The segmental and tonal structure of verb inflection in Babanki

In this study we provide a comprehensive phonological and morphological overview of the complex tense-aspect-mood (TAM) system of Babanki, a Grassfields Bantu language of Cameroon. Our emphasis is on the competing inflectional tonal melodies that are assigned to the verb stem. These melodies are determined not only by the multiple past and future tenses, perfective vs. progressive aspect, and indicative vs. imperative, subjunctive, and conditional moods, but also affirmative vs. negative and “conjoint” (CJ) vs. “disjoint” (DJ) verbal marking, which we show to be more thoroughgoing than the better known cases in Eastern and Southern Bantu. The paper concludes with a ranking of the six assigned tonal melodies and fourteen appendices providing all of the relevant tonal paradigms.


Introduction
The purpose of this paper is to provide a description of tense-aspect-mood marking in Babanki, a Grassfields Bantu language of the Ring subgroup spoken in Western Cameroon (Hyman 1980;Akumbu & Chibaka 2012). Similar to related Grassfields Bantu languages, we will show that Babanki distinguishes multiple past and future tenses as well as a progressive/non-progressive aspect distinction. Particularly striking is the discovery of a thoroughgoing conjoint-disjoint contrast similar to, but more pervasive than, the CJ/DJ distinctions which have been extensively documented in Narrow Bantu (see the papers in van der Wal & Hyman 2017 and references cited therein). The various tense aspect markers (TAMs) are expressed through an extensive system of multiple exponence, which may involve pre-and/or post-verbal particles, prefixes and suffixes, and tone. In the following sections we will first present preliminary aspects of Babanki morphology and tonology ( §2), then describe the seven indicative tenses as they appear in the perfective ( §3), the progressive ( §4), and their corresponding negatives ( §5). We then turn to the imperative, subjunctive, and conditional moods, first presenting their affirmative forms ( §6), then the corresponding negative forms ( §7). In our conclusion ( §8) we present an analysis integrating all of the relevant morphosyntactic features seen to determine the tonal patterns in the preceding sections. An overt class 19 subject concord marker (SM) fə́ is seen in the following example, agreeing with fə̀nyín 'bird': (1) fə-nyín fə́ n-lám lí kə-báyn 'A bird cooked fufu.' 19-bird 19.PFV.P3 N-cook P3 7-fufu As will be further discussed when we consider the different TAMs, in the above disjoint (DJ) form, the distant past (P3) is marked by a schwa which fuses with fə́, as well as by the prefix n-and the post-verbal particle lí. As we will see, a perfective morpheme /ə/ also occurs between the SM and the verb, but fuses with fə́ as well. In other tenses preverbal particles can have the shape CV, e.g. general past (P2) /tə/. While (1) clearly shows a SM, we will generally cite sentences where the subject is the name búŋ 'Bung' belonging to class 1, which does not have a SM.
Turning to the structure of the verb, the verb root may have the shape CV or CVC, while the verb stem can be CV, CVC, CVCV, or CVCCV. The bisyllabic stem forms derive diachronically from a root + suffix, which may be either identifiable as a "verb extension" (e.g. causative, pluractional), or can be lexically frozen on the root. In Table 2, the verbs cited in our study are presented in their root, stem, infinitive, and imperative forms. As seen, verb roots contrast high (H) and low (L) tone, marked with an acute (´) vs. grave (`) accent. Suffixes are underlyingly toneless and take the same tone as the root unless a conflicting suffix tone is assigned by a specific TAM.
