6.2.1 Within Iquito: Stress and Tone

Iquito is described as a low-density tonal language that also displays stress (Michael Reference Michael2011). The two prosodic components are identified through distinct acoustic correlates, namely pitch for tone and post-tonic consonant lengthening for stress. The tonal system is privative, employing a H/∅ pattern. That tone is contrastive is indicated through the existence of minimal pairs where stress remains constant, but the pitch peak is found on different positions, e.g. [máˈʃiku] ‘raft’ versus [maˈʃíku] ‘bird species’. Although largely independent from one another, tone and stress interact in the sense that every prosodic word contains at least one High tone (henceforth simply referred to as ‘tone’). In addition, both make reference to the colon κ. The current section presents the relevant facts. Note that the present chapter primarily focuses on stress and supplements the discussion with the tonal data when the latter are relevant. However, as the tonal facts are not yet fully understood, no formal analysis is offered at this time.

Iquito forms leftward bimoraic trochees (H) or (LL) with rightmost primary stress. That feet must be bimoraic rather than bisyllabic becomes evident in (1). To distinguish clearly between stress and tone, the following notation will be used: ˈ = primary stress, ˌ = secondary stress, ́ = H tone, H = heavy syllable, L = light syllable. In what follows, tone will only be indicated if relevant to the discussion, otherwise it will be omitted.

Normally degenerate (L) feet are not admitted, as (2c, e) clearly illustrate, but this ban is not absolute. The data in (3) present relevant examples.

Michael (Reference Michael2011:58) states that ‘a single light syllable at the left edge of the word is parsed into a degenerate foot in precisely those cases in which doing so results in a dipodic prosodic word’. In other words, degenerate feet are only justified in order to obtain a colon κ; in longer words like (2c) or (2e) where the colon-satisfaction has already been achieved through binary feet, the presence of a degenerate foot is not legitimized.

Notice that degenerate feet are only allowed at the left edge of the word, never at the right, hence forms such as *[(ˌH)(ˈL)] are disallowed. A HL sequence word-finally will instead receive a single stress on H, presumably creating a ternary foot (ˈHL), as in (4). While this is Michael’s chosen parsing, it is not however the only possibility; compatible with facts would also be a metrification that leaves more syllables unparsed, yet conforms to the bimoraic requirement, e.g. [(ˈH)L] or [(ˌL)(ˈH)L].

Beyond stress, the colon emerges as the domain in which lexical and metrical tone are incompatible. Since every Iquito word has to have at least one tone, in the absence of a lexical tone (T_L), a metrical tone (T_M) is inserted on the head of primary stress.

Metrical and lexical tones cannot coexist. Thus, when a prefix like /ki-/ with an input T_L is added to (5a), the T_M on ru no longer arises. Instead, only the lexical one on the prefix surfaces (6a). In longer forms however, both types of tone can coexist (6b). What at first blush looks puzzling easily dissolves once one realizes that the seemingly contradictory distribution is regulated by the presence of cola and the tones within or across them. In particular, T_L and T_M cannot coexist when they belong to the same colon, but they can across cola.

This co-occurrence prohibition does not affect lexical tones. While morphemes with lexical tones are not very frequent, it is possible to combine them. Whether the tones belong to the same colon or not is immaterial. Lexical tones are always preserved.

The distribution of lexical and metrical tones within and across a colon is summarized in (8). Still, many aspects in tone distribution and its interaction with cola are not yet understood.Footnote ² Hopefully, future fieldwork should help clarify the situation.

6.2.2 Beyond Iquito

The colon has occasionally been implemented elsewhere in the literature. Some of the more prominent examples follow. In Hungarian (Hammond Reference Hammond1987, but see Blaho & Szeredi Reference Blaho, Szeredi and Washburn2011), primary and secondary stress are associated with heads of cola, unlike tertiary stress. Explicit and more extensive reference to the colon is made in Green’s (Reference Green1997) dissertation, where the distribution of stresses in Munster Irish, East Mayo Irish, and Manx is claimed to be regulated by cola. In addition, Green (Reference Green1997; see therein for references) also endorses the colon for various other languages such as Passamaquoddy, Eastern Ojibwa, Asheninca, Garawa, and Neo-Štokavian.

Besides stress, cola seem to play a role in root/word-size restrictions as well as in tonal phonology. According to Ola (Reference Ola1995), several Benue-Congo languages, such as Kakanda, Ebira, Idoma, and Yoruba, set a maximally dipodic, i.e. a colon, size for roots. In Yoruba in particular, the maximum is also evident in diminutives, clefted nouns, and prefixes. A comparable, but quadrimoraic, maximum arises in Bella Coola, a language of the British Columbia (Bagemihl Reference Bagemihl, Czaykowska-Higgins and Kinkade1998; Topintzi Reference Topintzi2010). A similar requirement appears in Japanese hypocoristic formation with the suffix –tyan; for hypocoristics of long names (Poser Reference Poser1990:88), two foot-based templates are available: one with 2μ and one with 4μ. Thus, the base name gisaburoo can be truncated as gii-tyan or gisaburo-tyan and kenzaburoo as ken-tyan or kenzabu-tyan, respectively. A secret language used in the entertainment industry also activates a two-foot template (Poser Reference Poser1990:95–96); there, foot transposition typically occurs accompanied by either shortening of a form if it exceeds four moras, e.g. maneezyaa ‘manager’ becomes (zyaa)(mane) deleting one extra mora, or lengthening if the number of moras is not sufficient, thus mesi ‘meal’ becomes (sii)(mee).

Moving to the tonal domain now, in languages such as Kuria (Marlo et al. Reference Marlo, Mwita and Paster2013) or Matumbi (Odden Reference Odden, van Oostendorp, Ewen, Hume and Rice2011), a H-tone is assigned on the fourth mora, as shown next.

