In Nuer, a Western Nilotic language, a productive process of vowel mutation lowers certain vowels in the plural forms of reduplicated adjectives, while others remain unaltered. Sometimes, lowering is accompanied by diphthongization. This short paper asks what determines which vowels should lower, which should also undergo diphthongization and which should remain unaltered. The phenomenon is analyzed within Element Theory in which vocalic expressions are decomposed into a head element and a dependent element. A pre-specified, Semitic-type template is proposed alongside a constraint on Head Preservation. These two tools derive the entire set of attested and unattested mutations. It is then shown that the analysis can pave the way for a better understanding of other, similar vowel mutation processes in Nuer.
Nuer, a Western Nilotic language, is a monosyllabic language. Many morphological operations are construed as to not violate monosyllabicity. As a result, it is extremely non-concatenative. For instance, Frank (1999), and subsequently Baerman (2012), count more than 20 singular-plural patterns that do not violate monosyllabicity. Here are eight examples:
There seems to be little regularity in the operations attested. Still, it is interesting to note that not just any change is possible. For instance, bases with [a] do not diphthongize; bases with [i], when they lower, do not lower to [a]; etc. At least in the realm of vowel mutation, not everything is possible.
This short paper discusses a morphological operation involving one type of vowel mutation which I encountered in my elicitations, namely lowering. The output of this operation, unlike the complex singular-plural relations in (1), is both productive and (almost) perfectly predictable. The phenomenon is not included in the two previous grammatical descriptions of the language, namely Crazzolara (1933) and the pedagogical grammar by Eleanor Vandevort, published online by Marion Frank Wilson in 2003.
The operation under discussion concerns intensified, non-predicative adjectives. Such non-predicative adjectives always appear with a relativizer [mi] or [ti] in the singular and plural respectively (2a). Yet the relative clause can become predicative in the cleft-like construction in (2b). Such sentences can be literally translated as ‘It is the cow that is a/the strong one’; still, the main consultant of this work insisted that (2b) is not different in meaning from a regular predicative ‘the cow is strong’.
Number appears in the construction in (2b) on the main verb and on the relativizer. In addition, for numerous adjectives there is an “intensified” version of (2b), in which this distinction is obligatorily made on the adjective, too. In this case, the adjectival stem is reduplicated, and the plural stem further undergoes regular vowel mutation. This construction, shown in (3), is at the center of this paper. Its meaning can be paraphrased as ‘the cow is a really/very strong one’.
The sound change in the adjectival stem is regular in the sense that given the singular or basic form, it is almost always clear what the plural form will be. Three changes in the stem are apparent in (3): 1) diphthongization ([u] vs. [uɔ̤]); 2) lowering [u] vs. [ɔ̤], and 3) length, i. e. the short [u,u] vs. [uɔ̤, uɔ̤ɔ̤]. I have found that the occurrence of diphthongization and lowering is dependent on the vowel of the basic stem, while length is shared by all reduplicated plurals. 77 examples of such reduplication have been collected; (4) summarizes and classifies the behavior attested among them (breathiness is irrelevant for the phenomenon under discussion and will therefore not be marked in the ensuing analysis):
In some reduplicated plurals, for instance (4c-e), one finds imperfect reduplication in both quality and length. This paper abstracts away from this problem, assuming it has to do with the cross-linguistically well-established shortening and reduction in non-final closed syllables (Maddieson 1985). The vowels [ə,ɛ,a] seem to be non-contrastive in this position, which is in fact extremely rare in a monosyllabic language like Nuer. Importantly, my main consultant insisted that he pronounces the same vowel in both copies (and did so indeed, when pronouncing it unnaturally slowly). 
As can be seen in (4), while all vowels lengthen, not all vowels diphthongize, and not all vowels mutate. Still, all vowel changes involve lowering, the result of which is predictable. Accordingly, the questions to ask are:
In this paper, I will provide an analysis of the regularities in (4) that answers the questions in (5). The paper is structured as follows. The next section provides preliminaries on Nuer vowels and their analysis in Element Theory (Kaye et al. 1985; Backley 2011). Section 3 contains the analysis. A fixed template is proposed for the plural stem which has an optional position that may host a glide. The output of the lowering is shown to depend on a principle of Head Preservation: if the head of the basic vocalic expression can be preserved in the glide position, it may lose its status in the output main vowel. Section 4 discusses further applications of the proposed analysis and concludes.
2 The Nuer vowel system and element theory
I have found that the Nuer vowel system consists of at least the basic vowel phonemes in (6), with the status of the rare [æ] remaining unclear (this issue is tangential to the main topic of this paper). This description is almost entirely consistent with Yigezu’s (1995) description.
