2.1 H tone in stems

H tone spreads throughout the domain of stem morphology, i.e. prefixes, root and inner suffixes (Haas Reference Haas and Hyman1977, Hardy Reference Hardy1988, Martin & Johnson Reference Martin and Johnson2002, Martin Reference Martin2011: ch. 8). Verbs can differ in the spread of H tone in two places: at the beginning or at the end of the stem. These tonal differences are due entirely to the number and weight of stem syllables. An initial syllable's tone depends on its weight; a syllable ending in a short vowel (CV) is light, while a syllable ending in a long vowel, diphthong or coda (CVː, CVC) is heavy (Martin Reference Martin2011: 72). A light initial syllable has slightly lowered tone compared to the H tone of the rest of the stem (3a, c), while the H tone of a heavy initial syllable has the same height as the rest of the stem (3b).

1. (3)

   

The rightward extent of H tone depends on the syllable sequence that ends the stem. Following Haas (Reference Haas and Hyman1977) and Martin (Reference Martin2011), I distinguish even-parity stems, which end in a heavy syllable or an even number of light syllables, from odd-parity stems, which end in an odd number of light syllables; the ‘even/odd-parity’ terminology is mine, but the description is from Haas and Martin. In even-parity stems, H tone extends to the final stem syllable, as in (3). The following OS syllables either have L tone by default or contrastive H tone (§2.2). Since every OS begins with a vowel, the stem-final consonant is always the onset of the following syllable; §3.3 gives supporting evidence. Therefore, the verb stem /wanaj/ in (3a), which ends in a single consonant, is syllabified [wa.na.j]: it ends in two light syllables, and is even-parity.

In odd-parity stems, H tone extends one syllable beyond the final stem syllable, onto the following OS syllable. For example, the verb stems /homp-ip/ and /a-wanaj/ in (4) are odd-parity, and end in one light syllable [hom.pi.p] or three [a.wa.na.j]. H tone extends to the OS syllable after the final stem syllable, [p–as] (4a) and [j–as] (4b), which includes the imperative OS /-as/.

1. (4)

   

As shown in (3) and (4), there are two ways in which H tone spread differs among verbs, depending entirely on syllable structure. First, as noted above, a heavy initial syllable's tone has the same height as the whole stem, while a light initial syllable's tone is slightly lower. Second, H tone ends on the final syllable of even-parity stems (3), but goes one syllable further in odd-parity stems (4). Table II summarises these contrasts.

Table II Regular tone patterns in verb stems.

As first shown by Halle & Vergnaud (Reference Halle and Vergnaud1978), based on Haas's (Reference Haas and Hyman1977) generalisations, tone in Muskogee can be straightforwardly analysed with left-to-right parsing into iambic feet. More precisely, if the verb stem is exhaustively parsed from left to right into iambic feet – (ˈσ_μμ), (σ_μˈσ_μ) or (σ_μˈσ_μμ) – then H tone spreads from the first to the last stressed syllable, as in Table II. A verb starts with a (ˈσ_μμ) foot if the initial syllable is heavy, and with a (σ_μˈσ_μ) or (σ_μˈσ_μμ) foot if the initial syllable is light.

Even-parity stems can be exhaustively parsed into iambic feet, which include the last vowel, which has final stress and is where H tone ends, as in (3). Odd-parity stems, on the other hand, cannot be fully parsed into iambic feet. The final odd-numbered light syllable cannot form a well-formed foot by itself: Muskogee does not allow degenerate monomoraic (ˈσ_μ) feet (see Hayes’ Reference Hayes1995 analysis of the same patterns). In order to parse the final, light syllable of an odd-parity stem into an iambic foot, (σ_μˈσ_μ) or (σ_μˈσ_μμ), footing must extend to the following OS syllable, which has final stress and is where H tone ends (4). The examples in (5), from (3) and (4) above, show how iambic parsing models the spread of H tone (footing follows Martin Reference Martin2011: ch. 8).

1. (5)

   

The tone pattern of the majority of nouns in Muskogee is similar to verb stems, and can also be modelled by exhaustively parsing nouns into iambic feet (Martin Reference Martin2011: ch. 7). The only difference is that odd-parity nouns cannot parse a final odd-numbered syllable into an iambic foot, since there is no following syllable, and degenerate feet are impossible in Muskogee. The final syllable of an odd-parity noun has default L tone. (6) gives the tone pattern and iambic parsing of two representative nouns. The even-parity noun in (6a) is fully parsed into iambs; it has an unstressed light initial syllable with slightly lowered tone, followed by H tone to the end. In the odd-parity noun in (6b), H tone starts on the stressed heavy syllable, while the final syllable is unfooted and has L tone (footing follows Martin Reference Martin2011: ch. 7).

