Sibilant harmony in Nkore-Kiga is an interesting problem case for agreement-based theories of harmony, particularly Agreement by Correspondence. Previous work reports that anteriority agreement is controlled by the rightmost sibilant in the stem, and also that the quality of a sibilant is allophonically determined by the following vowel. In such a system, it is impossible for surface-oriented agreement constraints to derive strictly right-to-left harmony. However, we show that Nkore-Kiga does not work in quite this way: sibilants are conditioned not allophonically, but by morphology. This allows the facts of this case to be explained within existing Agreement by Correspondence proposals.
The purpose of this article is to discuss a problem related to directionality in agreement-based theories of consonant harmony, and to propose a simple solution: the problem does not actually arise in the known case that motivates it. The case in question is Nkore-Kiga, a Bantu language spoken primarily in Uganda. The problem at hand is a clash between allophonic conditioning of anteriority in sibilants and right-to-left anteriority harmony among those sibilants.
Previous work on Nkore-Kiga reports three generalizations:
Anteriority in sibilants is normally allophonic, conditioned by the following vowel.
[s z] before [i]
[ʃ ʒ] elsewhere
Sibilants deviate from the normal allophonic pattern due to harmony within the stem.
Harmony operates strictly right to left: the rightmost sibilant in the stem is conditioned in the normal way, and other, preceding, sibilants assimilate to match it.
These three generalizations, taken together, yield a pattern of consonant harmony that defies explanation in any theory where assimilation is driven by a need to have agreement or to avoid disagreement (Smolensky 1993, Baković 2000, Pulleyblank 2002), including the framework of Agreement by Correspondence (ABC; Hansson 2001, Rose and Walker 2004). The gist of the problem is that surface agreement can be obtained between two segments by changing either segment to match the other. The generalization that harmony operates from right to left, (1c), cannot be stated in terms of agreement; a simple AGREE constraint cannot choose between /ʃ . . . s/ → [ʃ . . . ʃ] and /ʃ . . . s/ → [s . . . s]. An intuitive way around this issue is to call on positional faithfulness: if some constraint protects one harmonizing segment, it provides an impetus to change the other segment to match. But this approach seems not to work for Nkore-Kiga, where the segment controlling harmony is determined by allophony and is not uniformly faithful.
In section 2, we present the puzzle in more detail and show how the pattern described in previous work cannot be derived with straightforward agreement-based harmony constraints—even when directionality is hardwired into the constraint definitions (as in, for example, Walker 2001 or Hansson 2001). In section 3, we consider the Nkore-Kiga data in closer detail, showing that the range of data that actually evidences the problem is at best scant. The solution we suggest is that the problem doesn’t actually arise. We find that the observed facts can be explained in a straightforward way by appealing to morphology, without building extra stipulations about the direction of assimilation into the theory of consonant harmony.
2 Nkore-Kiga Background and the Problem
Nkore-Kiga is a family of closely related dialects spoken primarily in Uganda, classified as E.13–14, in the Inter-Lacustrine group, within the Bantu language family. We follow Taylor’s (1985) convention of referring to Runyankore and Rukiga together as Nkore-Kiga. The generalizations and data reported in previous work on the sibilant harmony pattern (Hansson 2001, Hyman 2003) are generally not attributed more specifically within this group.
Previous work (Hansson 2001, Hyman 2003) reports that the anteriority of sibilants is conditioned by the following vowel, in a fashion that seems to reverse expected “naturalness”: [+anterior] sibilants [s z] occur before [i], while their [−anterior] counterparts [ʃ ʒ] occur before all other vowels (sibilants may not occur before consonants other than [w] and [j], which behave like the high vowels).2 The pattern is schematized in (3), and the examples in (4) are representative of this situation.
This allophonic pattern can receive a straightforward analysis with just simple markedness constraints *ʃi and *s, defined as in (5).3 If both these constraints dominate IDENT-[anterior], the result is that any underlying anteriority specification in a sibilant will always be overruled if inconsistent with the distributional pattern. The anteriority of a sibilant will be determined by defaulting to [s] before [i], and to [ʃ] elsewhere. This is shown in (6), where the worst possible input form is assumed—but note that any input would result in the same surface form.
(5) Basic constraint definitions
*ʃi: “No [ʃi] or [ʒi] sequences”
Dfn.: Assign one violation for each [−anterior] sibilant followed by [i] in the output.
*s: “No [s] or [z]”
Dfn.: Assign one violation for each [+anterior] sibilant in the output.
This type of allophony is rather odd crosslinguistically since [ʃ] is being prohibited in what is generally considered the absolute best context for a [ʃ], but the analysis of the case is straightforward. We turn now to the facts of harmony.
