Musk in modern perfumery is exclusively synthetic — natural musk (from deer) has been banned for decades. The synthetic family (Galaxolide, Habanolide, Romandolide, etc.) ranges from clean and powdery to slightly animalic and skin-like. "White musk" is a marketing term for the cleaner end of the family; "animalic musk" leans heavier into the body-warm character. Musks are ubiquitous because they're cheap, they fix other materials (extending longevity), and they smell like "clean skin" — exactly the impression most designer fragrances are aiming for in the dry-down.
Musk
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Quick definition
A class of materials with a clean, slightly animal, intimate character — found in almost every fragrance as a base note.