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Following Martin, I assume that verb stems and nouns are equivalent in terms of tone domains and iambic parsing. The different behaviour of odd-parity verb stems and nouns is due to following OS material in verbs. OS material allows odd-parity verb stems to foot their final light syllable; this option is unavailable to odd-parity nouns.

2.2 Contrastive and default tone in outer suffixes

While the extent of H tone in the stem is determined by metrical parsing, the OS tone pattern is morphologically determined. OS syllables have either H tone, which is subject to downstep, or L tone. I follow Martin (Reference Martin2011) in assuming that H tone is contrastive, while L tone is default. The unfooted OS syllables in (5a, b), containing the OS /-as/, have default L tone. Other OSs have contrastive tone on a specified vowel, like the first vowel of /-áɬiː/ in (7); this tone undergoes downstep to ^!H after the stem H tone. The second acute accent marks contrastive tone, while the first acute shows the end of H tone, following Haas (Reference Haas and Hyman1977) and Martin (Reference Martin2011).

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The occurrence of H tone in the OS cannot depend on metrical parsing. For example, /-áɬiː/ is always syllabified [Ca.ɬi:], with ^!H on the light, first syllable but L on the heavy, second syllable. If iambic parsing extended through the whole verb, there would be no match between tone and parsing: the OS syllable [ɬiːs] would have stress, not [ja] (8a). Since H tone is the only clear phonetic correlate of stress, (8a) is incorrect: [ja] has ^!H and [ɬiːs] L. Conversely, an iambic parse, where [(ˌja)] is stressed but not [ɬiːs], is metrically impossible, since a single light syllable is footed, but not a heavy syllable (8b).

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When multiple contrastive H tones occur in the OS, like /íʧk/ and /áɬiː/, each tone is successively downstepped, as in [piʧ.ka] (9a). The ^!!H tone on [ka] in (9a) is downstepped twice from the H tone of the stem (Martin Reference Martin2011; see Martin & Johnson Reference Martin and Johnson2002 for phonetic evidence).

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When a metrically unparsed OS syllable without contrastive tone precedes a syllable with contrastive tone, the syllables share the ^!H tone: [ji.ja] (9b). Otherwise, metrically unparsed OS syllables without contrastive tone have L by default, for example the final syllable [ɬiːs] in (7)–(9b). Multiple OS syllables can have default L tone, as in [a.tiːs] in (9c), which also has lengthened grade grammatical tone, glossed as lgr and described in §2.3.

Lastly, if an OS syllable with contrastive tone is parsed into the final iambic foot due to a preceding odd-parity stem, this OS syllable has H tone. For example, H tone spreads onto the syllable [ja] in (9d), because the odd-parity stem /a-wanaj/ causes this syllable to be footed.

Some nouns have lexically specified falling tone (HL) on one syllable, as in (10) (Martin Reference Martin2011: 82). Judging from the list of nouns with lexical falling tone in Martin (Reference Martin2011: 81–82), the syllable with falling tone is heavy, with either a long vowel or a short vowel + sonorant coda. If more than a light syllable (i.e. another foot) follows the lexical falling-toned syllable, this foot surfaces with downstepped H tone (10b).

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Based on the list of nouns with lexical falling tone and the examples in Martin (Reference Martin2011: 57–58), lexical falling tone never creates minimal pairs with nouns that do not have lexical tone. Several nouns with lexical falling tone in Martin (Reference Martin2011) are bird names, suggesting that falling tone may have an iconic function. What is important for the purposes of this paper is that the lexical tone in nouns does not occupy a different phonological domain from regular, level spreading tone. This distinguishes nouns from verbs, where regular tone occupies the inner phonological domain and contrastive, morphologically determined tone occupies the outer domain.