Sibilant harmony is reported in Nkore-Kiga within the stem, a domain consisting of the root and suffixes, to the exclusion of prefixes. Harmony is reported to hold among [s z ʃ ʒ]; affricates [ʦ ʧ] are not reported to participate (nor is surface [ʤ] derived from /ɡ/ before front vocoids). Given the allophonic distribution of the sibilants, however, two cases must be distinguished. In the first, (7), the two sibilants agree but this is consistent with both the allophonic requirements and any harmonic requirement.
In the examples in (8), however, the requirements of allophony and harmony conflict. In such cases, harmony overrides allophonic expectations.
On the basis of the normal sibilant allophony patterns, we would expect forms like *-siʃa and *-ʃaasire, rather than the observed forms -ʃíʃà and -sààsìrè. This effect is the evidence for sibilant harmony: sibilants deviate from the normal allophonic pattern in order to achieve anteriority agreement in the stem.4
As noted previously by Hansson (2001), the harmony in these examples is crucially controlled by the sibilant on the right. That is, the rightmost sibilant follows the expected C-V distributional pattern; the preceding sibilants deviate from the expected allophony in order to agree with it.
The generalization implied here is a pattern of strictly directional harmony. The rightmost sibilant is always the one that controls the result of agreement, irrespective of its quality. The [±anterior] value of the sibilant does not determine the direction of agreement.
The combination of allophonic conditioning and strict directionality makes such a pattern problematic for theories of consonant harmony framed in Optimality Theory, particularly ABC. To illustrate, we take the allophony to be handled by the constraints *ʃi and *s, as above, and we take the harmony constraints to be CORR·[+sibilant]5 and CC·IDENT-[anterior], defined in (9).
(9) Basic constraint definitions
CORR·[+sibilant]: “Sibilants correspond with each other”
Dfn.: For each distinct pair of output consonants X and Y, assign a violation if
X and Y are both [+sibilant] fricatives, and
X and Y are not in surface correspondence with each other.
CC·IDENT-[anterior]: “Correspondents agree for anteriority”
Dfn.: For each distinct pair of output consonants X and Y, assign a violation if
X and Y are in surface correspondence with each other, and
X is [+anterior], and
Y is [−anterior].
In order for harmony to force sibilants to deviate from the usual allophonic pattern, the constraints responsible for allophony must be dominated by the constraints that drive harmony. But, in order for the sibilant constraints to produce an allophonic pattern, they must both dominate faithfulness for anteriority, IDENT-[anterior], and they must be crucially ranked relative to one another.
The problem is that this ranking does not produce strictly directional harmony. The harmony constraints are satisfied by any sequence of corresponding and agreeing sibilants: they have no preference between [ʃ . . . ʃ] and [s . . . s] candidates. Each of the allophony constraints does have a preference between these forms, though. If the choice between these options gets passed down to the allophony constraints, the result will be a value-dominant harmony pattern (of the sort well-known from previous work on vowel harmony (e.g., Baković 2000), and also on consonant harmony (Hansson 2001), in which harmony always spreads one, dominant, value of a feature at the expense of the other value).
The tableaux in (10) and (11) illustrate the problem. Assuming for illustration that *ʃi dominates *s, the choice between different harmonized candidates will be made on the basis of which one yields fewer [ʃi] sequences—a pattern where [+anterior] is the dominant value. This means harmony will operate from right to left in forms that end in /. . . si/, as in (10). But, in forms that end in another vowel, harmony can operate from left to right, as in (11). If *ʃi is what makes the decision, then the directionality of harmony will not be consistent: the direction of assimilation will change to suit the preferred form of agreement. The result is harmony that systematically favors [+anterior] or [−anterior], rather than favoring assimilation in one particular direction. (The candidate in (11a) is the winner favored by the ranking; the candidate in (11b) is the expected form given the descriptions of the pattern, indicated with a frowning face because it loses. In both tableaux, (non)correspondence is indicated by (mis)matching subscript indices.)
The essence of the problem here is not unique to an ABC approach. It arises from the generalizations that (a) anteriority of a sibilant must be determined on the basis of a vowel, and that (b) this allophonic interaction must be overruled to attain sibilant harmony. The ranking contradiction arrived at in the ABC analysis above recurs in other theories in some form or another.
