Enharmonic intervals sound identical even though their spellings and names differ

Two intervals that occupy the same keys on a piano sound exactly the same regardless of how they are spelled or named — they are enharmonic equivalents. A minor third and an augmented second are the same three-semitone distance; the ear cannot tell them apart. Spelling and name are chosen for notational and harmonic correctness (letter classes, key, function), not for sound. This is why the tritone can be an augmented fourth or a diminished fifth, and why ear training focuses on the sound of an interval rather than its name: your ear does not obey the spelling rules that notation requires.

Examples

C to D-sharp (augmented second) and C to E-flat (minor third) are played with the same two keys and sound identical. For ear training you learn the sound; for writing on a staff you choose the correct spelling.

Assessment

Explain why a minor third and an augmented second sound the same but are named differently, and state which discipline (ear training or notation) each naming choice serves.