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Bermúdez-Otero (2013) argues that the Spanish lexicon stores whole stems complete with their theme vowels, rather than storing roots whose inflectional class features condition the insertion of particular theme vowels (as argued for in much Distributed Morphology (DM) work on Romance, such as Oltra-Massuet 1999, Oltra-Massuet and Arregi 2005). The argument turns on an apparent cyclicity paradox that Bermúdez-Otero (2013:65, 71) dubs the problem of the missing cycle. Bermúdez-Otero argues that this problem cannot be avoided if roots and categorizing heads are held to be atoms stored in the Spanish lexicon. The paradox can be circumvented only by embracing the notion of ‘‘stem’’ and taking the stem to be the unit stored as a lexical primitive.This conclusion, if correct, would have far-reaching implications for the theory of the architecture of the grammar, since the notion of stem does not and cannot have any status as a primitive in a theory that is committed to the ideas of syntactic hierarchical structure all the way down and the strictly local determination of conditioned allomorphy (such as DM; see Embick and Halle 2005). The notion that a morphologically complex unit like a stem could be stored, and behave as a unit with respect to conditioned allomorphy, is not compatible with either of these tenets. Therefore, if Bermúdez-Otero’s argument is right, it follows that some of the fundamental architectural claims of DM are wrong.In this squib, I point out that the problem of the missing cycle dissolves once the broader behavior of one of the crucial phenomena involved (the syllabification of /i/ as [i] or [j]) is taken into account. It turns out that the syllabification of /i/ in derived word forms is not based purely on whether or not the vowel is stressed on an earlier cycle; instead, it must be formulated in terms of the morphophonology associated with particular lexical categories (Smith 2001, 2011). I will argue that this phenomenon is the result of a rule that denuclearizes an unstressed /i/ in hiatus in nonverbal contexts. Syllabification of /i/ is therefore not a property inherited from earlier stress cycles, and the fact that its behavior contrasts with that of diphthongization (which does appear to be genuinely cyclic) thus does not constitute a cyclicity paradox. The general conclusion is this: since there is no problem of the missing cycle, there is no argument for stem storage, and therefore no threat to the idea of syntactic structure all the way down, nor to the strictly local nature of conditioned allomorphy.The argument is developed as follows. In section 1, I introduce the problem of the missing cycle, which Bermúdez-Otero takes to be the inevitable consequence of any non-stem-based approach to combinations of roots and theme vowels in Spanish. In section 2, I highlight crucial evidence discussed by Cabré and Prieto (2006) and by Cabré and Ohannesian (2009), which suggests that the behavior of /i/ syllabification is not reducible to cyclicity; instead, the distinction between verbs on the one hand and nouns/adjectives on the other appears to be at issue. The cyclicity paradox adduced by Bermúdez-Otero is therefore dissolved. In section 3, I sketch a DM analysis of the phenomena discussed by Bermúdez-Otero that does not require the storage of stems (using insights from Harris 1969, Roca 1997, and the DM approach to Spanish stress advanced in Oltra-Massuet and Arregi 2005). Section 4 is a brief conclusion.As Bermúdez-Otero (2013:67) points out, the problem of the missing cycle was recognized as early as the 1980s and was a focus of active discussion for some time (Harris 1989, Cole 1995), until the ascendancy of classical Optimality Theory pushed issues of cyclicity into the background. With these issues now very much at the forefront again, including in optimality-theoretic work (for various perspectives, see Benua 1997, Bermúdez-Otero 1999, Kiparsky 2000, Wolf 2008, Embick 2010), the importance of this apparent cyclicity paradox is quite rightly being reasserted. I will characterize the problem as it arises for a localist DM model (see Embick 2010) in the following paragraphs.Spanish famously has a set of roots that alternate between a form with a simple vowel and a form with a diphthong (Harris 1969, Bybee and Pardo 1981). As shown by the contrasting paradigms in (1), diphthongization is lexically restricted, but triggered by stress for roots that have it (data based on an expanded version of Embick 2012:28, (6)). Examples are given in Spanish orthography, with the addition of the acute accent to indicate stress location. The relevant (non)alternating vowels are underlined.We see that the same vowel e diphthongizes when stressed to ie in the forms in column (1a), but does not diphthongize even when stressed in column (1b). Similarly, the vowel o diphthongizes to ue in column (1c) when it is stressed, but remains o throughout column (1d).1If we now turn to morphologically derived forms and ask when stress is assigned and when diphthongization is triggered, it becomes apparent that we want a cycle of stress assignment to apply when a derivational little n is spelled out. For example, the alternating root in contar ‘to count/to tell’ (e.g., cuento ‘I count/I tell’) undergoes diphthongization in the nominal form cuento ‘tale’, as well as in forms derived from that noun (like cuentito ‘tale.DIM’ and cuentista ‘storyteller’). The derivation of a form like cuento ‘tale’ might therefore proceed as follows (taking the theory of Spell-Out in Embick 2010 as background):If we next consider what happens when a derivational n takes as its complement a structure containing a root that has