Consider an alternative account in Harmonic Serialism, along the lines of McCarthy 2011 and Kimper 2011, where harmony is driven by SPREAD constraints that want the autosegments linked to one segment to be linked to its neighboring segments as well. This spreading constraint must dominate the constraints responsible for the vowel-based allophony in order for harmony to override the allophony in mappings like /siʃa/ → [ʃiʃa]. But this ranking would also block allophony for the rightmost sibilant. A derivation like /sisa/ → siʃa → [ʃiʃa] is therefore problematic, because the crucial first step of inserting the unspread feature on the rightmost sibilant creates a new violation of the SPREAD constraint.6
We know of no straightforward way to ensure uniformly right-to-left harmony in cases like (10) and (11) without radical adjustments to all of the constraints involved. Even if we assume that surface correspondence is a nonsymmetric relation (as in Walker 2000b, Hansson 2001; cf. Walker 2000a, Rose and Walker 2004, Bennett 2015), which allows for CC·IDENT constraints to be direction-specific, we still do not get the right result. Consider a CRCL [IDENT constraint as in (12) that favors agreement only asymmetrically.
(12) CRCL [IDENT-[+anterior]: “Preceding correspondents agree for anteriority”
Dfn.: For each distinct pair of output consonants X and Y, assign a violation if
Y is a correspondent of X, and
Y precedes X, and
X is [+anterior], and
Y is [−anterior].
This constraint differs from the simpler, symmetric, CC·IDENT in (9) in that it penalizes disagreement in one direction ([ʃ . . . s]), while permitting sequences in the other order ([s . . . ʃ]). However, even building this directional asymmetry into the constraint does not have the desired consequences for directionality in assimilation. Forbidden [ʃ . . . s] sequences can be repaired to either [s . . . s] or [ʃ . . . ʃ], both of which satisfy the constraint because both have full agreement. Output-oriented agreement constraints like CC·IDENT cannot control how agreement is achieved; they can only restrict where it is necessary. The choice between [s . . . s] and [ʃ . . . ʃ] is fundamentally a question of what faithfulness constraints are violated. The difference is faithfulness, not markedness: both achieve agreement, but one does so by being unfaithful for [+anterior], while the other does so by being unfaithful for [−anterior].7
Leaving the choice of how to resolve agreement to general markedness constraints results in a value-dominant pattern. If the decision between [ʃ . . . ʃ] and [s . . . s] candidate types is passed down from the agreement constraints to general markedness constraints like *ʃi and *s, then harmony will favor whichever harmonized option is a better fit for the general allophony pattern.
Letting faithfulness constraints make the determination between the agreeing candidates also does not produce strict directionality. Bennett (2015:73ff.) proposes positional faithfulness as a general means of deriving strictly right-to-left harmony. In that proposal, a category of CC·ANCHOR-R-[F] constraints demands featural faithfulness only for the rightmost member of a group of correspondent consonants. These constraints are defined as in (13).8
(13) CC·ANCHOR-R-[anterior]: “Faithfulness to anteriority for a rightmost correspondent”
Dfn.: For each distinct pair of output consonants X and Y, assign a violation if
Y is a correspondent of X, and
Y precedes X, and
there is no other Z that corresponds with X and is preceded by X, and
the [anterior] value of X differs from that of its input correspondent Xˊ.
This constraint can produce value-insensitive directional systems, where agreement happens systematically from right to left, in order to avoid changing the rightmost of the harmonizing consonants. But in the reported Nkore-Kiga pattern, the rightmost sibilant—the one that should be controlling harmony—is determined allophonically: it is not necessarily faithful. If the rightmost sibilant is neutralized, then a faithfulness constraint that protects it will not make it control harmony.
The result, then, is that Nkore-Kiga seems to have harmony that is strictly and arbitrarily right to left. The generalization that the rightmost sibilant controls harmony—irrespective of both its surface quality and its underlying value—cannot be derived in a theory of harmony like ABC, nor any other theory of harmony based on achieving agreement on the surface. So, the Nkore-Kiga case would seem to be a counterexample for this general approach to harmony phenomena.
How can we resolve this problem? One option would be to abandon the ABC theory in favor of a more process-driven approach, where harmony is driven not by a need for agreement, but by some fundamentally different mechanism instead. We suggest, however, that the Nkore-Kiga data does not lead us to that conclusion. The problem isn’t that the theory is necessarily wrong; it’s that the facts of Nkore-Kiga don’t actually support the combination of generalizations that seemed to lead us to the problem.
3 Reevaluating the Data: A Problem That Isn’t
3.1 The Empirical Basis for Allophony
Earlier treatments of the Nkore-Kiga sibilant patterns come from Hansson (2001, 2010) and Hyman (2003), and the original source data comes from a dictionary and grammar by Taylor (1959, 1985). A search of Taylor’s grammar turns up numerous examples that undermine the premise that sibilants in Nkore-Kiga are in allophonic distribution. This evidence comes in several forms. First, a few minimal pairs and an abundance of near-minimal pairs (14) suggest that the distinction between [+anterior] and [−anterior] sibilants is actually contrastive.