2.3 Grammatical tone: grade morphology

The third type of tonal phenomenon in Muskogee involves the autosegmental morphology known as ‘stem ablaut’ or ‘grades’ in the Muskogeanist literature (e.g. Haas Reference Haas1940, Reference Haas and Hyman1977, Nathan Reference Nathan1977, Hardy Reference Hardy1988, Martin Reference Martin2011). Grade morphology consists of phonological changes to the final stem syllable, such as lengthening, shortening and nasalisation of vowels, infixation of [h] and [êj], and additional tones (Martin Reference Martin2011: ch. 8): falling (HL), high rising (HH⁺) and H tone that is subject to downstep and spreads rightward to the end of the word or next contrastive tone (H→). There are four grades in Muskogee: lengthened (lgr), aspirated (hgr), falling (fgr) and nasalising (ngr) (terminology from Haas, via Martin Reference Martin2011). Grades primarily encode aspect, labelled eventive, perfective, resultative stative and expressive in Martin (Reference Martin2011: ch. 28). This section focuses on the effects that grade morphology has on parsing and phonological domains; see Hardy (Reference Hardy1988: §4.2.1) and Martin (Reference Martin2011: chs 8, 28) for more details on the phonological, morphological and semantic effects of grade morphology.

In verbs with overt grade morphology, the final stem syllable is heavy, even if it is light in the non-graded form. In hgr forms, the final syllable's heaviness comes from coda h-infixation, while other grades cause vowel lengthening where phonotactically permissible (it is not found before a coda sonorant, as the syllable is already heavy). A stem that is odd-parity in non-graded forms therefore becomes even-parity in graded forms. A comparison of the zero-grade form in (11a) with the hgr form of the odd-parity stem /a-wanaj/ in (11b) shows this contrast. The stem-final syllable is light in the zero-grade (i.e. non-graded) form [na], but heavy in the hgr form [nah]. Iambic parsing and H tone therefore extends to the next, OS syllable [jas] in the zero-grade form, but not to [jis] in the hgr form. Because hgr does not add an additional tone to the verb, the difference in tonal patterns is due only to parsing.Footnote ²

1. (11)

   

In the graded form of the odd-parity stem in (11b), footing ends on the stem-final syllable, similarly to even-parity stems. In other words, the syllable-weight effect of grade morphology prevents footing from extending into the OS domain. The footing of (11b) is identical in other grades. The four grade forms contrast in their segmental and autosegmental content, not in parsing. (12) gives the other graded forms of the odd-parity stem /a-wanaj/: fgr (a), ngr (b) and lgr (c). In all the graded forms in (12), the final stem syllable is heavy and has final stress, unlike the zero-grade form in (11a).

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Table III gives paradigms of the zero grade and four graded forms of two stems: even-parity /wanaj/ and odd-parity /wanaj-ak/, and shows two important facts about grade morphology. First, the tonal and other phonological changes due to grade morphology affect only the stem-final syllable, with the exception of right-spreading H tone in lgr. Second, metrical parsing does not extend past the stem in graded forms, even for odd-parity stems. An OS syllable is only footed when it follows the zero-grade form of an odd-parity stem.

Table III Paradigm of grade morphology (from Martin 2011: 83–84).

The tone and footing of lgr forms require further consideration. Unlike the other three grades, lgr has phonological effects beyond the final stem syllable: its additional H tone spreads rightward into the OS, as in (12c). lgr H tone spreads either to the right edge of the word, as in the examples above, or to the next OS syllable with contrastive tone, such as [j-iʧ] from /-íʧk-/ in (13a), while following syllables have default L tone. lgr H tone also spreads leftwards to an unstressed light syllable preceding the stem-final syllable, such as /wa/ in (13b). When the stem has multiple feet, lgr H tone is downstepped ((12c), (13)); cf. the tone pattern of the stem /wanaj/ in Table III.Footnote ³

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Lastly, when lgr H tone spreads rightwards onto an enclitic, it is realised as HL (14a). Martin (Reference Martin2011: 96–97) uses this tonal pattern as a diagnostic for distinguishing OS morphemes from enclitics; compare (14a), with falling tone on the clitic /﹦ejs/, and (14b), with H tone on the homophonous OS sequence /-ej-s/.

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3.1 Phonological domains and recursive ω's

The data in §2 illustrate the prosodic properties of the two domains in Muskogee verbs. The inner domain has predictable H tone and exhaustive iambic parsing. The outer domain is unfooted, but distinguishes contrastive L and H tones, the latter subject to downstep. Grammatical tone occurs at the end of the inner domain, i.e. its boundary with the outer domain.

