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A tenday (ten-day) was a measurement of time, ten days long, analogous in some cultures to the concept of the Human civilization's week.
The tenday was used primarily by both the Vulcan and Romulan civilizations. (TOS novel: Spock's World; TOS - Rihannsu novels: The Romulan Way, Honor Blade, The Empty Chair)
It was also adopted, to a limited degree, by other Federation cultures. (TOS novel: Prime Directive)