(14) Minimal and near-minimal pairs
kw-àʃà ‘strike (of lightning)’
kw-ìzà ‘ease, darken’
kù-ʃììʃà ‘spoil, do wrong, sin’
kù-síìsà ‘ask for meat’
kù-sòòmà ‘do a stamping dance’
kù-ʃòmà ‘read, attend church’
òmù-zìɲgà ‘swarm, beehive’
kù-zêɲgà ‘wander, be dying’
kù-ʒèɲgà ‘become sodden’
(ò)bù-ʃà ‘in vain’
Additionally, the analysis whereby the distribution of [s] and [ʃ] is completely rule-governed predicts that morphemes will alternate under appropriate affixation. This is correct in some instances: for example, -g à ʃ-à ‘useful’ vs. -gàs-ìrè ‘useful (perf.)’. In other cases, however, morphemes are strictly nonalternating, as in (15).
Both Hyman (2003) and Hansson (2010) note that [s] may occur before vowels other than /i/ at least as the result of the so-called “short” causative suffix /-j-/, which may be covert (e.g., surface [-siisa] may come from underlying /-ʃiiʃ-j-a/, with /-j-/ responsible for the stem-final [s]); we consider this possibility in section 3.2. However, it is worth noting here that many of the instances of /s/ and /z/ before vowels other than [i] are not explainable in this way. For example, it is possible—if unintuitive—to posit such a causative suffix with the [s] in (14m) [òrù-sà] ‘permission’ (perhaps then derived from the root /-ʃà/ ‘in vain’?). However, a short causative analysis is not plausible for other forms like [kù-sòòmà] ‘do a stamping dance’, where the unexpected [s] is not root-final. It is also implausible for examples like [èzò] ‘that (cl. 10)’, which is a demonstrative, and for the nonalternating “long” causative suffix /-iis-/, which would then need to be analyzed as a double causative /-iis-j-/ in all instances. Such opaque analyses also do not explain the three-way contrast seen in (14m–o), where [ʃ] and [s] contrast not just with each other, but also with [sj].9
Given these apparent counterexamples to the basic allophonic conditioning pattern, one might wonder how phonotactically robust the sibilant-vowel interaction really is. To assess this, we used the set of stems from Taylor’s (1959) dictionary to calculate observed/expected (O/E) ratios for all combinations of sibilants and vowels, including the strident affricates /ʦ/ and /ʧ/ and the glides [j] and [w]. These values are presented in the table in (16).10 In this table, an O/E ratio of 1.0 indicates that a given sibilant-vowel combination occurs (on the surface) as often as expected on the basis of the frequencies of each sound. Ratios less than 1 indicate that a given combination is underrepresented, and ratios greater than 1 indicate that a combination is overrepresented. Cells where the O/E ratio is 0.5 or less or 1.5 or greater are highlighted. In calculating these values, we omitted surface [ʧ ʤ] derived by palatalization of /k t/ before front vocoids. We also controlled for the skewing effect of sibilant harmony, by excluding any sibilant that agrees with another following sibilant in anteriority (e.g., the [z] in [sazi] is included; the [s] is not). These results paint a picture of the basic phonotactic situation in the language.11
(16) Observed/Expected ratios for sibilant-vowel combinations from Taylor’s (1959) dictionary (excluding sibilant harmony)
Several key trends are evident from this body of data. First, although [s] is reported to occur only before /i/, we can see that it is actually attested before all of the other vowels as well, although there are very few examples before [u w]. The same is true of [z], modulo even fewer occurrences before [u] and a complete gap before [w]. Additionally, [s z] are not meaningfully underrepresented before [a], and there are a fair number of examples before [o e]. The underrepresentation before [u w]—complete for [z], incomplete for [s]—may motivate a constraint against the sequences [su] and [zu], a constraint we will represent as *su. However, the distribution is not otherwise indicative of an allophonic distribution like the one noted earlier: it is apparently not the case that all instances of /sa/ change to [ʃa], leaving [sa] unattested on the surface.
Turning to the nonanterior sibilants, we find that [ʃ] and [ʒ] are underrepresented before [i j] in a manner comparable to the underrepresentation of [s] and [z] before [u]. Again, this points more toward neutralization than toward allophony. That is, in general Nkore-Kiga exhibits a contrast between anterior and nonanterior sibilants. This contrast is neutralized to [s] and [z] before high front vocoids [i j] (*ʃi) and neutralized to [ʃ] and [ʒ] before [u w] (*su). This neutralization has a handful of exceptions. Additional possible restrictions on the distribution of [s] and [z] before other vowels constitute merely a tendency; they do not define gaps in the inventory of the language’s surface sequences. Thus, the analysis of the basic allophony situation as *ʃi ≫ *s ≫ IDENT-[anterior] appears to be incorrect. The more refined picture is one of contrast and neutralization before certain vowels, illustrated in (17).
