OIr. dúan “poem, song, verse composition” (ā, f; dil.ie/18966; LEIA D-208) has three possible etymologies:
(1) Watkins’ (Celtica 11) explanation from PIE *dh2pno- “portion, allotment” from the root *√deh2p- “to divide into portions (of a meal)” implies the concept of an apportioned gift by the poet, a gift that entails the patron’s liability to recompense the poet. It has achieved great popularity among Indo-Europeanists before the background of Indo-European poetic ideology. The main formal disadvantage is that the root *√deh2p- has otherwise left no trace in Celtic, so the word must have been inherited from a very early period; and that there is a – not too wide – semantic gap between the root and the OIr. word.
(2) Formally less isolated is the derivation of dúan from *doh3uno- “that which is given, gift”, a form that is derived either from the expanded verbal root *√deh3u̯- “to give” (LIV 107), or secondarily from the nominal stem *deh3-u̯r̥/u̯en- “the giving, gift” (NIL 61, 65). Irish provides a close semantic parallel for this in the fact that the inherited common noun for “gift, endowed skill”, dán < *deh3nu-, has taken on exactly this additional meaning “poem” in Modern Irish. Like in Watkins’ proposal, the motivation for the term is one of a relationship of mutual exchange, involving the person of the poet and his patron. The advantage of this explanation is that the reciprocal word for the price to be paid by the patron, OIr. dúas “gift, reward, recompense” < *doh3usteh2, is definitely derived from the Indo-European root *√deh3- “to give” (LIV 105–106), or from its expanded variant *√deh3u- “to give” (LIV 107). The relationship between OIr. dúan and dúas may thus have been that of a figura etymologica from earliest times (*doh3uneh2 ~ *doh3usteh2), or, if they derive from two different roots, it is easy to see that such a connection could have arisen by folk etymology within Old Irish, as soon as the two words were phonetically similar enough. This explanation of dúan from *doh3uno- has some pretty complex implications for the phonological history of Celtic, but I cannot go into this here.
(3) The third etymology, apparently the oldest one going back to Thurneysen in the 19th century, connects dúan via the reconstruction *dʰ(e)ugʰneh2 with the PIE root *√dʰeu̯gʰ- “to happen, succeed, achieve” (LIV 148–149), cf. Gr. τεύχειν “to make” which in Greek poetical diction can refer to the “making of poems” (Delamarre, Dictionnaire de la Langue Gauloise 146; West, IE Poetry and Myth 35). This explanation opens up an interesting perspective because it allows to connect dúan with the Gaul. verb dugiíontiío in the inscription from Alise-Sainte-Reine (L-15). This sole attestation of the verb is isolated in Celtic, so its exact meaning is unknown. However, it has long been believed to belong to the root *dʰeu̯gʰ- (for instance, see my own contribution to this on p. 166 of https://www.academia.edu/…/The_textual_arrangement_of_Alise…), and within the context of the inscription it makes most sense to read it as something like “(they) who worship”. If the root thus had acquired the meaning “to worship, to praise, to make a praise poem” in Proto-Celtic, both the Gaul. verb dugiíontiío and OIr. dúan as a resultative noun “praise, praise poem” can be brought under one semantic umbrella.
This word is part of a long study of the treatment of clusters of labial sounds + n in Celtic that I have been writing for almost four years now and hope to finish in the near future. The possible etymologies of dúan are also mentioned in my forthcoming article on “Metrical Systems of Celtic Traditions” (https://www.academia.edu/…/Metrical_Systems_of_Celtic_Tradi…).
DS [originally posted on Facebook 7.1.2016]