In the examples sə́ŋtə́ 'sift' has the pluractional suffix -tə (cf. sə́ŋ 'sift') while lJmsə̀ 'heat' has the causative suffix -sə (cf. lJm 'be hot'). Analyzing these (and more complex) forms requires further discussion of the tone system. The underlying /H/ and /L/ are subject to various tone rules which produce additional surface contrasts. The infinitive prefix ə́-in Table 2 causes a H tone root to be downstepped, marked by the down arrow (¯). We attribute this to a floating L which follows the schwa, i.e. /ə́ `/, and which also prevents the H of the prefix from spreading onto a L verb root. In addition, there is a third, derived surface-contrastive mid (M) pitch height, marked by a macron ( ̄ ). Falling HL ( ̂ ) and rising LH ( ̌ ) tones also occur, but are much more restricted. In the data to be presented they only occur on preverbal TAM particles and not on the verb stem itself. 3 M tones derive from two sources (cf. Hyman 1979; Akumbu 2019), illustrated in the following examples involving the H and L tone verb roots /lám/ 'cook' and /kùm/ 'touch': (2) a. lám kə̄báyn 'cook fufu!' (imperative) b. kùmə́ kə̄báyn 'touch fufu!' (3) a. Búŋ tə̀ làm kə̄báyn 'Bung cooked fufu.' (P2 conjoint) b. Búŋ tə̀ kùm kəbáyn 'Bung touched fufu.' In (2) we see that a noun class prefix, here /kə-/, raises to M between two H tones, the first of which is a H suffix on the verb (see below). As was also seen in Table 2, the L tone verb in (2b) has acquired an epenthetic schwa to avoid the rising tone that would otherwise result from combining the root L with the H suffix tone of the imperative (*kǔm). Such register raising of L to M occurs only in TAMs which assign a H suffix to the verb. The second source seen in (3a) owes its existence to a rule of L tone spreading (LTS), here applying from the P2 TAM marker /tə/ onto the H verb root /lám/ 'cook'. Since the language does not tolerate rising tones on lexical morphemes, the result in this case is to shift the H onto the prefix, producing an intermediate HL falling tone (làm kə̂báyn). The resulting L-HL-H sequence is then converted to L-M-H (cf . Hyman 1979;Akumbu 2019 In the following discussion we will almost exclusively cite forms where the verb is followed by the object noun kə̀báyn 'fufu' (a staple food) so that we can see whether the process of LTS occurs. In the following sections we first analyze the indicative tense-aspect contrasts starting with perfective ( §3), then progressive ( §4), and negative ( §5), and then turn to non-indicative forms in ( §6, §7). We end in §8 by outlining an analysis which ranks the TAM inflectional features seen to determine the different tonal patterns in the earlier sections.

Perfective forms
In this section we will introduce the temporal contrasts and describe their realization in the perfective aspect. As summarized in Table 3, Babanki distinguishes four present/past and three future tenses, which we refer to as P0-P3 and F1-F3. We indicate the pre-verbal segmental tense auxiliaries which are held constant across the perfective and progressive aspects as well as in the corresponding negatives. (F2 nè and F3 lù are also consistently present in non-indicative moods.)  Table 2 can be found in Appendix 1. (iii) The verb can occur at the end of a MCA sentence with DJ marking; it cannot occur at the end of a MCA sentence with CJ marking (there must be something following the verb).
(iv) There is no CJ/DJ contrast in negatives or relative clauses (where the verb can occur last).
(v) As we will see in subsequent sections, non-contrastive negative and relative clause marking of P (non-future) tenses looks like the CJ marking in main clause affirmatives (where one does not expect focus marking of truth value). While this is typical of CJ/DJ languages, the future tenses are different: their marking in negatives and relative clauses looks more like the DJ in main clause affirmatives.
(vi) The DJ forms are more segmentally marked than the CJ forms. As seen in Table 4, the DJ forms all involve a H tone schwa that precedes the TAM auxiliary. P0 and P3 also have a postposed marker /`lí/.
With this established, we now turn to consider the tonal patterns associated with each cell in the complex TAM system of Babanki. For this purpose we have prepared appendices of full sentences which are colorcoded for tone pattern. Although we will cite a subset of these forms in the text, readers will be referred to 4 Although they differ in form, the Babanki CD/DJ also parallels the contrast reported in non-future tenses in Aghem, a Western Ring Grassfields Bantu language (Anderson 1979;Watters 1979), as well as in certain other non-Bantu languages (Hyman & Watters 1984). More closely related within Central Ring, Kom also has a CJ/DJ contrast, again marked by different forms, as in the general past Ngóŋ tî jùm mēnywín (CJ) vs. Ngóŋ tí mēn jùm mènywīn (DJ) 'Ngong drove away the birds' (second author, personal notes). the relevant appendix for more examples. For ease of reference, we present an overview of indicative TA marking with color coding of the tone patterns in Table 5. Since we will consider each TA separately we will identify the tone patterns as we go. In §8, a fuller paradigm with all TAM forms is provided in Table 6 and the tone patterns identified in Table 7. For now, note that five different tone patterns have been identified, with progressive aspect (PROG) always assigning the same tone pattern to the verb, colored in green.

Conjoint forms
We start with the CJ forms, since they are segmentally and tonally simpler. Representative forms of all seven CJ tenses are provided in the first data column in Appendix 1, color-coded for tone pattern. Except for the P3, all of the cells are gray, indicating that the verb is preceded by a L auxiliary indicated above in Table 4. (The P0 auxiliary is a floating L tone.) While the L tone auxiliary has no effect on L tone roots, it causes H tone roots to become L by LTS, as in the P2 forms in (5).