While only some of the aforementioned accounts (e.g. Marlo et al. Reference Marlo, Mwita and Paster2013) consider the possibility of reanalysing these facts by means of cola, e.g. ‘assign a H-tone at the right edge of a colon’ instead of ‘assign a H-tone on the 4th mora’, this route is obvious and as Marlo et al. (Reference Marlo, Mwita and Paster2013) acknowledge, advantageous, as it requires no counting beyond the usually accepted limit of two.Footnote ³ An obvious alternative, and one that several authors actually allude to, as indicated previously, would be reference not to cola but to two feet, rather than just one. This would capture many of the facts above and would be compatible with counting considerations. Anticipating the discussion in Section 6.4.2, I claim that introduction of the colon – in at least some cases – is to be preferred since it offers better empirical coverage, superior analyses, and prediction of (attested) patterns that the dipodicity explanation fails to produce.

Before moving on to the analysis of Iquito by means of cola and the comparison across different OT accounts, it is at this point appropriate to address a concern an anonymous reviewer has raised that could jeopardize employment of the colon as a constituent. Consider Bella Coola for a moment, a language which, as mentioned, places a quadrimoraic maximum on roots. The reviewer observes that if we were to understand this maximum in terms of cola, then a string of the type [LHL], which satisfies maximality, should be interpreted as a colon footed – using trochaic feet for illustration – either fully as [(L)(HL)] or as [(L)(H)L], admitting both a degenerate foot and an unparsed L. But either representation makes some incorrect prediction; if (HL) feet are admitted, as the first footing suggests, then it should be the case that a string such as [(HL)(HL)] should also be possible by virtue of being a colon. Such a form though does not emerge, since it actually contains six moras. The same problem occurs with the other footing too; a form like [(H)(H)L] should be allowed, and yet it is not. Moreover, in Matumbi, tonal assignment at the right edge of a colon seems to violate Syllable Integrity (Prince Reference Prince1976; Hayes Reference Hayes1995:50, 121–123), the principle which prohibits syllable splitting in foot construction. For example, the form [ukeeŋgéembe] above would be footed as [{(u.ke)(eŋ.gé)}_κem.be] forcing at least the syllable [keeŋ] to straddle two feet.

However, both problems – as the reviewer also notes – disappear once we admit the possibility that feet in such languages are built directly over moras, not over syllables. Such a move would then allow us to build cola in Bella Coola of exactly 4μ and it would downgrade Syllable Integrity from an inviolable principle to a strong tendency. The latter is in fact the position advocated by Buller, Buller and Everett (Reference Buller, Buller and Everett1993) and Everett (Reference Everett1996) on Banawá, Blevins and Harrison (Reference Blevins and Harrison1999) on Gilbertese, Cairns (Reference Cairns2002) and Cairns and Raimy (Reference Cairns, Cairns, Raimy, Raimy and Cairns2009) on Southern Paiute, among others. Note that although it has been possible to reanalyse some of the relevant facts in a manner compatible to Syllable Integrity, e.g. Hyde (Reference Hyde2007a) on Banawá, in other cases such reanalysis has proven inadequate (cf. Cairns Reference Cairns2002 and Cairns & Raimy Reference Cairns, Cairns, Raimy, Raimy and Cairns2009 who challenge Hayes’s Reference Hayes1995 account of Southern Paiute). Thus, Blevins and Harrison (Reference Blevins and Harrison1999:219) end up treating Syllable Integrity as a violable constraint – defined as σ-int: Align the {R/L} edge of a foot with the {R/L} edge of a syllable – which if sufficiently low-ranked, produces overt violations of the principle. Presumably, that would also occur in Matumbi.

But, even if all the cases that challenge Syllable Integrity were subject to reanalysis, the κ-analysis outlined earlier might still remain unscathed. This is because Syllable Integrity is grounded on the idea that ‘stress is always perceived as stress on a syllable, not as stress on some smaller portion of a syllable’ (Hyde Reference Hyde2007a:262–263), but the Bella Coola or the Matumbi facts – perhaps crucially – refer to prosodic phenomena other than stress, namely root maximality and tone. We might thus be able to maintain Syllable Integrity as an inviolable principle with regard to to stress, but not with regard to general prosody.Footnote ⁴

What this suggests in turn is the possibility of footing in the absence of stress or the existence of additional foot structure alongside metrical foot structure (due to stress). The clearest example of a language of the former type is perhaps Japanese (Poser Reference Poser1990), whose accentual system is tonal in nature. Quite spectacularly, Japanese, a language that as we have seen already lacks stress, nonetheless makes use of rhythmic bimoraic feet for a number of prosodic phenomena, such as hypocoristic formation, reduplication, secret languages, and so on. Leben (Reference Leben2001) also clearly points to this type of language, when in his discussion of Hausa and Bambara, he argues for the existence of tone languages that offer evidence in favour of tonal, rather than metrical, feet. On the other hand, the second type of language can be illustrated by Serbo-Croatian, a pitch-accent language where tone docks on a position that is metrically defined. This leads Zec (Reference Zec1999) to claim that next to trochaic feet of the type (σ_μμ) and (σ_μ σ_μ), the language also employs feet of the type (σH_μμ) and (σH_μ) when H tone – associated with the first mora – is involved.

While the concept of ‘tonal feet’ has been used in some shape and form elsewhere (also see Zec Reference Zec1999; Kubozono Reference Kubozono, Miyagawa and Saito2008; Zec & Zsiga Reference Zec, Zec and Zsiga2010), there is no consensus as to how tonal feet are to be represented, nor as to how they should interact with metrical feet. The topic is complex and rather understudied (but see Leben Reference Leben2001 for some references) and certainly beyond the scope of the present work. What is of interest to us however is the implication this has; if multiple types of feet exist (metrical, tonal, prosodic-templatic), then it should not be surprising if cola can have access to or refer to any of them. Naturally, it remains to be seen how exactly this effect is generally achieved as well as what kind of interactions are allowed, both topics for future research.

