ONlwSG

aoidh 

Formerly (and occasionally still) spelt uidh, ùidh, aoi.

f. [əi], 

Cf. [oo-ee] (MacBain 1895, 225), (Lewis) [u̇i] [øi] (Borgstrøm 1940, 39), [ui], [əi] (Oftedal 1954, 394). AFB^˄ (s.v. aoidh) unaccountably gives /ɤj/.

gen. aoidhe [ˈəijə], ‘isthmus; ford’ is generally derived from ON eið nt. ‘isthmus’.

MacBain (1895: uidh; 1896: ùidh; 1911: idem); Henderson (1910, 138: ùidh, aoi); Christiansen (1938, 5, 24: aoidh); de Vries (1962: ‘hebrid[isch] aoidh’); MacLennan (1925: ùidh); Oftedal (1954, 394: aoidh; 1980, 172); Stewart (2004, 416: ùidh).

However, the Old Norse diphthong ei would formally yield SG [eː], and ON eið would be expected to yield SG [ei] after vocalisation of the fricative in Gaelic. ON eið was earlier CSc. *aið, before raising of the diphthong, which evidently fell together with EG aí, oí (cf. SG aoigh [ɯi], [əi] ‘guest’ < EG oíġi, oíġe, aíġe), hence SG aoidh.

Cox (1991, 492; 2002a, 169; 2007a, 140–41; 2022, 555–56)). McDonald (2009, 352) cites ON eið, *aið, without further explanation.