All vowels have breathy and non-breathy versions, except for [u,ə] which are always breathy. As a result, breathy voice is not marked on these two vowels except in narrow phonetic transcription. In the prototypical C_C# position, all vowels may be short or long. /i̤,u,o̤/ may be realized as [ɪ̤,ʊ̤,ɵ̤].
Nuer diphthongs are all falling diphthongs. Accordingly, in the present paper, the first of two distinct and consecutive vowel symbols is always a glide. As for rising diphthongs, although [Vy] and [Vw] sequences are attested, they are never followed by a consonant, suggesting that the offglide occupies a consonantal position.  Three onglides are attested: [i], [u] and (interestingly) [ɔ]. All falling diphthong with these onglides are attested (and in order to remain a falling diphthong, /ui/ is pronounced [ɥi]). As for breathiness, it seems that the onglide and the vowel of the diphthong must agree in this respect, and thus /u/ often becomes non-breathy by harmony. As we will see below, the range of possible diphthongs is relevant for the discussion of the lowering mutation.
Element Theory (Kaye et al. 1985; Backley 2011) proposes that universally, there is a limited set of basic units of sound. The combinations of these yield the attested systems with their varying phonetic complexity. Additional fine-tuning is achieved by assuming that in a complex expression, the relation between two elements may be a-symmetrical, one element being the “head” and the other the “operator”.
The vocalic elements in Element Theory are |A, I, U|. A formalization of the basic Nuer vowels within this framework is presented in (8). The basic vowels [i,u,a] are not complex expressions. The low, half-front vowel is distinguished from the back vowel in that both have the element |A|, but whereas it is the head of [a], in [ə] it is an operator (the expression is unheaded). High and low mid vowels are also distinguished through headedness: they are all complex expressions, but the elements |I, U| are heads in the higher vowels, and operators in the lower ones (head status is marked by an underscore).
After this preliminary formalization, we may return to the lowering phenomenon.
The diagram in (9) portrays the various lowering pathways that appeared in the chart in (8) above (ignoring the issue of gliding). One can see that all outputs have the element |A|. Furthermore, the role of headedness in the process is emphasized: the targets of change – when change occurs – are all headed by |A|.
Further evidence for the centrality of the concept of headedness can be found in (10), which now takes into account the glide. One can see in (10) that whenever the head of the basic vowel is not the head of the output vowel (10a,b), the former persists as a glide. In the two unaltered vowels (10f,g), the head of the base vowel is preserved.
To summarize, three generalizations emerge from the application of Element Theory to the data: 1) all outputs have A; 2) changing vowels are headed by A; and 3) all heads are preserved.
Besides the presence of |A|, another aspect of the plural form that is stable is length. I conclude that these two characteristics must be hard-wired into the form of any plural. I propose to formulate these facts by devising a plural “template” of the type common in Semitic languages (See e. g. Bat-El 2011; Lowenstamm 2003). The proposed template is presented in (11): is has an optional consonantal position after the first consonant and two main vocalic positions, pre-linked to a headed element |A|. Note that there is no need to restrict the optional position to glides, since there are never any initial consonant clusters in Nuer; only glides can occupy a non-syllabic, post-consonantal C-position. Again, I assume without discussion that the shorter length of the first syllable of reduplicated plurals (e. g. [buɔmbuɔɔm]) is the result of the first syllable being closed and word-medial.
The third generalization above is covered by a principle of head preservation:
We will now see that the template and principle in (11–12) motivate all and only the attested changes in the system.
3.2 Changing bases
Consider how a base with a high vowel like [gul] ‘round’ satisfies the proposed template in (13) below. The high vowel is linked to the glide position, because it can. It also spreads to the next position. This results in a headedness conflict in this position: the lexical vowel is headed by |U|, and the templatic position is linked to |A|. Because |U| has already been preserved in the glide position, it loses to |A|, yielding [ɔ] (i. e. |U,A|). This explanation also applies to bases containing the high vowel [i] as in (14).
The third vowel which was preservable as a glide was [ɔ]. Its satisfaction of the template is as in (15). There is no headedness conflict in the nucleus position because the head of [ɔ] is already |A|. In this representation we see a second principle that is important in (15): the non-head is not carried over to the nucleus position:
In bases with the parallel front [ɛ], the lack of diphthongization follows from the simple impossibility of [ɛ] to occupy the glide position. There is no principle of non-head preservation, and as we just saw non-heads are not carried over to the nucleus position. The non-preservation of the |I| element in [ɛ] is immediately explained.
