"Faoi" is pronounced [fwi] (fwee)

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

It should be, yes, but I'm adamant about the "fwai" (yes I'm too lazy to do IPA now). I heard it in a song by the Cór Thaobh a' Léithid too, so maybe it's some sort of over-enunciation?

Maybe the following word begins with a y-sound? Do you know what song it is, what verse, or maybe there's a video on Youtube? I know Cór Taobh a' Leithid has a few videos on Youtube
Go rabh maith agad

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

It's a classic - Tá mé 'mo shuí.

If you refer to the verse
"Do shúil ghorm ghlé faoi thréig mé aiteas is suairc", actually in the version I know (Altan's) they write "...fár thréig mé aiteas..." which looks more normal - as far as grammar is concerned.
Btw I don't think they pronounced fár as fʷai, it's just that they say fár thréig, and the sound of slender th here (at the beginning of a word before r) is like a slender ch... [fʷa(ɾ) çɾʲeːgʲ]
)

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

Sandhi!