This word replaced the preposition uin “of the” in the third version of the King’s Letter, appearing in the phrase nelchaenen ned Echuir “the thirty-first day of Stirring”. Both Carl Hostetter (VT31/30) and David Salo (SG/229) theorized that this replacement has a similar prepositional function, from either √NOT “count” or √NED “middle”. Fiona Jallings suggested it might be a temporal preposition, with sense “during” (FJNS/349).
On VT47/40, note 67, Patrick Wynne suggested that this word might be a cognate of the newly published Quenya word net(ë) “one more”. This theory is supported by the most likely interpretation of nelchaenen. This word seems to mean “thirtieth” rather than “thirty-first”, and Patrick Wynne suggested that nelchaenen ned means “thirtieth and one more” = “thirty-first”. I find this theory the most compelling, and use it here.