In (16) above, the (C) position first appears as optional. Bases with [ə] confirm this optionality: [ə] cannot be a glide, the non-head does not carry over to the nucleus position. The vowel [a] is correctly predicted to surface:
We have thus far covered all of the changing bases. The non-changing bases require no additional machinery, a fact that provides further support for the proposed analysis. Bases with [a] are not expected to lower (there is no headedness conflict) or diphthongize ([a] cannot be an onglide):
The remaining two vowels are [o] | U,A | and [e] | I,A |. Both may not be onglides and are headed by an element other than |A|. The head spreads to the nucleus position and a headedness conflict is created. Here Head Preservation becomes important: in this case, because the basic head cannot be preserved as a glide, it wins out over |A| in the nucleus position, yielding the high mid vowels [o] (19) and [e] (20). The impression that one has is that the vowel is unchanged, although under the present view, the non-head |A| originates in the template, rather than in the base.
Finally, to validate the hypothesis that non-heads are not carried over to the nucleus position, consider the case of bases with a diphthong, such as singular [ɲuɛnɲuɛn] and plural [ɲuanɲuaan] ‘lazy, smelly’. In such cases, the glide of the base occupies the glide position in the plural template, and the vowel [ɛ] behaves just like a normal base vowel, contributing only its head to the plural’s nucleus.
The prediction is made that bases with onglides and high mid vowels would not change: this is confirmed by items such pairs as singular [nied̪nied̪] and plural [nied̪nieed̪] ‘rude’.
To summarize, the data are economically and elegantly accounted for by the proposed fixed template and the rule of Head Preservation. This combination determines which vowels should change and/or diphthogize, and what the output of template satisfaction might be. Our three questions above are fully answered.
4 Conclusion and discussion
The analysis in terms of Elements, Head Preservation and headedness conflict accounted for all and only the attested changes, as well as for cases where there was no change. This unifying analysis was made possible by the use of Element Theory. It may be asked whether a theory based on features can achieve the same elegance for such a multiply-targeted process. One serious attempt is found in the awe-inspiring paper by Andersen (1993), which treats analogous data from the closely-related language Dinka. Anderson’s system has three predetermined vowel “grades”, which state what vowel will be mutated into what other vowel. Although the data in Andersen’s paper are much more complex than those presented here, and the account therein is much wider in scope, the way that the grades are derived in the present paper is doubtlessly much simpler than the feature-based rules proposed by Andersen. For the present data, a competing, feature-based account is not available, and this is not the place to develop one; it is nevertheless my contention that when devising such an account, one would be hard-pressed to find equivalents of headedness and Head Preservation. And while some sort of faithfulness to certain values on certain features can be assumed, this would be a lot more ad-hoc than the headedness notion, which is independently motivated by the organization of the vocalic system into four heights and by cross-linguistic generalizations and analyses (as explained in Backley 2011).
As for scope, this paper concentrated on mutation in reduplicated adjectives, where the changes are predictable. It is nevertheless noteworthy that the vowel-mutation operation analyzed here is not specific to this construction; it is rather general in the language, as both Vandevort (n.d.) and Crazzolara (1933) remark. One place where they are found very frequently (though less regularly) is in verbal inflection, in the distinction between the 1sg stem and other suffixed stems. Note that in this case the lowering is independent of length:
Much additional work is required in order to account for the possible changes in the verbal system, but the present analysis certainly seems promising in this respect.
Another issue that can be better understood with the use of the general lowering process described here is singular-plural pairs. Reconsider the pairs that appeared at the beginning of the paper, repeated in (23). As Storch (2005) discusses in detail for several Western Nilotic languages, the basic stem is not necessarily the singular, especially in [-count] nouns such as ‘food’ and arguably ‘erection’, or nouns which frequently appear in the plural. If one accepts that in some cases the plural is basic, as the arrows in (23) show, one may collapse four of Frank’s classes into a single one which utilizes the lowering process we have formalized in this paper.
There is still much irregularity and unpredictability in the nominal system. Yet it is encouraging to find that when vowel mutation is involved, it is much more often than not the same set of vowel mutations that one finds in reduplicated adjectives. 
To conclude, in this paper, the process of vowel mutation in Nuer was shown to follow a principle of head-preservation: if the head of the expression is preserved as a glide, it survives as a non-head in the nucleus position; and if the head of the expression is not preserved in the glide position (because only [i,u,ɔ] are possible glides in Nuer), it will head the nucleus position. Original non-heads are disregarded in the derived form. As was shown in this concluding section, the regularity extends well beyond the restricted domain that was at the center of this present paper, and seems promising for further research.
I would like to thank my main Nuer consultant, Taidor Lam, for accepting to work with me on his language. I also thank my colleagues at the Hebrew University of Jerusalem for their support of my small project, in particular Eitan Grossman and Nora Boneh. All errors are mine.
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