This root first appeared in The Etymologies of the 1930s as ᴹ√NYEL “ring, sing, give out a sweet sound”, with derivatives like ᴹQ. nyelle/N. nell “bell”, ᴹQ. nyello “singer” and N. nella- “sound (of bells)” (Ety/NYEL, EtyAC/NYEL), though an earlier hint of it might be seen in the Gnomish verb G. nelu- “ring (tr. & intr.)” from the Gnomish Lexicon of the 1910s (GL/60). Tolkien also mentioned this root in the first version of Tengwesta Qenderinwa from the 1930s (TQ1) as having a variant √NYOL, also meaning “ring” but representing a deeper sound (PE18/45).
In the second version of Tengwesta Qenderinwa from the early 1930s (TQ2), he gave the variants as √ŊYEL/√ŊYOL “ring”, in keeping with his decision to remove initial palatalized dentals from Primitive Elvish. A similar set of variants √(Ñ)GYEL/√(Ñ)GYOL “ringing” appeared in a list of sound roots from around 1959-60 (PE17/138).
Neo-Eldarin: For purposes of Neo-Eldarin, I think it is best to ignore Tolkien’s decision to remove initial palatalized dentals from Primitive Elvish, and I recommend retaining √NYEL as the root for “bell” words.
Tolkien used very similar forms for Elvish words for “cold” for all of his life. The earliest iteration of this root was unglossed ᴱ√RIŊI in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. rin (ring-) “dew” and ᴱQ. ringa “damp, cold, chilly” (QL/80). The root had similar derivatives in the contemporaneous Gnomish Lexicon such as G. rî “coolness, cool” and G. ring “cool, cold” (GL/65). In The Etymologies of the 1930s Tolkien gave the root {ᴹ√RINGĀ >>} ᴹ√RINGI “cold” with derivatives like ᴹQ. ringe/N. rhing “cold” (Ety/RINGI; EtyAC/RINGI). Primitive forms ✶riñgi “chill” and ✶riñgā appeared in Common Eldarin: Noun Structure from the early 1950s (PE21/80), and Christopher Tolkien mentioned √ring as the basis for cold words in the Silmarillion Appendix (SA/ring).