths invert to 5ths, and vice versa for all.) So if I focus on those rules, rather than just raising the lowest note an octave, then an Augmented 7th would invert into a Diminished 2nd.
Are those the rules that I should be following, rather than just raising the octave of the low note? I know that certain interval values overlap with each other and I’m assuming get their (Diminished, Augmented, Major, Minor) names chosen depending on their relation in the whole scale/key. I think I’m starting to overcomplicate things now. If anypne could help I would really appreciate it.
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