The Early Qenya word for a seven-day “week” is otsola. It is related to the word otso “seven”, and its Gnomish cognate ochlad is derived from ᴱ✶ot·g’lāta (GL/62). The Qenya word is probably derived from ᴱ✶otso-g’lā, where the second element is a reduced form of ᴱ✶galā > kala “daytime”.
Conceptual Development: In a very early list of weekday names, this word also appeared as ᴱQ. otsan (PE14/16, 21), where its second element was probably derived from sana “day” (GL/29).
Neo-Quenya: There are a couple later words for “week” in Quenya, namely ᴹQ. lemnar and Q. enquië. These describe five- and six-day weeks, respectively and are related to ᴹQ. lempe “five” and Q. enquë “six”. The Elves used a six-day week in Tolkien’s later writing (LotR/1107). The Númenóreans added a seventh day that was adopted throughout the human kingdoms of Middle-earth, but Tolkien did not give a name to this seven-day week.
The later Quenya word for “seven” remained otso, and the later word for the six-day week is a combination of enquë “six” with the abstract-noun suffix -ië. Therefore, otsola might remain a valid Quenya word for a seven-day week, though a revised form !otsolë might fit later Quenya structure better.