Interestingly, though the affricates are not reported to participate in sibilant harmony, their basic distribution patterns like the sibilants in terms of following vowels. The [+anterior] affricate [ʦ] is underrepresented before all vowels, but especially so before [a o u w]; this parallels the distribution of [s]. The [−anterior] [ʧ], on the other hand, is underrepresented not just before [i], but also before [a]. Taken together with the sibilant O/E values, this points to a gradient tendency over the lexicon, and not to a pattern of predictable allophony in the phonology of the language.
3.2 Lack of Allophony Changes the Problem
If the sibilants of Nkore-Kiga do not have a genuinely allophonic distribution pattern, it puts a much different slant on the directionality problem. If there is neutralization of /ʃi/ and /si/ to [si], but no change (allophonic or neutralizing) of /sa/ and /ʃa/ to [ʃa], then some cases of agreement can be explained without invoking anything direction-specific about harmony. To see this, consider a hypothetical disharmonic input /saʃi/, appropriate perhaps for examples like-ʃààʃà/-sààsìrè ‘be in pain (perf.)’ (8e). In this case, neutralization of /ʃ/ to [s] before [i] happens to produce agreement. This is shown in (18). The agreement here looks like harmony controlled by the rightmost sibilant, but the control and the harmony are actually both vacuous. The input /saʃi/ is realized as [sasi] simply because the /ʃ/ is neutralized but the /s/ is faithful; the harmony constraints play no crucial role in the decision.
The point here is that a subset of situations where harmony might appear to be strictly directional actually fall out just from having asymmetric neutralization, rather than proper allophony. The same outcome arises in the other direction with inputs like /suʃa/: neutralization due to the *su constraint would cause such an input to surface as [ʃuʃa].12
A further subset of cases can be approached in a similar way, represented by inputs like hypothetical /ʃisa/. Here, neutralization of /ʃi/ to [si] together with faithful retention of /sa/ should result in a disharmonic /ʃ . . . s/ sequence surfacing as [s . . . s], again irrespective of harmony. This is shown in (19).13
So, the lack of allophony means that some kinds of mappings necessitated by the agreement pattern are explained without invoking harmony, and therefore do not support the problem framed above.
We can narrow the scope of the problem further by also considering the effects of a CC·ANCHOR-R constraint (Bennett 2015) for anteriority. As noted above, this is a feature-specific positional faithfulness constraint that assigns violations only for the rightmost member of a set of surface correspondents. In harmonizing forms where the rightmost sibilant is faithful, such a constraint can serve to nail down the rightmost sibilant and prevent it from assimilating or undergoing neutralization—thereby forcing that segment to control harmony. This means that disharmonic inputs like /siʃa/ can be explained without adding further stipulations about directionality into the constraints responsible for harmony. This is shown in (20): CC·ANCHOR-R-[anterior] favors the harmonic candidate that does not change the rightmost sibilant. This is necessarily the candidate where other sibilants change instead—a right-to-left assimilation pattern.
Between the cases where harmony follows automatically from the neutralization of /ʃi/ to [si] (but not in the other direction) and the cases where right-to-left harmony can be derived from faithful preservation of the rightmost sibilant (using CC·ANCHOR-R), the vast majority of potentially relevant inputs are explained. The table in (21) illustrates this. If we consider inputs with two sibilants, for all permutations of [+anterior] and [−anterior] on each, followed either by [i] (the neutralization context) or by [a] (representing a nonneutralizing context), there are 16 possibilities (abstracting away from the voicing distinction between [s ʃ] and [z ʒ]).
What remains, then, in accounting for the Nkore-Kiga pattern, are the forms where (a) the rightmost sibilant is unfaithful, (b) the unfaithful sibilant controls harmony, and (c) harmony forces a sibilant to the left to be unfaithful as well. These conditions are met only for inputs like (21c), where /ʃa . . . ʃi/ surfaces as [sa . . . si], with neutralization of /ʃi/ leading to harmony for another /ʃ/ that should not otherwise neutralize. These are a subset of forms like those in (8), the examples given in previous work as evidence for allophony and harmony.14
We suggest that the correct explanation for these remaining forms lies in the morphology. Evidence that points to /ʃ/ becoming [s] before [i] comes overwhelmingly from combinations of roots with three morphemes: the perfective suffix /-ire/, the agentive nominalizer suffix /-i/, and the “short” causative extension suffix /-j-/. This same collection of morphemes is responsible for a broad array of consonant mutations in various eastern Bantu languages,15 and Nkore-Kiga is no exception here. These suffixes systematically cause various alternations in root-final consonants, including affrication of stops, assibilation of /r/ and /h/, and—importantly—shifting of /ʃ ʒ/ to [s z]. Some examples are given in (22) (from Taylor 1985, Poletto 1998; see also Hyman 2003).