already been categorized as v, we find that diphthongization does not apply. Combining the root √CONT- with v, and then combining the result with the agentive nominalizer -dor, yields cont-a-dór ‘counter’ and not *cuenta- dór. To account for this pattern, it seems that we need to say that spelling out v does not trigger a cycle of stress rules. This has the desired effect in a form like cont-a-dór, as shown in the derivation in (3).Here, the stress rules do not apply until n is spelled out, there is no stage of the derivation at which the alternating vowel is stressed, and there is therefore no opportunity for the diphthongization rule to apply. All that is needed is a difference in the cyclic nature of v and n, a difference that has been motivated for other languages (see, e.g., Bobaljik 1998 on Itelmen, Bobaljik 2008 on Arabic, Smith 2011 for general discussion). Desired effects of the same sort can be achieved for deverbal adjective forms like cont-á-ble ‘countable’ versus adjectives derived directly from alternating roots like viéj-o ‘old’ (cf. envej- ec-ér ‘to age’2), if we say that stress rules are triggered upon the spell-out of a categorizing little-a head.However, there is another apparently cyclically determined process that seems to indicate that v does trigger a cycle of stress assignment in Spanish. The evidence comes from the syllabification of /i/ as part of the onset of a rising diphthong (hence as [j]) or as a nucleus (hence as [i]). As Bermúdez-Otero (2013:69, (73) and (74)) points out, this choice appears to be determined by whether the /i/ in question is stressed in the stem form from which a more complex form is derived. We can see that the /i/s in the forms related to limpiar ‘to clean’ in (4) are consistently syllabified as [j], whereas those related to ampliar ‘to extend’ in (5) are consistently syllabified as [i]. The difference correlates with the fact that the /i/ is unstressed in the stem form limpia but stressed in the stem form amplia.Since the syllabification of /i/ as [i] in (5b) seems to be cyclically transmitted from the stress-conditioned hiatus in (5a), we conclude that stress must have been assigned to /i/ on the v cycle. But this entails that the spell-out of v does trigger a cycle of stress rules, contra the assumption we needed in order to correctly derive cont-a-dór in derivation (3). Paradox!Bermúdez-Otero offers the following summary of the problem (2013:71, adapted from his (78)):Bermúdez-Otero’s answer is that conta- and cuenta- are stored as independent lexemes that compete to realize the stem of the verb contar. The competition between these stems is resolved by the stemlevel phonology in the second cycle, once stem-level affixes like -ble and -dor are on the scene. Bermúdez-Otero argues that this is the only way to avoid the cyclicity paradox identified in the previous paragraph, and from this he concludes that the stem storage approach is not only viable, but necessary.3 In the next section, I challenge this conclusion.I begin by noting something about the logic of the argument from /i/ syllabification embodied in (6). The force of this argument depends heavily on the ‘‘transmission’’ we see in (5) being purely a matter of cyclicity and not, for instance, something special about the verbal domain.4 Only then can it be maintained that the syllabicity of /i/ in (5b) is directly being caused by its being stressed in (5a). Otherwise, rather than stress being the cause (via cyclicity) of the syllabification facts, it could be some independent factor about /i/ in combination with certain facts about verbs that leads to /i/’s being stressed in (5a) and being syllabified as a nucleus in (5b).It turns out that evidence exists that morphosyntactic category is relevant here. The key data have been discussed by Cabré and Prieto (2006) and by Cabré and Ohannesian (2009). As Cabré and Prieto (2006:222) put it, ‘‘contrary to what happens in verbal paradigms, underlying stress does not crucially affect the vocalic outcome in derived nominal forms. Conversely, deverbal forms can maintain the hiatus outcome for conservative speakers . . . .’’5 As shown in (7) and (8), syllabification of /i/ as [i] only takes place where the base of derivation is verbal; in noun-adjective and adjective-noun derivations, a stressed /i/ in the base form is syllabified as [j] if the stress moves to a later vowel.6If the syllabicity of /i/ in derived forms were determined by /i/’s being stressed on an earlier cycle, there would be no difference between the derived forms in (8) and those in (7): both should have syllabic [i]. Since the denominal forms surface with [j] regardless of whether or not /i/ is stressed in the base form, we must conclude that the syllabicity of /i/ is not purely cyclically determined. Instead, the correlation between /i/’s being stressed in one form and being syllabic in derived ones must be accounted for in terms that mention the categorial difference between verbs and nouns/adjectives in some way.Once this fact is recognized, the problem of the missing cycle is dissolved, and it becomes possible to analyze both diphthongization and /i/ syllabification without appealing to stem storage. The next section is devoted to showing how this is possible.I follow Harris (1969) and Roca (1997) in assuming that the difference between syllabic (and therefore stressable) /i/s and nonsyllabic ones is present underlyingly: some /i/s are underlyingly linked with a nucleus, whereas others are not.8 This difference will be represented in underlying forms via underlining, so that the root in the form limp[j]a ‘he cleans’ will be underlyingly /limpi/, but the root in the form ampl[í]a ‘he extends’ will be underlyingly /ampli/. On the present