(5) a. Búŋ tə̀ zh€̀ kə̄-báyn 'Bung ate the fufu.' Bung P2 eat 7-fufu b. Búŋ tə̀ làm kə̄-báyn 'Bung cooked the fufu.' Bung P2 cook 7-fufu c. Búŋ tə̀ səŋtə́ kə-báyn 'Bung sifted the fufu.' Bung P2 sift 7-fufu The L of P2 /tə/ spreads and delinks the underlying root H of /zh€/ 'eat', /lám/ 'cook', and /səŋtə/ 'sift'. 5 In (5a,b), where the verb stems are monosyllabic, this frees the H, which then joins the L of the following class 7 noun prefix /kə-/ to form a HL falling tone, subsequently simplified to M (kə̂-® kə̄-). In the case of bisyllabic /səŋtə/ in (5c), the H delinks on the first syllable, with the suffix -tə́ maintaining the (spread) H tone, i.e. /səŋtə/ ® sə́ŋtə́ ® sə̀ŋtə́). Since the H of bisyllabic verbs is not reassigned to the following noun, the /kə-/ noun prefix remains L, as it also is after a L tone verb. Recall that suffixes are toneless, taking their tone from the root. As we will see, some TAMs assign a L suffixal tone that may cause a bisyllabic H root stem to be realized H-L (as in progressive forms -see §4), while other TAMs assign a H suffix tone that may cause a bisyllabic L root stem to be realized L-H (as in the P3 CJ as well as the imperatives seen in Table 2.) A glance at the other CJ tenses in Appendix 1 will reveal that with the exception of P3 they all share the same tone pattern. P3 is also exceptional in being the only perfective tense that requires a nasal prefix on the verb (also in the DJ). The H tone verbs undergo LTS and have the same realization as the other CJ tenses: First, the monosyllabic verbs acquire a second H tone schwa syllable seen most clearly after the CVC root in (8b), while the schwa assimilates to the vowel of a CV root, as in (8a). The H tone -ə́ also conditions the class 7 prefix /kə-/ to become M. Given that the L verbs show this different pattern, we have encoded the P3 CJ cell blue.

Disjoint forms
We are now ready to consider the corresponding DJ forms in the second data column of Appendix 1. These all involve a DJ marker /ə/ occurring between the subject and the verb (which however fuses with the /á/ auxiliary in the F1 In (11) we see that the verbs are realized H followed by the downstep of ¯l í, which we interpret as triggered by a floating L tone. In (12) the H of the DJ auxiliary /ə/ spreads through the toneless nasal prefix onto the verb, creating a HL sequence. In (12a,b) an extra mora is observed which avoids the creation of a HL falling tone on the roots: *[lê], *[kûm]. Since /`lí/ is preceded by a L tone, there is no contrastive downstep, although Babanki is subject to automatic downstep or "downdrift". In the above forms and elsewhere where present, a nasal prefix is underlyingly toneless, realized M between H tones, otherwise L if preceded or followed by L. 6 As seen in Appendix 1, the P0 DJ forms are identical to the P3 DJ except that they lack a nasal prefix. This leaves the future DJ tenses, which have a still different tone pattern and hence are encoded yellow. As seen in Appendix 1, the H of the DJ marker /ə/ spreads onto the future auxiliaries /à/, /nè/, and /lù/. Rather than creating a HL falling tone, the result is that the L of these markers is delinked. As seen in the F2 DJ forms in (13) The corresponding L tone verbs show that the future DJ forms also involve a post-verbal H which fuses with the L tone of the noun prefix /kə-/, converting it to M: (14) a. Búŋ ə́ né lè kə̄-báyn 'Bung will lose the fufu.' Bung PFV F2 lose 7-fufu b. Búŋ ə́ né kùm kə̄-báyn 'Bung will touch the fufu.' Bung PFV F2 touch 7-fufu c. Búŋ ə́ né l€msə́ kə̄-báyn 'Bung will heat the fufu.' Although only tonal, the presence of a second post-verbal DJ marker is of course less surprising given the post-verbal DJ marker /`lí/ in the P0 and P3. This completes our discussion of the CJ and DJ perfective forms. In the following section we examine the same tenses in the progressive aspect, provided in the third data column of Appendix 1.

Progressive forms
The first important thing to note is that the progressive forms do not distinguish CJ from DJ. There is only one form per tense which is marked by a nasal prefix except in the P0 and a /L/ schwa suffix on the verb. In most cases the L /-ə/ suffix is realized with the same tone as the verb root: (15) a. Búŋ lám-ə́ kə-báyn 'Bung is cooking fufu.' We therefore propose that the H of the root spreads and delinks the L of CV-ə̀ and CVC-ə̀ stems, producing an all H verb stem in (15), while H tone spreading is blocked when the verb stem has a suffix such as the /-tə/ in (17). In all cases the progressive L keeps the following /kə-/ suffix L. As seen in the above forms and in the third column of data in Appendix 1, what is significant is that all progressive forms have the same tonal pattern throughout all of the tenses, which overrides the distinctions found in other columns. 8 We have shaded this pattern green.