The mutations in (22) have an important consequence for sibilant harmony: in words where the rightmost sibilant is mutated from /ʃ/ to [s], the sibilants are generally not on equal footing. In roots like /-ʃààʃà / ~ [-sààsìrè] ‘be in pain (perf.)’, the rightmost sibilant in the perfective form has its anteriority conditioned by the morphology, whereas the preceding sibilant does not. Consequently, right-to-left harmony in such forms is readily interpretable as the result of the morphologically conditioned sibilant taking priority. This is a straightforward control-type interaction, quite akin to the positional faithfulness interaction seen with CC·ANCHOR, but where the factor that imparts control of harmony onto one sibilant is defined on the basis of morphological changes rather than simply position.
If the consonant mutations are taken to be a crucial part of the realization of this group of suffixes, then we can understand a failure to implement them as violating a constraint on morpheme realization—call it MORPHREAL (in the same spirit as Kurisu’s (2001) REALIZEMORPHEME). In favoring a particular form for the rightmost sibilant, this constraint has the effect of disambiguating between the harmonized candidates and favoring the one where the expected form for the rightmost sibilant determines the result of agreement.
Is there a principled reason why causing mutations on a preceding consonant can be considered an integral part of these particular morphemes? In the case of the short causative /-j-/, the answer seems to be a definite yes. In many cases, the mutations induced by this morpheme are its only exponence. This is illustrated clearly by pairs of related stems like those in (24).
What about the other suffixes that cause mutations? Here, the situation is a bit murkier. However, it is worth noting that the vowels in these suffixes were historically superhigh vowels (Hyman 2003).16 The high vs. superhigh distinction was morphologically significant in Proto-Bantu; so, historically, it would have played a crucial role in morpheme disambiguation (e.g., between the applicative *-id-, which does not cause mutations, and the perfective *-id-e, which does). As the high vs. superhigh distinction was lost in Nkore-Kiga, it is not unreasonable that the spirantization induced by superhigh vowels (but not by regular high vowels) would have become a crucial factor for identifying these morphemes.
Clearly, the exact properties of MORPHREAL need to be defined, and several factors are involved. The selectional requirements of the relevant morphemes are local—affecting strictly the consonant preceding the mutation-inducing suffix. The effects all involve anterior coronal outputs, although the input consonants may belong to several places and manners. The short causative may or may not involve a segmental realization that is independent of the mutation per se. While the treatment of these properties is both important and interesting, it would take us well beyond the needs of this article.17 For directionality, the crucial point here is simply that in the segment of Nkore-Kiga data that manifests the directionality puzzle, there is a demonstrably morphological basis for harmony to operate right to left: the rightmost sibilant in these cases is not allophonically determined; rather, it is set by the morphology.
Nkore-Kiga raises an interesting conundrum for how directionality needs to be handled in the Agreement by Correspondence framework (and in agreement-based theories of harmony more generally), but it raises this problem in some possible world other than the one we inhabit. The facts on the ground show that the right-to-left directionality observed in Nkore-Kiga can be handled as an emergent phenomenon and that it does not provide solid motivation for deviating from a simpler ABC theory where correspondence and agreement constraints are symmetric. Where the rightmost sibilant in a stem is faithful, right-to-left harmony can be derived by positional faithfulness, using a positional faithfulness constraint like CC·ANCHOR-R. Cases where the rightmost sibilant is unfaithful break down into two groups. Those where the neutralization of /ʃ/ to [s] happens to yield anteriority agreement (e.g., /sa . . . ʃi/ → [sa . . . si]) require no further explanation; they display only vacuous harmony. The other cases, where the rightmost sibilant is unfaithful and crucially does control harmony, reduce to a very specific and localized set of morphological effects. As long as the mechanism responsible for stem-final consonant mutations (e.g., MORPHREAL) takes precedence over the factors that bear on the direction of harmony (e.g., CC·ANCHOR-R and *ʃi), the direction of assimilation will respect the morphological conditioning of root-final sibilants. So, when the rightmost sibilant is not faithful, right-to-left harmony still follows, either from the morphology tipping the balance or from the basic phonotactics causing agreement independent of the formal mechanism that drives the harmony.
The broader point at issue here is the role of directionality in the ABC framework. We have tried to show that while the particular case of Nkore-Kiga points to an interesting potential problem for a theory that does not allow parametric control over the direction of assimilation, the problem is not empirically borne out. A theory with symmetric correspondence and nondirectional CC·IDENT constraints (as in Bennett 2015) is compatible with the right-to-left pattern found in Nkore-Kiga. This case intuitively seems like one of the best lines of evidence for building directionality into ABC theory, but it does not hold up as such. We speculate that some other cases of strict directionality in other kinds of harmony might be handled in similar ways, without needing to adjust the core of the theory of harmony.