More generally, and as will be discussed in more detail in Section 6.4.2, this chapter is in line with recent approaches which acknowledge the role language-specificity plays in prosodic universals, either in terms of imposing language particular (instead of universal) prosodic hierarchies (Schiering et al. Reference Schiering, Bickel and Hildebrandt2010) or by suggesting that (the same) prosodic categories may be active to different extents depending on the language (Hyman Reference Hyman2011). It seems that in the present context, either approach will do, so I will not take any specific stance. For current purposes it suffices to point out that such views enable us to accept the data of e.g. Bella Coola maximal quadrimoraic roots as evidence for the existence of κ as a prosodic category active in the language, without necessary implications about the prosodic categories below and above it, for which we have no actual evidence.

6.3.1 Harmonic-Serialism-cum-standard-assumptions

The first account to be considered here is also the one claimed to be the most successful. At its core, it implements the HS stress account of Pruitt (Reference Pruitt2010), dubbed IFO (Iterative Foot Optimization). Details about Harmonic Serialism can be found in McCarthy (Reference McCarthy2008a, Reference McCarthyb; Reference McCarthy2010a), but for current purposes, it suffices to spell out the basics, namely that HS is a serial version of OT that involves multiple iterations. Like classic ParOT, it employs a single constraint ranking throughout (in contrast to e.g. Stratal Optimality Theory), but instead of a single /input/ → [output] mapping, it allows multiple sequential mappings of this type, the so-called iterations. In this framework Gen is more constrained in the sense that beyond the faithful candidate, the remaining candidates may only exhibit a single change per iteration compared to the input, a property dubbed gradualness. For instance, for an input such as /lab/, possible outputs like [labi] or [lap] are acceptable, but not one like [lapi], since it exhibits multiple changes, i-epenthesis and a featural change. Notice that in classic ParOT, the latter candidate would be acceptable. It will become evident that exactly this property will allow the HS analysis of Iquito to fare better than the corresponding ParOT one. The repeated procedure is completed with convergence, that is, when an output is the same as the most recent input, a fact that designates such output as the final output.

Some additional background from Pruitt (Reference Pruitt2010) is also needed to follow the proposed analysis. Gen is assumed to only produce maximally disyllabic feet and create metrical structure which cannot be altered or removed (strict inheritance). Consequently, feet like (LLL) cannot even be generated, hence they are not considered at all. FtBin requires that feet are binary at some level of analysis (μ, σ) (Prince & Smolensky Reference Prince and Smolensky1993/Reference Prince and Smolensky2004), effectively permitting feet that are minimally bimoraic and maximally disyllabic.

The only additional ingredient we need to capture Iquito is the constraint Have-κ, which states that each word must contain (at least) a colon. The simple ranking Have-κ >> All-Ft-R, FtBin generates all the desirable results. For ease of presentation, abstract examples will be used throughout with L(ight) and H(eavy) syllables. Tone is omitted. The patterns our analysis will need to capture are summarized in (10).

Starting from the simplest /LL/ case, no candidate in (11) can satisfy Have-κ, since none contains minimally two feet. And yet, (11a) wins, as it fully satisfies the lower-ranked constraints. On the second iteration – for which no tableau is shown – convergence is achieved resulting in (11a). Crucially, and unlike ParOT, no candidate [(ˌL)(ˈL)] for input /LL/ or for /(ˈLL)/ – after the first iteration – can be considered. In the first instance, gradualness is violated, since construction of two feet constitutes two changes (hence the name IFO); in the second case, strict inheritance (and possibly, also gradualness) is violated, as the metrical structure already built is altered.

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First Iteration: /LL/ → (ˈLL)

     Convergence on Second Iteration, i.e. (ˈLL) → [(ˈLL)]

For input /LLL/ again only a single foot can be constructed at the first iteration favouring (12b), which presents the best possible structure in terms of alignment and binarity. On the second iteration however, construction of a second, albeit unary, foot is licensed, because by doing so, the dominant colon-constraint can now be satisfied. Thus, (12b) wins and produces convergence on the next iteration.

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First Iteration: /LLL/ → L(ˈLL)

Second Iteration: /L(ˈLL)/ → (ˌL)(ˈLL)

     Convergence on Third Iteration

Jochen Trommer (p.c) observes that this tableau raises an issue as to what counts as a step. The idea is that an output such as [{(ˌL)(ˈLL)}_κ] from input /L(ˈLL)/ potentially violates gradualness, as it constructs both an additional foot, as well as a colon. If that is the case, then the winner should be [L(ˈLL)], which of course is wrong. Assuming this reasoning is correct, Trommer suggests that a way-out is the use of a constraint such as Wd=2Ft ‘a word contains (at least) two feet’ instead of reference to the colon. While this is possible, it is not plausible, since the lack of colon makes it more difficult to account for tone placement in languages such as Matumbi, discussed in (9) previously.

The point however remains; for the analysis to work as suggested, construction of a colon should not count as an independent step. I argue that this indeed is the case. In fact, this falls out from recent investigations of the structure of Gen. McCarthy (Reference McCarthy2010b:11Footnote ⁶) claims that ‘Gen determines how much and what kind of information is available to Eval at each step of the derivation. Since there is no look-ahead, all of the information necessary to determine whether the right candidate wins has to be available at the point where it is crucial for that candidate to win’. He thus permits instances where Gen must receive a broader understanding so as to allow for two processes to apply in one-go, cf. syncope and resyllabification in Arabic, as well as for cases where Gen must be more limited, so that a single, rather than multiple, application of an operation is admitted.