To summarize thus far, while the input tense markers are the same as in Table 3, the following curious fact should be noted: the PST tenses show the same segmental marking as the CJ forms in column 1, while the FUT tenses have the same /ə/ preceding the tense auxiliary as in the DJ forms in column 2. There are tonal differences, however. 9 First, except in the P3, the PST tenses have a H tone following the tense 8 As will be seen in §5 and §6, the same tone pattern is also found throughout the negative progressive paradigm as well as in non-indicative moods. 9 The preverbal high tone effects in the future progressives seem to correlate with the postverbal high tones of the futures in the DJ paradigm. So on purely formal grounds one might come to think that actually the progressive future forms retain periphrastic traits in that the tense markers (two of which, F1 nè and F2 lù, have been identified as originating in erstwhile verbs) are inflected for the DJ (accounting for the tonal effects in the yellow cells of Appendix 1), whereas the verb itself is segmentally marked for the progressive by the marker combination N-… -ə̀. This leaves us with the (open) question of the semantic link between both categories, i.e. the progressive paradigm and the disjoint perfective paradigm in the future tenses. Taking this line of argumentation one step further and giving it a slightly different spin, one might as well see the quirky extra H tone in all progressive past tenses, except P3, in the same context, i.e. as taking part in a general progressive pattern of ́ N-… -ə̀, possibly representing (relics of) an erstwhile periphrastic construction of an auxiliary plus nominalized main verb. Under this assumption, P0 and P3 stand out in auxiliary which produces a rising tone in the case of P1 and P2: /yì´/ ® [yǐ], / tə̀/ ® [tə̌]. The same H tone accounts for the tonal differences between the P0 CJ and the corresponding progressive: (18) a. /Búŋ ` lám kəbáyn/ ® Búŋ làm kə̄báyn 'Bung has cooked the fufu.' b. /Búŋ ´ lám-ə̀ kəbáyn/ ® Búŋ lámə́ kəbáyn 'Bung is cooking the fufu.' As seen in (18a), a L tonal morpheme precedes the verb in the P0 CJ which links to the verb, causing its H to delink. The delinked H then causes the following /kə-/ noun prefix to become M. In contrast, in (18b) a H tonal morpheme precedes the verb in the P0 progressive, and the verb is realized H-H with its schwa suffix. The /kə-/ noun prefix is therefore not affected.

Negative forms
From the summary in Table 5  As mentioned, there is no CJ/DJ distinction in the negative, although it is tempting to identify the omnipresent negative H tone schwa as the same ə́ observed in the DJ, summarized above in Table 4. 10 Table  2 also shows that the progressives have the same tones as in the affirmative, again shaded in green. Thus compare the following sentences with those in (15) and (16) Bung PFV NEG F2 N-touch-PROG 7-fufu that they do not share the full package of markers, P0-PROG lacking N-and P3 lacking the preverbal H (and possibly also the progressive N-, since the nasal prefix might as well be interpreted as the ordinary P3 marker). 10 It is well known that both DJ and negation involve an inherent focus, hence form a natural class (see Hyman & Watters 1984).
The downsteps on ¯l ámə́ in (21a) and ¯n é in (21c) show that there is a floating L following kó. One might have proposed that the underlying representation of the negative indicative marker is /kò/ which would undergo H tone spreading from the preceding /ə/, exactly as the F2 auxiliary /nè/ undergoes after the DJ marker /ə/ in (13) and (14), and similarly in other future tenses in Appendix 1. However, since the nonindicative negative marker is /kə/, as in kə́ nzhJJ́ kə̀báyn 'don't be eating fufu!', it is equally likely that the negative indicative marker is /kó `/.
Before concluding this section, we should note that there are some tonal differences between the perfective affirmative and negative paradigms. What is curious is that the P tenses take the same tones as the corresponding affirmative CJ forms (shaded in gray except for P3 blue), while the F tenses take the same tones as the corresponding affirmative DJ forms (shaded in yellow). We will return to this in §8, where we propose a ranked set of morphosyntactic tone assignment rules.

Non-indicative affirmative forms
In the preceding sections we have seen that Babanki distinguishes seven tenses in indicative forms: P0-P3 and F1-F3. In this and the following section we describe the non-indicative forms which by their semantics are all future-oriented. As a result each of them has only three forms which correspond to indicative F1-F3. In addition, there is no CJ/DJ contrast. As we will see, only what we identify as F1 is really different from indicative marking in its tonal patterns.
