11.2.1 Harmony

Finite-state models of phonology have also been applied to more sophisticated phonological and morphological phenomena. Let's consider a finite-state model of a well-

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Figure 11.3 The transducer for the ix-insertion rule 11.2. The rule can be read whenever a morpheme ends in a sibilant, and the following morpheme is word-final z, insert [ix].

Figure 11.4 The transducer for the z-devoicing rule 11.3. This rule might be summarized by Devoice the morpheme z if it follows a morpheme-final voiceless consonant.

known complex interaction of three phonological rules in the Yawelmani dialect of Yokuts, a Native American language spoken in California. $ ^{4} $

First, Yokuts (like many other languages including for example Turkish and Hungarian) has vowel harmony. Vowel harmony is a process in which a vowel changes its form to look like a neighboring vowel. In Yokuts, a suffix vowel changes its form to agree in backness and roundness with the preceding stem vowel. That is, a front vowel like /i/ will appear as a back vowel [u] if the stem vowel is /u/. This Harmony rule applies if the suffix and stem vowels are of the same height (e.g., /u/ and /i/ both high, /o/ and /a/ both low): $ ^{5} $

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Figure 11.5 The transducer for the ix-insertion rule 11.2 and the z-devoicing rule 11.3 run in parallel.

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The second relevant rule, Lowering, causes long high vowels to become low; /u:/ becomes [o:] and /i:/ becomes [e:], while the third rule, Shortening, shortens long vowels in closed syllables:

Lowering				Shortening
?u:t'+it	→	?ot'ut	“steal, passive aorist”	s:ap+hin	→ saphin
mi:k'+it	→	mek'+it	“swallow, passive aorist”	sudu:k+hin	→ sudokhun

The three Yokuts rules must be ordered, just as the ix-insertion and z-devoicing rules had to be ordered. Harmony must be ordered before Lowering because the /u:/ in the lexical form /?u:t'+it/ causes the /i/ to become [u] before it lowers in the surface form [?ot:t'ut]. Lowering must be ordered before Shortening because the /u:/ in /suduk+hin/ lowers to [o]; if it was ordered after shortening it would appear on the surface as [u].

The Yokuts data can be modeled either as a cascade of three rules in series, or in the two-level formalism as three rules in parallel; Fig. 11.6 shows the two architectures (Goldsmith, 1993; Lakoff, 1993; Karttunen, 1998). Just as in the two-level examples presented earlier, the rules work by referring sometimes to the lexical context, sometimes to the surface context; writing the rules is left as Exercise 11.4 for the reader.