Etymology
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moist (adj.)

late 14c., "slightly wet; well-irrigated, characterized by moistness," from Old French moiste "damp, wet, soaked" (13c., Modern French moite), which is of uncertain origin. Perhaps from Vulgar Latin *muscidus "moldy," also "wet," from Latin mucidus "slimy, moldy, musty," from mucus "slime" (see mucus). Alternative etymology [Diez] is from Latin musteus "fresh, green, new," literally "like new wine," from musteum "new wine" (see must (n.1)). If this wasn't the source, it influenced the form of the other word in Old French. Related: Moistly; moistness (mid-14c.).

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moisture (n.)

"diffused and perceptible wetness," mid-14c., from Old French moistour "moisture, dampness, wetness" (13c., Modern French moiteur), from moiste (see moist).

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moisten (v.)

"make moist or damp," 1570s, from moist + -en (1). Related: Moistened; moistening. The earlier verb was simply moist (mid-14c.), from Old French moistir.

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musty (adj.)

1520s, "moldy, sour," perhaps a variant of moisty "moist, damp" (see moist), but musty, of bread, "containing must" is attested mid-15c., and from 15c.-19c. must also was a variant of musk. Related: Mustiness.

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hygro- 
word-forming element meaning "wet, moist; moisture," from Greek hygros "wet, moist, fluid; weak, soft, flexible." Beekes says possible cognates include Old Norse vokr (accusative vokvan) "moist, wet;" Latin uvidus, udus.
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humid (adj.)

"moist or accompanied with moisture; containing, or formed or effected by, water or vapor; wet, damp," early 15c., from Old French humide, umide "damp, wet" (15c.) or directly from Latin humidus "moist, wet," variant (probably by influence of humus "earth") of umidus, from umere "be moist, be wet," from Proto-Italic *umo- "wet" (also source of Latin umidus "wet, moist," umiditas "moisture," umor "moisture, fluid," umectus "moist, wet"), perhaps from PIE *uhrmo- "wet," from the same source as Latin urina [de Vaan].

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dewy (adj.)

Old English deawig "of or pertaining to dew; moist with or as with dew;" see dew + -y (2).

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masto- 

before vowels mast-, word-forming element meaning "female breast, mammary gland," from Greek mastos "woman's breast," from madan "to be wet, to flow," from PIE *mad- "wet, moist, dripping" (source also of Latin madere "be moist;" Albanian mend "suckle;" see mast (n.2)).

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hygrology (n.)

"science of bodily humors," 1787, from French or German hygrologie, which are earlier, or from hygro- "wet, moist; moisture" + -logy.

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hygrometer (n.)
"instrument for measuring atmospheric moisture," 1660s, from French hygromètre, from Greek hygro- "wet, moist; moisture" (see hygro-) + -meter. Related: Hygrometry; hygrometric.
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