The story we tell here has two morals. The first is the importance of up-close examination of data. On the surface, Nkore-Kiga appears to have a strictly directional harmony pattern; on closer examination, this is not determinably the case. The second moral is that phonological generalizations may emerge as a conspiracy of multiple factors—in this case, morphology and phonotactics. Accordingly, before we abandon a simple theory of one phenomenon in favor of more complex machinery, we should consider how much of the empirical ground is covered by the simpler theory interacting with other simple theories.
In this appendix, we provide the raw counts used in establishing the observed/expected values reported in (16). As stated above, these counts are based on the set of stems from Taylor’s (1959) dictionary and include all combinations of sibilants and vowels, including affricates and the glides [j] and [w].
(25) Number of raw examples of sibilant-vowel combinations in stems in Taylor’s (1959) dictionary (including affricates derived from velars)
(26) Sibilant-sibilant cooccurrences in stems of Taylor’s (1959) dictionary
1Taylor (1985) notes [ʧ] and [ʤ] as palatalizations of /k ɡ/ before high vowels (ergo Kiga = [ʧiɡa]). He also characterizes [d] as an allophone of /r/ occurring after /n/, and the normal allophone of /b/ as [υ]. Taylor does not give /ʦ/ as a segment in his inventory, nor does Poletto (1998), but it is attested in examples given by both.
2 The characterization of the [−anterior] sibilants as [ʃ ʒ] comes from Taylor (1985) and Poletto (1998). To our knowledge, no articulatory study of these sounds has been done yet. But it is worth noting that similar fricatives in Kinyarwanda have been found to be retroflex (Walker, Byrd, and Mpiranya 2008), in which case the distribution might not seem so phonetically unnatural.
3 These specific definitions of the constraints responsible for allophony are not essential. For example, instead of *ʃi ≫ *s, we could have *sa,se,so,su ≫ *ʃ, and the puzzle arises in the same way. Similarly, feature-based definitions of the relevant constraints would result in the same problem.
4 Agreement does not extend beyond the stem domain, into prefixes: [z-a-iƷa] ‘they (cl. 10) have arrived’ (Taylor 1985:122; tones not given). This bounding parallels sibilant harmony in other Bantu languages, such as Kinyarwanda (Kimenyi 1979, Walker, Byrd, and Mpiranya 2008, Bennett 2015), and can be handled in the same way as in those cases, by imposing appropriate domain specifications on the relevant constraints.
5 For purposes of illustration, we abstract away here from the distinction between fricatives and affricates. This constraint can be taken as shorthand for CORR·[+sibilant, +continuant].
6 Even some process-based theories exhibit a similar indeterminacy. For example, Nevins (2004) analyzes root-internal agreement with a process of checking. In order to explain the Nkore-Kiga pattern with this mechanism, checking needs to hold between the sibilants in a word. But in order to derive the allophony, checking would also need to hold between each sibilant and the immediately following vowel. The choice between [ʃa . . . ʃi] and [sa . . . si] depends on which vowel-sibilant interaction takes precedence over the other—a fact that cannot be stated in terms of the agreement interaction between the sibilants, and a result that cannot be obtained by checking both sibilants and both vowels in the same operation.
8 While the name CC·ANCHOR clearly alludes to the L-ANCHOR constraints of Nelson (2003), the formalization is very different. Nelson’s L-ANCHOR constrains the alignment of bases in reduplication, and her proposal crucially denies the existence of any R-ANCHOR constraint. CC·ANCHOR-R, on the other hand, is a positional faithfulness constraint, in the same form as positional faithfulness constraints proposed by Beckman (1998), Lombardi (1999), and others. The only notable difference is that the position that CC·ANCHOR-R refers to is defined in terms of surface correspondence structure, rather than in terms of prosody or morphology. In this respect, CC·ANCHOR-R is much more reminiscent of input-output faithfulness constraints that hold specifically for the right edge of some domain, proposed by Jurgec (2011). There are also intuitive similarities to alignment constraints in other domain-and spreading-based theories of harmony, including those of Cole and Kisseberth (1994) and McCarthy (2004), though the ABC framework used here does not formally invoke any notion of a span or featural domain.