Iquito is interesting as it simultaneously displays both possible modifications of Gen. In line with Pruitt (Reference Pruitt2010), it parses one foot at a time (limited Gen). This has proved of paramount importance in the consideration of candidates for a /LL/ input, where a candidate like [(ˌL)(ˈL)] cannot be considered in the first iteration. At that point [(ˈLL)] wins. Due to Strict Inheritance, this parsing cannot be undone, effectively banning [(ˌL)(ˈL)] from being considered as a winner. In the case of /LLL/ inputs on the other hand, [L(ˈLL)] wins at the first iteration. Next, the addition of a second (here, degenerate) foot applies, leading to the form [(ˌL)(ˈLL)], whose bipodicity fulfils the prerequisite of having a colon. The latter’s formation in the same step (broader Gen) ensures [{(ˌL)(ˈLL)}_κ] is the winner.

A further remark that is presently relevant is McCarthy’s (Reference McCarthy2010b:12, 26) observation that Gen is limited to a single unfaithful operation at a time, but places no limit to the number of faithful operations. In the case McCarthy discusses, resyllabification is a faithful operation, since it never appears to be contrastive in a single language. While the contrastiveness of feet, let alone of cola, is less clear, it could potentially be argued that colon formation is also a faithful operation. Foot-parsing on the other hand has been assumed by Pruitt (Reference Pruitt2010) to occur serially, pointing to a non-faithful contrastive operation. Evidence for this idea can be found in the existence of underlying foot structure in lexically stressed languages or the presence of both trochaic and iambic feet in the same language (as argued for Larike or Wichita in Goedemans & van der Hulst Reference Goedemans, van der Hulst, Dryer and Haspelmath2013).

Assuming that colon formation occurs in one step alongside (single-)foot parsing, we may now return to the remaining cases. Degenerate feet also appear in [(ˌL)(ˈH)] forms. Their production is comparable to the one in (12), the only difference being that an additional constraint, informally stated here as *(ˈLH), rules out a candidate like (13a) in the 1st iteration. A (LH) trochee seems very unlikely anyway. Thus, the constraint in question should not be surprising. The exact location of this constraint is unclear. Its present placement is however sufficient for illustration purposes.

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First Iteration: /LH/ → L(ˈH)

Second Iteration: /L(ˈH)/ → (ˌL)(ˈH)

     Convergence on Third Iteration

Tableau (14) demonstrates the lack of a degenerate foot. As before, during the first iteration, all possible candidates violate Have-κ. The chosen winner at this stage merely constructs a binary left-headed foot at the right edge of the word. On the second iteration, formation of a second foot is welcome, as it offers satisfaction to Have-κ. Unlike the previous cases though, the construction of a degenerate foot on the third iteration is no longer justified. The colon-constraint has already been satisfied, so there is no trigger for a unary foot anymore. Foot-alignment and foot-binarity will thus opt for a non-fully parsed winner.

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First Iteration: /LLLLL/ → [LLL(ˈLL)]

Second Iteration: /LLL(ˈLL)/ → [L(ˌLL)(ˈLL)]

Third Iteration: /L(ˌLL)(ˈLL)/ → [L(ˌLL)(ˈLL)]

     Convergence on Fourth Iteration

It is in cases like this one where the power of the step-wise analysis and the gradualness hypothesis is unravelled. The distinction in the behaviour of odd-parity words that exclusively contain light syllables (among other instances), with the 3σ-ones allowing for degenerate feet versus the 5σ-ones which ban them, comes naturally under the idea of the colon as the triggering mechanism of degenerate feet and the serial foot-construction. In a global ParOT account, as will be shown next, this is not the case. Because this approach can ‘look ahead’ it will produce more degenerate feet than actually attested, unless prevented by another constraint that blocks such structures.

Finally, the form /HL/ surfaces as [ˈHL], which, recall, may be interpreted as [(ˈHL)] or as [(ˈH)L]. Our current analysis promotes the former, i.e. (15c). As a minor point, note that the winner violates the constraint *ˈHL (not shown here) – after Pruitt (Reference Pruitt2010) – which consequently has to be low ranked.

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First Iteration: /HL/ → (ˈHL)

     Convergence on Second Iteration

For reasons of space, remaining patterns such as (ˌLL)(ˈLL) or (ˌL)(ˈHL) are not displayed here, but the interested reader should be able to confirm that the proposed analysis also correctly produces them.

6.3.2 ParOT-cum-standard-assumptions

An analysis on the other hand that utilizes exactly the same constraints as in Section 6.3.1, but which is set in the classical Parallel OT mechanism, only partially delivers, even when various relevant modifications are applied in the way constraints are ranked or are to be understood. The problem can be resolved if an additional constraint is added to this set. While this eventually captures the empirical facts, I will argue in Section 6.4.1 that it does so in a less elegant way than the HS account. In what follows, the incorrectly predicted winners are surrounded by the symbol ✦ (where applicable) and marked with in tableaux, whereas correct winners appear on the left side.

The first analysis to be considered adopts the ranking in Section 6.3.1, the only difference being that left rather than right-foot-alignment is employed. A summary of the (in)correct results is laid out in (16). The tableaux in (17) focus on the wrongly generated patterns.

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/LL/ → (ˈLL)  ✦ *(ˌL)(ˈL) ✦

/HL/ → (ˈHL)  ✦ *(ˌH)(ˈL) ✦

The problem, as hinted at before, is that global OT overgenerates; by looking-ahead, it produces more degenerate feet than are actually allowed. HS sidesteps this problem, because it can only parse one foot at a time, thus in words of the /LL/ type, only <(L)L, L(L), (LL)> are viable candidates, but crucially no *[(L)(L)]. This latter option is perfectly feasible in ParOT and due to global evaluation, Have-κ will wrongly pick it out as the winner. The same applies to /HL/ words.

An anonymous reviewer suggests that a somewhat different ranking – shown in (18) – solves the problem, but this is not quite the case. To his/her original suggestion, I have also added consideration of Parse-σ, as it slightly improves the results. This modification eventually fails too, which is why I have chosen not to present it in the main text in any detail. The interested reader may consult the Appendix for further discussion.