We start with the singular imperative forms which were already shown in Table 2 above. As seen in Appendix 3, the bare F1 imperative has the same tone pattern as the indicative F1 DJ and negative, shaded yellow, while the F2 and F3 imperatives share the grey-shaded pattern of their corresponding CJ forms, as in (23b,c) involving the H tone verb /lám/ 'cook' and the L tone verbs /kùm/ 'touch' and /l€msə/ 'heat': 11 (23)  However, the F1 plural imperative shows a H tone prefix, which links to a following L verb. As seen most clearly when the L verb is bisyllabic, a H-¯H downstep sequence is created: /ghəŋ ´ l€msə́ kəbáyn/ ® ghə̀ŋ lJḿ¯sə́ kə̄báyn 'you pl. heat the fufu!'. 12 In the case of a monosyllabic verb a H¯H contour is expected on the one syllable. Instead, since such contours are not permitted, the second H is deleted, with the preceding L, now delinked, preserving the L on the prefix of 'fufu'. 13 Finally, note that the F2 and F3 forms in (24b,c) are identical to the F2-F3 indicative forms in Appendix 1. The same is true of the corresponding hortative forms in (25) In the following section we will see that, with the exception of the conditional negative, the corresponding negative forms largely tell the same story.

Non-indicative negative forms
As seen first in the following singular imperative forms taken from Appendix 9, the negative markers are consistently different in indicative vs. non-indicative forms. Whereas we established /kó `/ as the indicative negative marker, the forms in (29) show that the nonindicative marker is /kə/, which however fuses with the F1 marker /à/ in (29a). The H of /kə/ spreads onto the tense marker, delinking its L, which then triggers a downstep on a following H: /kə́ à/, /kə́ nè/, /kə́ lù/ ® ká `, kə́ né `, kə́ lú `. Finally, although /kùm/ 'touch' lacks the final H tone schwa seen in the affirmative imperative, it is clear that all of the above forms have a H suffix, hence a M tone on the prefix kə̄-. The corresponding negative plural imperatives taken from Appendix 10 appear in (30). This paradigm is exactly identical to that of the corresponding affirmatives in (24), except for the presence of kə́ occurring before the subject, here the second person plural pronoun ghə̀ŋ. The hortatives in (31) differ only in the presence of the first person plural pronoun yúwù, from Appendix 10, and similarly the subjunctives in (32)  While the F1 doesn't have an overt tense marker, the F2 and F3 markers nè and lù appear before another morpheme díʔ followed by the negative morpheme kə́. Since dìʔ is identical to the copular verb /dìʔ/ 'be', we interpret the above historically as 'if Bung will be not cook, touch, heat...'. The main verb lacks a H prefix in the F1, although the F1-F3 all have a H suffix. We have thus colored these cells yellow in Appendix 13, indicating that the tones are identical with the indicative future pattern, which is in turn the same in the affirmative and negative (see Appendices 1 and 2). Finally, as seen in Appendices 8 and 14, the affirmative and negative past conditional forms all take the same (yellow) tone pattern. The following representative examples show that instead of the pre-subject complementizer sə́tsɛ̀n, the auxiliary form tí occurs after the tense marker in the past conditional: The same auxiliary + negative sequence dìʔ kə́ is used as in the future negative conditional. This completes our survey through the different verb paradigms which we have been able to consider in our study. We conclude in §8 by outlining an integrative analysis followed by discussion.

Towards an integrated analysis
In the preceding sections we have presented the different Babanki tense, aspect, and mood distinctions, both affirmative and negative. While we have presented a subset of examples of each, a full and systematic presentation of all of the forms we have considered is found in Appendices 1-14. While we have given partial interpretations and analyses, we have yet to pull it all together into one coherent picture. This is our first goal in this section. Our second goal, however preliminary, will be to comment on what we think is the most promising conceptualization of the Babanki verb inflectional system and others like it.