9 Larry Hyman (pers. comm.) points out that in many of the minimal and near-minimal pairs, verbs with counterallophonic [s] and [z] often have transitive meanings (e.g., [kw-àsà] ‘chop’) and that this is expected if those verbs were historically causative, even if not obviously interpretable as such on the basis of the synchronic forms and Taylor’s glosses. Additionally, he notes that the long vowel in [kù-sòòmà] ‘do a stamping dance’ is likely a reflex of a historical *io sequence, so counterallophonic sibilants in long vowel contexts do have a historical basis. Our aim here is not to seek out possible flaws in the previous characterization of the Nkore-Kiga pattern, which is highly insightful. We only want to point out that straightforward allophony does not seem to explain the observed synchronic pattern, and this has crucial implications for the analysis of the harmony system. It would be extremely interesting to establish what exactly the properties of directionality were at a stage where the Nkore-Kiga sibilant distribution was transparent, but we do not take this up here.
10 Observed values here are observed in Taylor’s (1959) dictionary. Expected values are calculated by multiplying the number of occurrences of a given consonant by the number of occurrences of a vowel, then dividing by the total number of stems.
11 We note that some issues are left uncontrolled: we have not normalized for vowel length, excluded forms with disharmonic sequences of sibilants, excluded stems that appear multiple times (as different words, when combined with different prefixes), excluded ideophones that may have [s] or [ʃ] for sound-symbolic reasons, or attempted to correct any skew based on position. Additionally, being a dictionary, the set of words does not include many forms produced by normal suffixation—for example, forms of the “long” causative /-iis-/. We also have not excluded forms that could be analyzed as having a covert suffix /-j-/, which might derive a surface [s] or [ʦ] from other segments. Finally, Hansson (2001:439ff.) notes an effect of voicing, whereby anteriority disharmony is more permissible between sibilants that also disagree in voicing; we have not tried to include any detailed analysis of this issue.
A more detailed statistical analysis of the data would be worthwhile, but the rough counts here are sufficient to give a basic picture of the phonotactics, leaving harmony effects aside. A table based on raw counts, including harmonic sequences of sibilants, can be found in the appendix. The appendix also gives values when surface [ʧ ʤ] derived from /k ɡ/ are included, though there is no evidence for chain shifts like /ɡi/ → ʤ → [ʥ].
12 We abstract away from potential conflicts between *su and *ʃi here. Inputs like /suʃi/ and /ʃisu/ should create a situation where these constraints conflict. Our analysis predicts that in such cases, we should not find strictly right-toleft harmony. Such inputs are difficult to construct in Nkore-Kiga, however: Taylor (1985:160) notes only one suffix that starts with /-u/, and it appears not to be very common; the grammar does not give any examples of sibilant-final stems with this suffix. Additionally, words containing both [i] and [u], each following a sibilant, seem relatively rare. The only instance of Si . . . Su in Taylor’s dictionary is ekishigyeshu [èʧìʃìʤèʃù] ‘blood clot’, which does not alternate (and thus could plausibly have /ʃi . . . ʃu/, and surface faithfully). The dictionary includes six stems with the reverse order, Su . . . Si. All are disharmonic nouns, all with [ʃu/Ʒu . . . zi]: for example, akashuzi [àkà-ʃúzì] ‘bug’. Four of these stems are nouns derived from verbs with final /r/ followed by the agentive nominalizing suffix /-i/. In no cases do we find the type of mapping that sets up the constraint conflict, that is, /ʃu. . . ʃi/ → [su . . . si].
13 Here, the agreement does not obviously work in a right-to-left fashion. But the resulting output [sisa] could nonetheless be construed as the result of right-to-left harmony if we posit a covert /i/ after the stem-final sibilant.
14 We might also expect a second set of related forms with the structure /sa . . . su/, if Nkore-Kiga had the requisite morphology to put such inputs together.
16 Including the short causative, which is represented by some other authors as -y-, --, or--.
17 The particular approach we are currently exploring is that proposed by Archangeli and Pulleyblank (2012, 2014, 2015a,b). In the approach taken there, choosing between allomorphs is central to the theory, allomorph choice being dictated by general phonotactics in some cases and by morpheme-specific selectional requirements in others. For the cases governed here by MORPHREAL, the appropriate patterns would be ensured by morpheme selection.
We want to thank Dr. Connie Tukwasibwe, Blake Allen, and Gunnar Hansson for assistance in obtaining and processing Kiga data. For helpful discussion and commentary, we thank Gunnar again, as well as Larry Hyman, Jaye Padgett, Gillian Gallagher, two anonymous LI reviewers, an audience at ABC↔C at the University of California, Berkeley, and participants at the 3rd African Linguistics School in Ibadan, where the problem addressed in this article came to our attention. This work was supported in part by grants from the Rhodes University Research Committee, the South African National Research Foundation, the American Philosophical Society (to Bennett), and the Social Sciences and Humanities Research Council of Canada (to Pulleyblank).