Which word means cleverly amusing in tone?

The word that means cleverly amusing in tone is "facetious." This term describes a manner that often employs flippancy or humor, especially in situations where a more serious tone might be expected. A facetious comment is not just lighthearted; it cleverly plays with ideas or situations to create humor, often in a way that requires a degree of perceptiveness to appreciate fully. This nuance makes "facetious" a fitting description for something that is both clever and amusing, indicating a wit that is intentional and engaging.

The other options do not convey the same tone or meaning. "Serious" denotes a lack of humor and gravity, failing to capture the clever amusement suggested by the question. "Sarcastic" can have an amusing quality but often carries a biting or mocking tone that isn't necessarily cleverly amusing. "Melancholic" refers to a deep sadness or gloom, completely opposite to the idea of clever amusement.