A different route to the problem is to suggest that rather than modifying the constraint ranking, we could simply slightly alter the definition of constraints, whose understanding is not uniform across the literature. In particular, we can interpret FtBin as enforcing strictly bimoraic feet, i.e. 2μ-FtBin.Footnote ⁷ In fact, this produces even worse results. Using the ranking in (18) – the most successful in our ParOT examination so far – not only do we derive the wrong form *[(ˌLL)(ˈLL)L], but others too, such as *[L(ˈH)L] instead of [(ˌL)(ˈHL)] or *[(ˌH)(ˈL)], as depicted in (19).Footnote ⁸

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/HL/ → (ˈH)L or (ˈHL)  ✦ *(ˌH)(ˈL) ✦

A third strategy yet, and one that two of the reviewers have suggested, involves the addition of a constraint to the constraint set. As the reader will have noticed through examination of (16), the problematic winners for this account are [*(ˌL)(ˈL)] and *[(ˌH)(ˈL)], whereby the primary stress belongs to a degenerate foot. So, one should seek to somehow eliminate them. There are at least two ways to do that. In the light of facts which suggest that in some languages primary stress (or head feet) exhibits special behaviour, various approaches pose primary-stress-specific constraints (e.g. McGarrity Reference McGarrity2003; Pruitt Reference Pruitt2012); it is thus reasonable to consider a constraint that bans degenerate head-feet. Such a constraint has been suggested in McCarthy (Reference McCarthy2008a:519) in terms of FtBin-σ_head.Footnote ⁹ Alternatively, one can employ a version of NonFinality that militates against stressing light syllables, while allowing for final stress on heavy syllables. Because such a constraint is discussed in the next section anyway, I will utilize the former constraint for illustration purposes, but the concerns raised in Section 6.4.1 should hold equally well for both.

Adopting the constraint ranking achieved in Section 6.3.1 and complementing it with the high-ranking FtBin-σ_head produces the desirable results, as illustrated by means of a few representative tableaux that follow. The enforcement of a single bimoraic foot in (20) is due to the newly introduced constraint, which explicitly bans a degenerate foot in primary stress position. Crucially, it has to be ranked above Have-κ. This top-most constraint is also responsible for the correct production of [(ˈHL)] instead of *[(ˌH)(ˈL)].Footnote ¹⁰

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/LL/ → (ˈLL)

In (21) the winner has enough structure to not only form a binary head-foot and thus avoid violation of FtBin-σ_head, but to also construct a degenerate foot with secondary stress, as imposed by the high ranking Have-κ. The low ranking binarity and alignment constraints reveal their power in longer words. In (22), all reasonable candidates satisfy the two dominant constraints and it is the job of the lower ones to decide in favor of (22c) that lacks degenerate feet.

(21)

/LLL/ → (ˌL)(ˈLL)

(22)

/LLLLL/ → (ˌL)(ˈLL)

6.3.3 ParOT-cum-non-standard-assumptions

The preceding discussion has shown that in ParOT a slight enrichment of the constraint set compared to the one assumed in the HS analysis is required, so that it captures the Iquito facts. In Section 6.4.1, I will claim that such enrichment is not purely superficial. Instead, it highlights a difference between the standard ParOT versus HS model that renders the latter technically more elegant. Because of that conclusion, it is worthwhile to consider another alternative within the ParOT paradigm. A good candidate for that is Brett Hyde’s model (Reference Hyde2002, Reference Hyde2007b, Reference Hyde2012), since it constitutes a comprehensive theory of stress relying on somewhat different principles than those previously employed.

Before proceeding with the particulars of the analysis, some preliminaries are in order. Since gridmarks are fundamental in this framework, I will call this theory GM for ease of reference. The basic architecture of GM contains both inviolable conditions in Gen as well as standard violable constraints. The former include:

While most of these are self-explanatory, some additional remarks will appear as the discussion unfolds. At the outset, a property needs to be mentioned that is alluded to through (23c). Besides gridmarks, independent reference to heads is made, which are represented through vertical lines. Moreover, intersecting and stressless feet are admitted.

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Intersecting feet in Hyde (a–c: in Hyde 2002: 317; d in Hyde 2002: 324, ex. 14a)

For example, (24a) contains two trochaic feet over three syllables. Stress is on the first and second syllables. These positions are also heads. An intersection appears on the second syllable since it is at the same time the tail of the first foot (diagonal line), as well as the head of the second foot (vertical line). Examples (24b, d) are representationally identical to (24a) with the exception that there is no stress on the second syllable (b) or the first syllable (d), hence stressless feet are permitted, indicating that there is no one-to-one correspondence between stress and feet in this framework. Example (24c) contains one trochaic and one iambic foot, with stresses on the first and the third syllable, respectively. The second syllable is a tail for both feet. Note that (24a, d) also present gridmark sharing on the second syllable.

Before moving on to the Iquito analysis, we need to present the constraints that will be administered. Example (25) states just the subset of constraints pertinent to us presently. Informal versions are given here. The interested reader should consult Hyde (Reference Hyde2002) for the formal definitions.

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/LL/ → ˈLL  correct: establishes NonFinal >> Have-κ

Starting with the simple [ˈLL] case, the ranking NonFinal >> Have-κ, Hds-R, *Clash is sufficient, ensuring that a single stress on a binary trochaic foot at the left edge of the word will be the winner. To produce the degenerate foot found in a /LLL/ sequence, the role of Have-κ has to be promoted, so that it dominates the Hds-R and *Clash constraints.