Martin's account leads to two further generalisations. First, the inner and outer domains form a single word, not two consecutive words. Second, the inner domain is more deeply embedded than the outer domain. In a prosodic hierarchy model (e.g. Selkirk Reference Selkirk1984, Reference Selkirk, Beckman, Dickey and Urbanczyk1995), these generalisations yield a recursive-ω structure: the inner domain forms a ω_min and the entire word forms a ω_max. The outer domain is not a separate ω, but is inside ω_max and outside ω_min. (16) illustrates ω-recursion in Muskogee.

1. (16)

   

ω_min has the wordhood attributes of stress culminativity and exhaustivity (Selkirk Reference Selkirk, Beckman, Dickey and Urbanczyk1995), as it is exhaustively footed with primary stress on the ω_min-final syllable. ω_max has the wordhood attribute of isolability: there can be pauses before or after the verb but not between the stem and the OS (Jack Martin, personal communication). Syllable structure and obstruent voicing also support the structure in (16).

While footing provides evidence that a right-edge ω boundary ends the inner domain, there is no evidence that the outer domain starts with a left-edge ω boundary, which would be predicted if an OS formed its own ω or ω_min. Martin's discussion of syllabification (2011: 70–71) and examples throughout show that Muskogee allows onsetless syllables only at left ω edges, for example at the beginning of a word or the second member of a compound. In compounds where the first member is consonant-final and the second vowel-initial, Martin indicates a syllable break between the two parts of the compound, evidenced by an intervening glottal stop for some speakers. A final plosive in the first member is voiceless, showing the plosive is a coda (Martin Reference Martin2011: 62, 71). The syllable break between the consonant [k] and the vowel [a] in (17), adapted from Martin (Reference Martin2011: 71), shows that each member of the compound forms a ω.

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Conversely, a glottal stop never intervenes between the stem and the OS, and a stem-final plosive between two voiced sounds is always voiced, as in (18) (Jack Martin, personal communication). There is thus no left ω edge between the inner and outer domains.

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Modelling the inner domain as a ω_min allows a straightforward description of surface prosody. ω_min is exhaustively parsed into iambic feet, and has H tone throughout, but syllables dominated only by ω_max, but not ω_min, are unfooted. A verb in Muskogee may have multiple unfooted syllables, like [jiʧ.ka.tiːs] (19a) and [ka.ɬiːs] (19b). These syllables are unfooted, since parsing them into feet incorrectly predicts the tonal pattern where the syllables [ka.ˈtiːs] and [ˈɬiːs] do not have the attested L tone.

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In the recursive-ω model, the OS syllables [jiʧ.ka.tiːs] and [ka.ɬiːs] in (19) are unfooted because they are outside ω_min. An alternative where the outer domain forms its own ω must stipulate that exhaustive footing applies to some ω_min's but not to others. These unfooted syllables are still part of the same ω_max as the footed syllables [(waˈnaː)] (19a) and [(aˌwa)(naˈja)] (19b). ω_max is the domain of tonal downstep: H tone in ω_min triggers downstep of following lexical H tones in ω_max outside ω_min, while additional lexical H or HL tones trigger successive downstep in verbs and nouns (see Johnson & Martin Reference Martin and Johnson2002 for acoustic evidence and Martin Reference Martin2011: chs 7–8 for details). An alternative, single-ω model of the verb cannot account for the extent of iambic footing without positing another ω-internal category, such as a PStem (Downing Reference Downing2006, Dolatian Reference Dolatian2020).

ω_max is the domain of plosive voicing: between voiced sounds within ω_max, /p t ʧ k/ are voiced. In addition, fricatives /f s/ are lightly voiced between voiced sounds in ω_max (Martin Reference Martin2011: 62). Plosive voicing is possible, but not obligatory, between ω_max boundaries when two words are phrased together (Martin Reference Martin2011: §4.1, §5.1, §6.4, Jack Martin, personal communication), e.g. an object and a predicate, as in (20). While the resyllabified [n] cannot show voicing, Martin gives similar examples with voiced obstruents in this position. Voicing occurs between the stem and OS, i.e. across a ω_min boundary, which cannot be the relevant domain for voicing.

