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The underlying representation of nasalized vowels: derived forms
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In this topic it is shown that nasalized vowels in morphologically complex forms, like (do) rinst/rɪn+st/[rɪ̃st](you) walk should be analyzed as deriving from the sequence oral vowel + /n/.

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The nasality of a vowel is a function of the nasal consonant by which it is followed, which is expressed by the vowel nasalization scheme). According to this scheme, a nasal vowel derives from the sequence oral vowel + /n/. This is an unproblematic assumption as to forms like those in (1):

Example 1

cf.
Transparent cases of nasalization with the verb stem rin /rɪn/, the adjectives brún /bryn/ and fyn /fin/, and the prefix ûn- /un/
(do) rinst /rɪn+st/ [rɪ̃st] (you) walk
(wat) brúns /bryn+s/ [brỹs] (something) brown
(it) fynst /fin+st/ [fĩst] finest; most subtle
ûnsin /un#sɪn/ [ũsɪn] nonsense
(ik) rin /rɪn+∅/ [rɪn] (I) walk
(hy) rint /rɪn+t/ [rɪnt] (he) walks
brún /bryn/ [bryn] brown' (base form)
bruner /bryn+ər/ [brynər] browner
fyn /fin/ [fin] fine; subtle (base form)
fine /fin+ə/ [finə] fine; subtle (inflected form)
ûnaardich /un#a:dəɣ/ [una:dəx] unpleasant

The upperfour forms are realized with a nasal vowel, the bottomseven with the sequence oral vowel + [n]. The verb stem rin/rɪn/, the adjectives brún/bryn/ and fyn/fin/, and the prefix ûn-/un/ all end in /n/, which in most instances surfaces as such. Inflected forms, derived forms and/or compounds show an alternation between forms with the sequence nasal vowel + continuant consonant on the one and oral vowel + [n] on the other hand. The sequence oral vowel + [n] may precede a vowel or a consonant, provided that the latter is not a continuant. The nasal vowel and the sequence oral vowel + [n], thus, have a complementary distribution. This is a strong indication that both derive from one underlying representation, viz. oral vowel + /n/.

References:
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