(SD:129) The word is translated ”thirty-first”, but clearly seems to mean literally ”thirtieth”: nel-chaen would express 3 (times) 10, plus -en as an adjectival ending to make this an ordinal. The conceptual validity of this form is however questionable, since Tolkien later dropped the root KAYAN (whence -chaen) as a root for words for ”10”.
Sindarin
nelchaenen
ordinal. *thirtieth
nelchaenen
ordinal. thirtieth
a pherhael ar am meril suilad uin aran o minas tirith nelchaenen ned echuir
to Samwise and Rose the King’s greeting from Minas Tirith, the thirty-first day of Stirring
nelchaenen
thirtieth
A word appearing as nelchaenen “thirty” in the King’s Letter from around 1950 (SD/129), but more likely an adjectival form meaning “✱thirtieth”. Compare tolothen “eighth” from the same document based on toloth “eight”.
Neo-Sindarin: For purposes of Neo-Sindarin, I would use ᴺS. nelphaen for “thirty” based on later pae(n) “ten”. As an adjective I would use nelphaenui “thirtieth”; compare paenui “tenth”.