approach, this underlying difference is the factor that independently gives rise to the stress facts in verbs and to the syllabification facts in forms derived from verbs. To account for the verb stress facts, I will adopt Oltra-Massuet and Arregi’s (2005) stress system, which is set against the background of the parameterizable stress system of Idsardi (1992), Halle and Idsardi (1995).9 The part of Oltra-Massuet and Arregi’s rule system that is relevant here is as follows. I will assume that these stress rules are triggered once TP is spelled out (which will usually mean on completion of the CP phase).10Sample derivations are given in (10), showing that whether or not /i/ is stressed in forms derived from /limpi/ and /ampli/ follows from the postulated underlying difference between the two, given the general rule system in (9). For motivation of the syntactic decomposition of the Spanish verb presupposed here, see Oltra-Massuet and Arregi 2005.11The syllabification facts in forms derived from verbs will also follow so long as we assume that /i/ is syllabified separately from a following vowel only if underlyingly specified to do so; otherwise, it is syllabified as a glide.What makes nonverbal categories different? Recall that we are assuming that the spell-out of v does not trigger a cycle of stress rules, whereas the spell-out of nonverbal little-x’s does (this is central to the DM account of the lack of diphthongization in deverbal nominals like cont-a-dór ‘counter’). It is natural, then, that only stress rules associated with these nonverbal categories can be lexically specific in nature, and indeed we find that, unlike verbs, nonverbs show a variety of lexically specified stress patterns.To analyze these patterns, I will again follow Oltra-Massuet and Arregi’s (2005) system, but with one adjustment to accommodate cyclic stress assignment. Bringing in cyclic stress assignment is crucial in order to explain, for instance, how the diphthong in the adjective viéjo ‘old’ (cf. the root-derived noun vej-éz ‘old age’) is cyclically transferred to the deadjectival verbal form a-viej-ár ‘to make old’ (see also footnote 2). Specifically, I will remove the stipulation that only the highest derivational little-x’s trigger the insertion of right parentheses, and I will add a Conflation rule to the system (Halle and Vergnaud 1987). In addition, I restrict the Clash Avoidance Constraint so that it regulates clashes within the same cycle and does not apply across cycles. All of the rules that will be relevant here are listed in (12).I now give sample derivations involving the pair nav[í]o ‘ship’ and nav[j]éro ‘ship owner’ from (8), as well as the adjective ámpl[j]o ‘broad, ample’, which has initial stress and syllabifies /i/ as a glide, even though its root /ampli/ has an underlyingly syllabic /i/. The exceptional stress pattern is derived via the presence of a right bracket to the left of the final vowel in the underlying form of the root.We come at last to the reason why /i/s with an underlying nucleus do not survive in forms derived from nonverbs, even when the /i/ is stressed in the base form. For the case of ámpl[j]o, this will follow from a general rule of the phonology that deletes the nucleus of an /i/ in hiatus contexts if that /i/ is not tonic or immediately pretonic. Data from Cabré and Prieto 2006:18 show that such a rule is needed anyway, even in the verbal domain, to account for verbal forms in which stress occurs further to the right than the theme vowel (compare am.pl[i].- á.mos ‘we extend’ with am.pl[ j]a.ré.mos ‘we will extend’). The more interesting case is the contrast between nav[í]o ‘ship’ and nav[j]éro ‘ship owner’ on the one hand, and ampl[í]a ‘he extends’ and ampl[i]- áble ‘extendable’ on the other. I suggest the following rule, which applies after Conflation on stress cycles triggered by little-x and deletes the nucleus associated with an unstressed high vowel when another vowel follows. This denuclearized high vowel will subsequently be resyllabified as a glide. This rule coexists with other glide denuclearization processes in Spanish, which differ in their conditioning environments (and in their ordering relative to other processes of Spanish phonology). (For more detailed studies of glide denuclearization and its various subcases, see Harris 1969, Hualde 1991, Harris and Kaisse 1999, and Colina 2012.) Importantly, the rule in (14) is barred from applying in v domains; this is probably connected with the fact that v is not cyclic in Spanish phonology.The fact that (14) does not apply in v domains accounts for the difference between ampl[i]áble (with hiatus) and nav[j]éro (with gliding), as can be seen in (15).In this squib, I have shown that the problem of the missing cycle in Spanish phonology is not a problem, because the missing cycle in question is, in fact, missing across the board (v itself does not trigger a cycle of stress rules in Spanish). The syllabification of /i/ as [ j] or [i] appeared to indicate the contrary, but I have shown that cyclic transfer cannot have anything to do with this phenomenon. If it did, there would be cyclic transfer of the syllabic [i] in navío to nonverbal derived forms, but this is not what happens: nav[j]éro (Cabré and Prieto 2006, Cabré and Ohannesian 2009). I offered an analysis of this phenomenon in terms of differences in the morphophonology associated with particular lexical categories (Smith 2001, 2011). Since the syllabification of /i/ is not a cyclic phenomenon, the paradox associated with the problem of the missing cycle dissolves, and so too does the argument that stem storage is necessary to circumvent it (paceBermúdez-Otero 2013).
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