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Lastly, only the edges of ω_max allow an extra [s] in fast speech (‘contracted’ or ‘casual’ in Martin Reference Martin2011: 71). In contracted speech, [sC] onset clusters are allowed at a word's left edge (21a), while [RCs] clusters (R = sonorant) are allowed at the right edge of a word – but not a stem (21b). The distribution of [sC] and [RCs] clusters at the left and right edges of the entire word can be modelled with [s] as an appendix to ω_max.

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In contrast to verbs, the entire nominal word forms a single ω, with both ω_min and ω_max properties. Like ω_max in verbs, the nominal ω is an isolable unit and the domain of obligatory plosive voicing (Martin Reference Martin2011: 62, 72–73), it has lexically contrastive tone and downstep (§2.2, Martin Reference Martin2011: 81–82) and allows [sC] clusters at its left edge (Martin Reference Martin2011: 71; Muskogee nouns end in vowels, so right-edge clusters cannot diagnose ω_max). Like ω_min in verbs, the nominal ω is exhaustively parsed into iambic feet, except for a single light syllable at the end of the word, which has L tone.

§3.2 demonstrates that the different ω-structures of nouns and verbs come from their different morphosyntax: verbs have two phases, while nouns have one. An interface model in which each phase of a word maps to a ω accounts for verbs having two ω's and nouns one.

Both nouns and verbs can also host enclitics, like /﹦ejs/ in (22a) (cf. (14a)), and /﹦taːt/ in (22b) (Martin Reference Martin2011: 80–81). I place enclitics after the right edge of ω or ω_max.

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This section has argued for unbalanced ω-recursion and against either consecutive ω's or balanced ω-recursion, where the outer, OS domain is a ω, as in (23a). However, the data are compatible with other models. The inner domain may be modelled as a first phonological cycle, in which metrical parsing occurs, making Muskogee an ‘early stress’ language, in Newell's (Reference Newell2008) terms. The entire word is the output of the second cycle, without additional footing, but with voicing and downstep (23b). The inner domain may also be modelled as the output of the stem-level grammar in Stratal OT, as in (23c) (Kiparsky Reference Kiparsky2000, Bermúdez-Otero Reference Bermúdez-Otero, Hannahs and Bosch2018). Feet are parsed at the stem stratum, while voicing and downstep occur at the word stratum. §4 investigates each of the models in (23).

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3.2 Morphosyntactic domains and phases

Morphosyntax assigns material either inside or outside ω_min. A suffix's affiliation with the stem or OS must be morphological, as it cannot be based on phonology (Martin Reference Martin2011: 87–88). For example, the stem-level suffix /-ak/ (plural) and the OS /-ak/ (impersonal agent) are homophonous, but occupy different morphosyntactic and phonological domains, as in (24). /-ak/ (plural) is a stem-level suffix, in ω_min, as shown by foot parsing and H tone (24a), whereas /-ak/ (impersonal agent) is an OS, in ω_max: it is unfooted and has ^!H tone from the following OS /-áɬiː/ (24b).

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In (24), the tone of the syllables [ja.ka] depends on the morphosyntactic affiliations of two /-ak/ suffixes, since their segmental material is identical. These data also show that the rightward extent of footing (and ω_min) is crucial for establishing tonal patterns.

Following Guekguezian (Reference Guekguezian2020), I claim that these two domains are spelled out at two phases, vP and CP (Chomsky Reference Chomsky, Martin, Michaels and Uriagereka2000, Reference Chomsky and Kenstowicz2001). Stem morphology encodes the extended verbal domain or vP: the lexical root, agreement with patient and goal arguments, and information about event and argument structure, location and direction. OS morphology encodes InflP-level morphosyntax, spelled out at the CP phase: tense, mood, negation and agreement with agent arguments. For example, the stem-level suffix /-ak/ in (24a) is in the vP phase, since it may agree with patients (though it can agree omnivorously with agents, as in (24a); Martin Reference Martin2011: 210–211, Kimberly Johnson, personal communication) and affect event structure (Haas Reference Haas1940). The OS /-ak/ in (24b) is in the CP phase: (exclusively) agent agreement is in InflP in Muskogee.

Grade morphology (at the right edge of ω_min) primarily expresses aspectual semantics (Haas Reference Haas1940, Hardy Reference Hardy1988: 135–149, 288–299, Martin Reference Martin2011: ch. 28). Grade morphology encodes Asp, the highest head in the Muskogee vP, and is phasal following Guekguezian (Reference Guekguezian2020). Following a reviewer's suggestion, I posit that the CP-phase head is encoded by verbal enclitics, which provide discourse content and are used in clausal subordination (Martin Reference Martin2011: ch. 42).