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Candidates (27b, d) consist of intersecting feet, whereas (27a, c) prefer a unary foot on the left edge in accordance to FootCap (23d). Also (27a, b) contain two stresses, as opposed to (27c, d) that present just one. NonFinal is of no importance here, so it should fall onto the relative high-ranking Have-κ to eliminate the single-stressed (27c, d), as desired. For this to happen, Have-κ is to be crucially understood as referring to having two prominences per word (gridmarks), rather than two particular prosodic constituents, i.e. feet, otherwise (27c, d) – in the oval – would wrongly qualify as winners. Notice that even if the constraint Map Gridmark were to be included in the ranking (cf. (30)), it would still not suffice to exclude both losing candidates. It would rule out (27c) by virtue of the stressless first foot, but it would still not eliminate (27d), as it conforms to the definition of Map Gridmark: ‘A foot-level gridmark occurs within the domain of every foot’ (Hyde Reference Hyde2002:319). In fact, Hyde’s (Reference Hyde2002:324) candidate (14a) is identical to (27d) and is considered to fully satisfy Map Gridmark. Consequently, Have-κ – under the interpretation of requiring two prominences per word – is indispensable in producing (27a, b), both of which empirically correspond to the winner. To my understanding, there is no constraint in Hyde’s system that would choose one over the other, hence no single winner can be chosen, offering ambiguity in the representation.

To correctly generate the [ˌLˈH] and [ˌLˈHL] forms, an amendment to NonFinal must be made, such that final stress is banned on L but not on H syllables. Such a provision is made (cf. Hyde Reference Hyde2007b:300) through the constraint NonFin (X_F, X_μ, σ) ‘No foot-level gridmark occurs over the final μ-level gridmark of a σ’, which effectively allows stress on final H, under the idea that this version of NonFinal penalizes prominence on the second (and final mora) of a heavy syllable, but the assumption here is that stress docks onto the first mora of H. This version of NonFinal allows all of (a–c) to escape violation of that constraint, leaving it to Have-κ to decide between some of the candidates. As before, single-stressed options are ruled out and the remaining ones fare equally well. Once more, variability in the representation emerges.

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/LH/ → ˌLˈH        correct result with *variability* in representation

As for the longer words that consist of light syllables throughout, the situation is clear-cut. However, some constraints need to be added to the mix, to generate the right results. The tableaux are presented here for completeness, but for reasons of space they are only briefly discussed.Footnote ¹¹

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/LLLL/ → ˌLLˈLL       correct result

Alternating rightward trochees with two prominences (29a) are correctly selected over those with a single prominence (29c) because of Have-κ, while the addition of PrWd-L ensures that (29b) will not be rendered an equally plausible winner as (29a).

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/LLLLL/ → LˌLLˈLL    correct result

/LLLLL/ inputs correctly map to a winner that only contains two stresses, as in (30b). A degenerate foot without prominence (30a) can be avoided if Map-GM is appropriately ranked, whereas (30d) – a double-headed intersecting foot – is wiped out by independently high-ranked PrWd-L. The remaining candidate (30c), i.e. the true contender in terms of additional stresses, is eliminated due to a low-ranking *Clash violation.

6.4.1 Evaluation of Analyses

To summarize, Section 6.3 has explored three alternatives couched within OT for the analysis of Iquito. The first utilized IFO à la Pruitt (Reference Pruitt2010) within Harmonic Serialism (Section 6.3.1), the second employed ParOT with standard assumptions (Section 6.3.2), and the third one applied Hyde’s GM model (Reference Hyde2002, Reference Hyde2007b, 2010; Section 6.3.3).Footnote ¹² On empirical grounds, it was shown that all three are able to produce the data in question. I nonetheless argue that the first of these is to be preferred. Conceptually speaking, HS neatly captures the degenerate-foot-only-with-colon effect directly through the model’s architecture. In both the other alternatives, extra factors have to be introduced. Moreover, IFO, as is shown next, appears to be more restrictive in comparison to ParOT. It also requires an understanding of the colon that is compatible with other facts that support such a constituent (Section 6.2.2). Finally, IFO’s technical implementation requires no additional constraints or representations, unlike GM. These points are developed in detail in the text that follows.

As we have seen in Section 6.3.1, the ranking Have-κ >> All-Ft-R, FtBin has proved sufficient to produce the Iquito pattern under HS. On the other hand, in the remaining two accounts, the constraints used – either identical to those of HS, as in Section 6.3.2, or the comparable ones in Hyde’s model – had to be supplemented by an extra constraint, FtBin-σ_head or NonFinality, whose sole purpose was to explicitly rule out candidates *(ˌL)(ˈL) and *(ˌH)(ˈL) that were otherwise predicted to win.

In IFO this effect comes naturally as part of the model’s architecture – as applied elsewhere with success (Pruitt Reference Pruitt2010) – and complemented by the high-ranked Have-κ, which all analyses have to enlist anyway. There is thus no need for an additional mechanism or constraint to block the undesirable forms. Due to gradualness, a candidate like [(ˌL)(ˈL)] will never be constructed in a single step; instead [(ˈLL)] will be preferred.

This is not to say that [(ˌL)(ˈL)] can never be produced though. On the contrary, we want to be able to derive it, in the light of e.g. the Armenian hammock pattern mentioned in footnote 9. In Standard Parallel OT, this schema is in fact exactly what we would expect to get by default for /LL/ [and /HL/ forms] given the main ranking in Sections 6.3.1 and 6.3.2 (i.e. Have-κ >> All-Ft-R, FtBin), unless another constraint blocks its generation. In HS, it is the other way round; we expect the production of [(ˈLL)] forms, unless there are other, additional requirements/constraints that impose the construction of unary feet. In that latter case though, the unary feet will not be created in one go, but rather iteratively, i.e. /LL/ → [L(ˈL)] → [(ˌL)(ˈL)], in line with gradualness.

