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Those are both names for the same interval, where the top note is 6 half-steps (semi-tones) away from the bottom. It is also known as a tritone, and is halfway between an octave.

If you start on C, the augmented fourth above is F-sharp, and the diminished fifth is G-flat. They sound the same (they are enharmonic).

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Q: What are the values of augmented fourth and diminished fifth in music?
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