A root appearing in Tolkien’s later writings with a variety of glosses: √MAY “make (in artistic sense as ποιήτης [Greek: make, create])” in Quenya Notes (QN) from 1957 (PE17/145, 163), {√MAGA >>} √(A)MAY “suitable, useful, proper, serviceable; right” in Definitive Linguistic Notes (DLN) from 1959 but this note was crossed through (PE17/172), √MAY “excellent, admirable” elsewhere in DLN (PE17/172), again as √MAY “excellent, admirable” in notes contemporaneous to the Quendi and Eldar essay from 1959-60 (PE17/150, 163) and finally as √MAY “beautiful” in notes from the late 1960s (VT47/18).
Two notable derivatives of √MAY were S. mae “well” (PE17/17, 163) and Q. Maia (PE17/163; VT47/18), but elsewhere these two words were derived from the root √MAG “good (useful)” (PE17/16, 162; PE19/46, 62, 75, 94). In the aforementioned notes from the late 1960s, however, Tolkien said “maga was distinct from maʒa and maya” (VT48/18). For purposes of Neo-Eldarin, I would assume the root √MAY was distinct from √MAG, having the meaning “excellent, admirable, beautiful” and by extension the creation of beautiful things such as art, to allow the retention of 1957 words like Q. maitar “artist” (PE17/163).
A possible precursor to this root is unglossed ᴱ√MAẎA from the Qenya Lexicon of the 1910s with derivatives like ᴱQ. mai “too much” and ᴱQ. maira “excessive, strong” (QL/60); perhaps a more extreme version of its later sense “excellent”. The entry also included ᴱQ. mairu “(horse ?); mane, flowing hair”, but Tolkien marked this word with a “?”, perhaps indicating he was unsure it was from this root (QL/60).
This root first appeared as unglossed ᴹ√RIG in The Etymologies of the 1930s with derivatives like ᴹQ. ríe/N. rhî “crown” and ᴹQ. rína/N. rhîn “crowned” (Ety/RIG). The root was then altered to ᴹ√RIƷ (EtyAC/RĪ). A similar root √RIK with derivation ✶riknā >> Q. rína (all unglossed) appeared in the first layer of composition for the Outline of Phonology from the early 1950s, but this section was revised in green ink around 1970 and the root did not appear in the revisions (PE19/85-86 and note #79).
The root √RIG appeared a number of times in Tolkien’s writings from the 1950s and 60s, variously glossed “wreath, garland, crown” (PE17/59), “twine” (PE17/182), and “twine, wreathe” (PM/347), but √RIƷ “wind about, wreathe” also appeared in notes on the names of Galadriel and Celeborn from 1968 (NM/349, 353). Thus it seems Tolkien vacillated between √RIG and √RIƷ with a brief aside to √RIK in the early 1950s.