With these data in mind, one could of course say that ParOT and HS are after all effectively comparable: where ParOT requires a constraint to block [(ˌL)(ˈL)] forms, HS needs other(s) to generate exactly those. It would then seem to be a matter of taste which particular model to use. Other languages though prove more enlightening; while Armenian posits two degenerate feet in disyllables, there are other languages, such as Pattani Malay (Yupho Reference Yupho1989), which typically foot every syllable into a unary foot also in longer words, thus [(ˌmã)(ˌkɛ)(ˈnɛ̃)] ‘food’ (Yupho Reference Yupho1989:135). In such a case, simple reference to the colon would not suffice to foot everything by means of degenerate feet. Instead, simultaneous satisfaction of constraints such as Ft-Hd-L and Ft-Hd-RFootnote ¹³ ought to be utilized regardless of whether the analysis is placed within ParOT with standard metrical constraints or its HS counterpart. If it is correct that ParOT needs such constraints anyway, then it not only requires a way to block unary feet in certain contexts in languages such as Iquito,Footnote ¹⁴ but it also needs to be able to generate them in languages such as Pattani Malay. HS thus becomes more restrictive; Iquito’s pattern is simply derived through the architecture of the model. It is only for Pattani Malay that something extra needs to be said, along the lines just outlined.

While HS’s technical superiority as far as Iquito is concerned is equally applicable to GM too, there is a shortcoming that is specific to that latter model only. Recall that in its original interpretation Have-κ necessitates the presence of minimally two feet in the structure. In GM though, this requirement could be satisfied even if there were only one stress in the word, as in (27c, d), in which case they’d wrongly be winners. This was the reason why Have-κ had to be understood as referring to a demand of two prominences per word (gridmarks), rather than of a particular prosodic constituent. In turn, that would call instead for a constraint such as Have-2-Stresses or Have-2ndary-StressFootnote ¹⁵ whose grounding remains at this point unclear. Assuming for a moment that such a constraint is justified, then it would effectively dissociate the pattern found in Iquito from most of the languages mentioned in Section 6.2.2, where reference to the colon seems necessary. Worse still, it might suggest an entirely different treatment for phenomena within Iquito itself, namely stress and tone, despite the existence of preliminary evidence in Section 6.2.1 which suggests that both make reference to the same prosodic domain – what has been called colon in the present chapter. To put it differently, the GM account can handle the data, but because of its assumptions, it must explain the Iquito stress facts by making reference not to foot structure itself, but to prominence. The price to pay is loss of insight, both within the language (cf. tonal facts), as well as cross-linguistically, since the κ – if one insists to maintain the label – in Hyde’s theory bears no resemblance to the prosodic element required in many of the languages in Section 6.2.2. On the other hand, the ordinary understanding of footing in IFO, and for that matter, in Standard ParOT, is able to maintain this connection.

A more general problem in GM is the admission of intersecting feet, as this implies a proliferation of possible foot configurations. While some structures are explicitly banned in Hyde’s model, such as the cross-intersecting foot in (31) [cf. Hyde Reference Hyde2001:53], others could in principle be produced, although – to my understanding – are never discussed. The first half of the structure in (30d) that involves a doubly headed intersecting foot is an example of that type. Also observe that if it weren’t for high-ranking PrWd-L, this form would be predicted to win under the ranking in (30).

A somewhat related issue concerns the richer representations that GM heavily relies on. For example, Hyde (Reference Hyde2002:323–324) argues that intersections are to be preferred over unary feet because they can avoid clashes/lapses, as illustrated in the partial tableau in (32).

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Intersections versus unary feet

In Iquito, it was exactly in cases with degenerate feet (cf. (27 & 28)) that monosyllabic or intersecting feet could emerge, but unlike (32), no constraint seemed to choose between those. This situation is shown in (33), a partial reproduction of (27), where either (a) or (b) could win.

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/LLL/ → ˌLˈLL    correct result with *variability* in representation – partial copy of (27)

While empirically this has no serious repercussions for the data in question, it does nonetheless seem to entail that both structures coexist in the language, an ambiguity that could potentially be thought of as a weakness in the light of absence of supporting data. Perhaps more importantly, it becomes hard to conceptualize what a degenerate foot is really in Iquito. Not only can it be a truly unary foot, as in (33a) and as standardly assumed, but it can also look identical to a normal binary foot as indicated by the second part of the intersecting foot in (33b). Intuitively though we would presumably want to maintain the empirical difference between a degenerate and a binary foot, but for at least some cases, as in Iquito, this contrast is neutralized. All in all, given that the introduction of intersecting feet remains a controversial topic, also potentially producing unnecessary complications, an analysis that achieves the same – if not better – results without them is advantageous.

6.4.2 Why the Colon Is not a Problem

Independently of which of the aforementioned OT stress models one eventually subscribes to, it should be evident that the bigger picture remains ultimately the same regardless. More specifically, a vital point throughout has been the use of the – less accepted – prosodic colon κ. This section thus wishes to conclude the chapter by addressing two concerns that have not been voiced till now, but will undoubtedly trouble some readers. First, is the introduction of the κ a problem? And second, can we entertain an alternative explanation of the facts and thus make do without it?

Inclusion of κ into the prosodic hierarchy (e.g. Selkirk Reference Selkirk1972, Reference Selkirk, Anderson, Laver and Myers1981; Nespor & Vogel Reference Nespor and Vogel1986) places it between the prosodic word and the foot, as shown in (34). The question is whether such a move burdens the hierarchy unnecessarily, given that in many languages there are no arguments in favor of the use of the colon whatsoever.

Note however that this problem is not inherent to κ. For example, Schiering et al. (Reference Schiering, Bickel and Hildebrandt2010)Footnote ¹⁶ show that Vietnamese visibly only makes use of σ and φ as domains for phonological processes, but not of ω and π, both of which happen to be well-accepted and well-argued-for prosodic categories. Would that imply then that we should discard the prosodic word ω and the foot π? Perhaps yes, with regard to Vietnamese, but most likely no when these are viewed as possible prosodic constituents cross-linguistically. Indeed, this possibility is sanctioned by the proposal of Schiering et al. (Reference Schiering, Bickel and Hildebrandt2010) that prosodic categoriesFootnote ¹⁷ are language particular, in the sense that prosodic structure should be constructed based on the individual processes at work in the language, instead of imposing a limited number of domain types defined a priori (2010:705). In other words, the prosodic hierarchy is emergent rather than fixed. A weaker version of this idea is adopted by Hyman (Reference Hyman2011), who argues that Gokana organizes its phonology around moras, whereas syllables play at best a cursory role. He then goes on to maintain the universality of the prosodic categories but suggests that these might be exploited to different degrees across languages (2011:82).

