There are several criteria we must consider when reconstructing the various sounds that may have been indicated by these digraphs. The first and most important of these is the comparison of Gothic with other Old Germanic languages. This criterion takes examples of words with the au or ai digraph and compares them to their cognates in other Old Germanic languages, as well as to the reconstructed Proto-Germanic form. Where we find a consistent type of sound across several forms, and in the reconstructed form, it is reasonable to assume the same type of sound is at work in Gothic.
Comparison of Gothic baíran “to bear” to cognates in other Old Germanic languages shows a short vowel: see OHG beran, ON bera. Similarly, daúhtar “daughter” is cognate with OHG tohter and OE dohtor, suggesting the au in this word represents a short vowel. Applying this same principle of comparison to other words suggests that under certain conditions these digraphs are used to represent a diphthong, under others a long monophthong. (Robinson 64)
Another criterion which is helpful for determining the value of these digraphs is the Gothic spelling of Biblical names. For instance, ai is used both to render Greek ɛ in the name Aíleisabaíþ “Elizabeth”, and the long Greek monophthong αι in the second syllable of Haíbraius “Hebrew” (Robinson 65). By carefully considering the list of attested forms, their cognates in other Old Germanic languages, and their use in rendering the spelling of Greek names, we can derive the following rules (Wright 1910):
aí appears only before r, h, and ƕ
ai appears only before a following vowel
aú appears only before r and h
au appears only before a following vowel
This theory has recently been challenged: if these sounds were uniformly distinct, why would Wulfila, whose orthography is otherwise very precise, not have represented them using individual symbols? This objection posits a two-way distinction: a short vowel (ai as [e] and au as [o]) before consonants, and a longer vowel (ai as [e:] and au as [o:]) before vowels. But whether a three-way distinction existed in Wulfila’s time, Robinson maintains it is useful for the modern study of Gothic, since the suggested vowels aí ái and ai each derive from different sources in the proto-language. (Robinson 67)
Robinson, Orrin W. Old English and its Closest Relatives: A Survey of the Earliest Germanic Languages. Stanford, CA, Stanford Univ. Pr., 2003.
Wright, Joseph. Grammar of the Gothic Language. Oxford, Clarendon Press, 1910.
 Wright notes the possible exceptions of aíþþáu, waíla, and the reduplicated syllable of pret. strong verbs belonging to Class VII.
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