The tritone (6 semitones) is spelled augmented fourth or diminished fifth depending on context

The tritone — 6 semitones, exactly half an octave — can be named two ways depending on the letter classes involved. F to B is spelled across four letter classes so it is a type of fourth; because it is one semitone larger than a perfect fourth it is called an augmented fourth. B to F is spelled across five letter classes so it is a type of fifth; because it is one semitone smaller than a perfect fifth it is called a diminished fifth. The same two pitches, different spelling, different names. Context (voice-leading, key, harmonic function) determines which name is correct.

Examples

F up to B is an augmented fourth (tritone) because B is the fourth letter class above F. B up to F is a diminished fifth for the same distance because F is the fifth letter class above B.

Assessment

Given the interval F-B on a piano (white keys only), explain why it is an augmented fourth, and why the same sound spelled B-F becomes a diminished fifth. What changes — the sound or the name?