Entertaining this hypothesis and assuming for exposition purposes the Schiering et al. (Reference Schiering, Bickel and Hildebrandt2010) view, we would then say that Iquito’s emergent prosodic hierarchy must include κ next to other levels (π, μ, and maybe σ) that the stress and tonal systems exploit, but without any implication that other languages will utilize κ too unless there is positive evidence that actively supports it.

Turning now to the second question, we need to consider alternatives that potentially render the colon redundant. The best contender for colon-replacement would be the reference to two feet that Poser (Reference Poser1990) offers for some of the prosodic templates in Japanese. Such an option is reasonable, given that it imposes no new constituent and keeps in line with counting up to two. I will argue that for some data, including possibly Iquito itself, such an alternative is viable. For many other cases though, such solution either requires considerable additional modifications – a move that undermines the whole enterprise, since theory-enrichment is not after all avoided – or fails completely.

Let us start by reconsidering Matumbi (see (9) for data), where the H-tone is placed at the right edge of the second foot. How is this to be formally understood? Under the two-foot approach, one could imagine an analysis whereby the tone is attracted to the R edge of the rightmost foot, under the assumption that only two feet are created or whereby the H tone is placed at the right edge of the first foot, but the actual first foot is rendered extrametrical, thus effectively positioning the tone at the edge of the second foot. None of these solutions is particularly satisfactory; the first relies on a very specific footing, imposed basically by the desire to ‘skip’ the first foot, whereas the second one achieves this effect through extrametricality, an established mechanism at the right edge of the word, but at best questionable at the left edge of the word, with some researchers even denying it altogether (Gordon Reference Gordon2002; Hyde Reference Hyde2002; but see Buckley Reference Buckley2009). Employing the colon instead produces a more straightforward account: the H tone is attracted to the head of a right-headed moraic colon at the left edge of the stem (Marlo et al. Reference Marlo, Mwita and Paster2013:12).

Another argument, germane to counting, is perhaps even stronger; if phonology – with the caveat in footnote 3 – indeed counts up to two, then we could actually expect other languages to place maxima of the type ‘two cola’, although these may not be worded in this way. Western Apache (Greenfeld Reference Greenfeld1972) and Wapishana (Tracy Reference Tracy and Grimes1972) instantiate exactly that. Greenfeld (Reference Greenfeld1972:273) speaks about the higher phonological unit in W. Apache – what he calls the ‘meter’ – that roughly corresponds to the grammatical phrase, as the one that consists of one to four phonological feet. Similarly, Tracy (Reference Tracy and Grimes1972) calls attention to the ‘contour’ which ‘groups together feet that have syntactic relationships’ and mentions that this comprises one to four feet (possibly more). Although it is an issue what exactly the concepts ‘meter’ and ‘contour’ here allude to, this reference to up to four feet should not be overlooked. Obviously the range of prosodic sizes here can be better re-worded as ‘one foot to two cola’.

Support for κ comes from yet a third source; more specifically, the colon seems to be serving as the domain of phonological processes. For example, in Canadian English, raising of the diphthong /aɪ/ to [əi] is triggered by a voiceless segment within the prosodic word, as in [ɹəit] ‘write’ versus [ɹaɪd] ‘ride’. In the latter, raising fails due to the following voiced d. The triggering element can belong to a weaker foot, but not to a stronger one, a fact that Bermudez-Otero (Reference Bermudez-Otero2004) interprets as an indication that Raising applies within the prosodic domain κ, hence [_ω[_κ[_π ˈnəi][_π ˌtɹeɪt]]] ‘nitrate’ where raising emerges, as opposed to [_ω[_π ˌsaɪ][_κ[_π ˈfɑːnɪk]]] ‘syphonic’ where it does not. Simple reference to dipodicity would be insufficient to characterize the domain in question and would require supplementary reference to strong and weak feet. Accepting the colon as a domain on the other hand captures the generalization neatly.

6.5 Concluding Remarks

To sum up, the present chapter has examined the stress data of Iquito and focused on the contextual emergence of degenerate feet. In line with Michael (Reference Michael2011), it has been claimed that the language normally avoids unary feet, but permits them exceptionally to satisfy a requirement that a word contains a prosodic colon κ. Evidence for such a prosodic constituent has been supplied both from Iquito itself, as well as from a host of different languages and phenomena, including tone association in Matumbi, prosodic templates in Japanese and Bella Coola, and Canadian raising, among others. A recurring theme throughout the chapter – emphasized in Sections 6.2.2 and 6.4.2 – has been the proposal that introduction of the colon in the prosodic hierarchy is unproblematic given recent approaches that accept language-specificity in prosodic universals, either by means of language particular (instead of universal) prosodic hierarchies (Schiering et al. Reference Schiering, Bickel and Hildebrandt2010) or by suggesting that (the same) prosodic categories may be active to different extents depending on the language (Hyman Reference Hyman2011). In addition, it has been argued that while alternative proposals that avoid reference to the colon may be workable for some of the data under consideration, it is only the colon that manages to cover for all the data uniformly. What is more, its admittance makes certain predictions that no other alternative does. As Section 6.4.2 has shown, these predictions are indeed borne out.

On the formal side of things, three different OT accounts of stress have been entertained for the analysis of the Iquito facts (see Section 6.3). Despite their differences, an indispensable component of all has been the constraint Have-κ that imposed the formation of a colon where applicable. It has been suggested that while all three eventually manage to capture the Iquito data, it is only the approach couched within Harmonic Serialism that proves technically superior and whose own architecture, namely gradualness, offers a straightforward explanation of the partial emergence of degenerate feet (Section 6.4.1).