We begin by recapping the preverbal "auxiliaries" in Table 6, where the different cells in the paradigm are also color-coded for tone pattern. 16 As seen most clearly in the F2 and F3 indicative negative sequences, ə́ kó ¯n é` and ə́ kó ¯l ú`, there is a maximum of three segmental slots, which we can label as FOCUS, NEGATION, and TENSE. The only filler of the focus slot is the DJ marker /ə/, which we assume is the same morpheme as the [ə] that precedes the indicative negative marker /kó`/, but does not occur with the non-indicative negative marker /kə/. 17 This leaves the P0-P3 and F1-F3 tense markers which were presented in Table 1 above and are held constant throughout the paradigm. Except for the unassociated L tones, the intention in Table 6 is to show the output forms, including tonal variations that were discussed in earlier sections, e.g. P1 yì, yî, and yǐ. We have proposed that the underlying forms of the tense markers are as they appear in the first (CJ) column, where they all have underlying L tone. Although the L tone does not appear in the P0 or P3 DJ (whose tone pattern is irregular), it is only the F1 that is inconsistent in its segmental marking: /à/ appears only in the indicative affirmative and the singular imperative negative, where ká` is the realization of /kə/ + /à/. In the progressive H and L tone verbs begin with their base tone, hence without any interaction with what precedes. This might be attributable to the fact that, except in the P0, progressives take a nasal prefix that may effectively block any tonal interaction with what precedes. 18 The progressive is in fact quite special in the paradigm. As discussed in §4, progressive forms are consistent in their tone pattern: Except in the P0, the verb takes a toneless nasal prefix, and all progressives assign a L tone -ə̀ suffix, which however assimilates to the H of a monosyllabic H tone verb: /n-lám-ə/ 'cook.PROG' ® n-lám-ə́. Outside the progressive, it is only the P3 that also takes a nasal prefix. Curiously, the P3 also assigns a schwa suffix, but only to L tone monosyllabic verbs, e.g. to /kùm/ 'touch' in Búŋ ə̀ 16 In Table 6, PF stands for perfective and PR for progressive. The three dots (...) in the non-indicative columns indicate the position of the subject, which follows the negative marker kə́ but precedes the tense marker. Note also that the yellow non-indicative P0-P3 cells refer exclusively to conditional clauses, which receive the same auxiliary markers in the corresponding empty green progressive cells to their right. 17 Note that /ə/ is not restricted to main clause indicatives, as it can also occur in a relative clause, e.g. kə̀báyn á Búŋ ə́ kó ¯n é ¯l ám 'the fufu that Bung will not cook (F2)'. 18 There are potentially two problems with this idea. First, as we have said, the P0 doesn't take a nasal prefix, but is tonally identical to the other progressive forms. Second, although the tone patterns are irregular, P3 non-progressives also place a nasal prefix on the verb, but do allow a tonal interaction with the preceding auxiliary: L tone spreading occurs in the P3 CJ and negative, while H tone spreading occurs in the P3 DJ, e.g. ə̀ + nshítə́ ® ə̀ nshìtə́ 'collected', ə́ + nshìsə̀ ® ə́ nshísə̀ 'removed'. ŋkùmə́ kə̄báyn (CJ) and Búŋ ə́ ŋkúmə̀ lí kə̀báyn (DJ), both meaning 'Bung touched the fufu'. The same pattern is found only in one other cell, the affirmative singular imperative, which again assigns the schwa suffix only to monosyllabic L tone verbs: kùmə́ 'touch!'.
Finally, there is the issue of assigning prefixal and suffixal tones. In accounting for the surface realizations it is necessary to control for whether the verb stem is mono-or bisyllabic. Recall that we have analyzed bisyllabic verbs as having an underlyingly toneless second syllable which will take the same tone as the tone of the root unless overriden by a suffixal tone. With this in mind, Table 7 characterizes the six color-coded stem-tone patterns in terms of their preceding and following tonal environments. (T stands for the base /H/ or /L/ of the verb root.) Only the grey pattern lacks a suffix. The P0 and P3 orange DJ cells are unique in requiring a non-suffixal formative /`lí`/ following the verb. What is striking is that four of the six rows show an agreement between the pre-verb tone and the first tone of the verb stem: grey and blue L vs. orange and gold H. In the first group L tone spreading causes a H-H verb to be realized as L-H, while in the second group H tone spreading causes a L-L verb to become H-L. The (L) of the yellow row indicates that a L is sometimes present, but does not interact with the verb stem other than to cause a H verb to become downstepped, e.g. kə́ + à + lám + kə̀báyn ® ká ` lám kə̀báyn ® ká ¯l ám kə̄báyn 'don't cook the fufu!' Finally, concerning the last row, shaded green, we have already seen that there is no tonal interaction between the auxiliary and the verb stem in progressives. Turning to suffixes, both the P3 (orange) and progressives (green) assign a L, while yellow, blue and gold assign a H. Except for the gold pattern a schwa suffix also appears, although with the restrictions that are indicated. The H tone schwa is only found after L verbs -and is only discernible when the verb is monosyllabic. This is because a schwa would merge with the second vowel of a CV(C)CV verb stem. In fact, among the 757 verbs in Akumbu (2008), 323 verb stems are bisyllabic. Of these all but 19 have the shape CV(C)Cə. Of these 19, all but five have the shape CVʔV where the vowels are identical, and three are clearly compounds. This leaves the following two verbs: báŋlí 'be ripe', bóbó 'carry (child) on back', on which a surface schwa does not accompany the suffixal L in the progressive: Búŋ yǐ mbóbò kə̀báyn 'Bung was carrying the fufu' (P1). While this accounts for why the schwa is visible only on monosyllabic verbs, e.g. directly on CVC roots or as an assimilated extra mora on CV roots, it does not explain why only the progressive assigns a schwa to both H and L roots. A clear generalization is that monosyllabic H tone roots never take a schwa outside the progressive. Our intuition has been that the schwa appears in contexts where a contour tone would otherwise arise. Derivations with the verb /kùm/ 'touch' representating the orange and blue patterns show this relation in (36). Since falling tones are not allowed on roots, the "repair" is to insert a schwa to take the L part of the contour.
