This root is attested only in The Etymologies (Ety/ÑGAN), where it was glossed “play (on stringed instrument)” and was the basis of various words, mostly from its extend form √ÑGANAD. Neither it or any of its derivatives appear in later writings. The later Quenya words Q. tanta- “to harp” and tant(il)a “harp” (VT41/10) might indicate its replacement by another root (?√TANAT or ?√KYANAT), but none of the derivatives of √ÑGAN(AD) were given new meanings, so perhaps this root remained valid.
Conceptual Development: The Early Qenya root ᴱ√KᴬNTᴬN is probably the precursor of ᴹ√ÑGAN(AD). The strongest indication of this was the shift of the ᴱQ. vorokantele “monotonous repetition” in the Qenya Lexicon (QL/45) to ᴹQ. vorongandele “continual repetition (harping on one tune)” in The Etymologies (Ety/ÑGAN).
ᴱQ. kantl “large harp” (< ᴱ√KᴬNTᴬN) might have developed conceptually into the later Q. tant(il)a “harp”, which might be an indirect derivative of an unattested root √KYANAT (<< ᴱ√KᴬNTᴬN) via Telerin in the same way that Q. telpë “silver” developed from √KYELEP under influence of T. telpe*. This is entirely speculative, however.
Neo-Eldarin: For Neo-Eldarin purposes, I would suggest using ᴹ√ÑGAN(AD) and its larger set of derivatives over hypothetical √TANAT or √KYANAT, which has only Quenya derivatives. For example, nande was used in NQNT over tant(il)a.