Similarly, in (36b), when the suffixal H is assigned to the verb, this creates an intermediate LH rising tone. Again, a schwa is inserted, this time to take the H part of the LH contour. Whether the schwa is epenthetic, as we have represented it in (36), or whether it represents a historical retention, there is a potential problem with the assumption that schwa appears as an automatic response to avoiding contours. Recall that the yellow pattern also introduces a schwa, but only in the affirmative singular imperative, exemplified in (37a).
(37) a. kùmə́ kə̄báyn 'touch the fufu!' /kùm ´/ + /kəbáyn/ ® kǔm kəbáyn ® kùmə́ kə̄báyn b. Búŋ ə́ né kùm kə̄báyn 'Bung will touch the fufu.' (F2) /kùm ´/ + /kəbáyn/ ® kùm + kə̂báyn ® kùm kə̄báyn While we have given the same derivation in (37a) as was seen in (36b), the question is why we get a different result in (37b) and every other yellow cell. In this derivation the suffixal H does not get assigned to the verb root, but rather to the following prefix kə̀-, thereby producing an intermediate HL falling tone. As shown by Hyman (1979) and Akumbu (2019), a L-HL-H sequence is simplified to L-M-H by a general contour simplification process. 19 What this shows is that the appearance of a schwa appears to be partly phonologically and partly morphologically conditioned. One way to accomplish this is via a "cophonology" approach (Inkelas & Zoll 2007). In the P3 and the affirmative singular imperative, inserting a schwa is chosen as a better repair to the constraint against contours on root morphemes, while in the future (yellow) pattern, assigning the H to the prefix is the chosen resolution.
We suspect that other morphologically conditioned responses will be needed elsewhere, perhaps to account for why H tone spreading converts the P1 and P2 markers /yì/ and /tə/ to yî and tə̂ by H tone spreading, while the F2 and F3 markers /nè/ and /lù/ instead become né` and lú`. We leave this issue for now to consider the more general question of how to assign the appropriate morphological marking to the right cells in the paradigm. Since much of the segmental marking is largely consistent (e.g. tense markers, negative markers, progressive nasal prefix, and schwa suffix), we will concentrate on tone, i.e. on the six color-coded patterns. We begin by noting that we have two extremes: Blue and orange cells are quite restricted, while green cells are quite general. It would seem therefore that we need to do two things. First, we need to isolate those cells for which a special statement will be needed. These can be considered the equivalent of tonal "exceptions". Second, we can also isolate all of the green cells since their tone pattern is totally predictable. In previous work by the second author (e.g. Hyman 2016) the strategy pursued has been to first assign the general patterns, here the progressive (green), then look at the remainder to assign the next most general pattern among the non-progressives, then assign the next most general pattern, and so on. The idea is that by going from general to specific, the assignments may be simpler to state, the last assignment being the elsewhere case. The opposite strategy is also possible, where the most specific and unpredictable patterns are first assigned, leaving the more and more general ones to be accounted for next. In this approach the progressive would become the default tone pattern. 20 It seems to us that the most likely approach would be an OT-style account ranking the tone assignments by morphosyntactic feature combinations. This too is not an easy task, but at least it is coherent: while the 19 This same process is responsible for the M tone prefix found after monosyllabic /H/ verbs in the grey pattern: /Búŋ yì lám kəbáyn/ ® Búŋ yì lǎm kə̀báyn ® Búŋ yì làm ´ kə̀báyn ® Búŋ yì làm kə̂báyn ® Búŋ yì làm kə̄báyn 'Bung cooked the fufu' (P1). We are not proposing that so many steps are needed in such a derivation, only that the H of /lám/ has to shift onto the L prefix to derive the M tone. Bisyllabic H tone verbs do not raise the L prefix to M in the grey pattern: Búŋ yì sə̀ŋtə́ kə̀báyn 'Bung sifted the fufu'. 20 Babanki does not appear to lend itself to an assignment based on a layered morphological structure as Inkelas (2011: 75) proposes for Hausa. In that kind of approach, the tonal patterns would be assigned first to the innermost brackets, then to the next set of brackets, erasing the earlier assignment in case of conflict. Babanki seems rather to be more like the other cases discussed by Hyman (2016), where there is a paradigm of tone patterns dependent on combinations of features. single feature PROG(ressive) assigns an undominated tone pattern, overriding all others, certain morphosyntactic feature combinations will be very restricted, e.g. those requiring the blue and orange tone patterns. To show how this might be done we adopt the following "marked" privative features: To these we need to add the tenses: P0, P1, P2, P3, F1, F2, F3. In order to see how these features might be applied to the Babanki data, consider the following table, where we indicate which feature combinations receive which tone pattern: In Table 8 the six patterns are ordered with the intended ranking such that green is highest ranked and grey is lowest. In fact, the intention is for grey to be the default or elsewhere case. Thus, everything to the right of the first column is non-progressive. As a result of the ranking, once orange has assigned its pattern to the P0 DJ and P3 DJ, the blue pattern can now be assigned without regard to any feature other than P3. Similarly gold has targeted only the F1 subjunctive, leaving the F2 and F3 subjunctives untouched. This leaves us with yellow and grey. Here we meet a problem that will require a choice. Since we have ranked yellow higher than grey we have to be sure that it doesn't misappropriate certain cells, particularly the negative (non-progressive) subjunctive F2 and F3. These must remain grey. In Table 8 we put a [-sbjv] place holder, which violates the privativity of the features in (38). If we had changed the rankings, as in Table 9, we run into a different problem: Since SBJV F1 has already been assigned to gold, we can designate grey for the remaining affirmative and negative F2 and F3 subjunctives. However, we now need to refer to the "unmarked" value CJ in order not to assign grey to future DJ tenses. Since DJ was needed to assign the orange tone pattern, we have the equivalence of [±DJ]. Both analyses thus have problems. 21 Two potential solutions seem possible. One is to change the feature values. If we could refer to the DJ, indicative and imperative negatives as having a special feature [+F], this could be required in assigning the yellow pattern to them (as well as to the conditional negative), thereby eliminating the [-sbjv] in Table 7. Similarly, if we assigned a special feature to the future CJ and the F2 and F3 imperatives affirmative and subjunctive affirmative and negative, we could use that feature in Table 8. Perhaps there are other such ad hoc moves one could consider.
Another solution is to split up one or more of the columns. Since we would like to keep grey as the default, let's try modifying Table 9 by treating the CJ-like F2 and F3 non-indicatives as receiving their grey pattern first: 22 While perhaps not as aesthetic, splitting the grey pattern in two does allow us to simplify the yellow assignment considerably. Not only do we not need the [-sbjv], but also IMP NEG: This feature combination will be taken care of by IMP F1 (which will cover affirmative and negative) and FUT NEG (which will cover the IMP F2 and F3). The one detail we haven't accounted for is the yellow pattern of the conditional negative which, recall, is a periphrastic construction whose main verb could be considered nonsubjunctive. 23 To conclude, we should perhaps mention still another strategy: Conflate two of the colors! As we have tried to indicate, the tonal patterns on the verb stem are very much determined by their tonal surroundings. The yellow and gold patterns look very similar except that the latter has a preverbal H tone prefix, which is lacking in the yellow pattern. The above tables are designed only to account for the tones, not for the markers that occur before or after the verb stem. While we haven't pursued this or other conceivable approaches, we point this out for anyone who would like to try their hand at coming up with a more comprehensive account that includes these markers. Since we include all of the data we have considered in the appendices, we hope we have provided enough to work on there -but invite others to expand the coverage both in Babanki and in related languages in the future.  22 The reasons for favoring grey to be the default are, first, that it realizes the unmarked feature values "indicative" and "CJ", and second, that it is morphologically unmarked, being the only pattern not to involve a suffix (cf. Table 6). 23 Note that the H tone of díʔ from in the F1 suggests a H marker preceding the input verb dìʔ 'be', thus making it fall into line with the gold subjunctive cells. The F2 and F3 nè dìʔ and lù dìʔ look like they carry the grey pattern. Thus, while the auxiliary verb shows the expected subjunctive pattern, the main verb shows a different (yellow) one.