(25) illustrates the phase structure I assume, following Guekguezian (Reference Guekguezian2020); ‘ΦH’ indicates phase heads and ‘SD’ their spell-out domains. While the specific phasal claims are mine, they are based on the description and analysis of Muskogee verbal morphosyntax in Haas (Reference Haas1940), Nathan (Reference Nathan1977), Hardy (Reference Hardy1988), Martin (Reference Martin2010, Reference Martin2011) and Johnson (Reference Johnson2019a). The association of morphological categories in the verb with the structure in (25) also follows much generative research (see e.g. Burzio Reference Burzio1986, Pollock Reference Pollock1989, Kratzer Reference Kratzer, Rooryck and Zaring1996, Travis Reference Travis, Tenny and Pustejovsky2000, Ernst Reference Ernst2002, Pylkkänen Reference Pylkkänen2008). (25) differs minimally from Johnson's (Reference Johnson2019a) case-assignment-based analysis in the identity of the lower phase head: Asp here, but v* for Johnson. Lastly, (25) is similar to structures proposed for morphologically complex verbs in Turkish (Newell Reference Newell2008, Fenger Reference Fenger2020), Ojibwe (Newell Reference Newell2008, Piggott & Newell Reference Piggott and Newell2016, Miller Reference Miller2018) and Kiowa (Miller Reference Miller2018), inter alia.

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Crucially, as a reviewer points out, the morphological elements ‘stem’ and ‘OS’ in (25) do not correspond to the whole spell-out domains at the vP and CP phases. Rather, the stem and the OS form the portion of the verbal word spelled out at each phase, separate from argument and adjunct XPs. As (27) and (29) below show for the vP phase and CP phase, verbal material consists of heads in the clausal spine, as well as pronominal and adverbial prefixes. The syntactic material forms a word through some postsyntactic amalgamation operation (Noam Chomsky, personal communication), such as m-merger (Matushansky Reference Matushansky2006, Pietraszko Reference Pietraszko2017) or lowering/raising (Harizanov & Gribanova Reference Harizanov and Gribanova2019). I claim only that postsyntactic word-formation occurs after each spell-out, so that the two phases are reflected in the verbal word.

(26) shows the stem's morphosyntactic categories and their positions (Martin Reference Martin2011: 26–27). These include adverbial prefixes denoting direction and location, instrumental, dative and patient agreement, the root, and suffixes denoting spontaneous and prospective aspect and plural agreement.

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I assume that the morphosyntactic structure in (27) derives the template in (26), which is not independently needed. While I claim that Asp is phasal in Muskogee, I use the term ‘vP phase’ for cross-linguistic comparison. The specific position and labels of material in (27) are not crucial here; see Guekguezian (Reference Guekguezian2020) for further analysis of Muskogee, and Tyler (Reference Tyler2020) for the verbal morphosyntax of the related language Choctaw.

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Martin's (Reference Martin2011: chs 23–24) morphological root includes both lexical information and functional categories of voice/transitivity (v/Voice: middle and direct causative) and patient number agreement (AgrPat). I assume that argument structure prefixes in Muskogee verbs are pronouns (= D) in the specifiers of AgrPatP and ApplP: /is-/ (instrumental), /im-/ (dative) (Martin Reference Martin2011: ch. 22), /iː-/ (reflexive), /iti-/ (reciprocal) (Reference Martin2011: ch. 21) and patient agreement (Reference Martin2011: ch. 20). Haas (Reference Haas1940: 144) translates the omnivorous plural suffix /-ak/ (Kimberly Johnson, personal communication) as ‘several (distributively) [to (do something)]’, suggesting it also encodes event structure, like the Asp1 suffixes distributive /-red/, spontaneous /-ip/ and prospective /-ahan/. Semantically, grades in Asp2 have scope over the lower aspectual markers /-ip/ and /-ahan/ (Martin Reference Martin2011: chs 28–29).

The OS's encode InflP categories: tense, which distinguishes remoteness (Martin Reference Martin2010) or evidentiality (Johnson Reference Johnson2019b), mood (/-is/ (indicative), /-as/ (imperative) and /-a/ (interrogative)) and /-íko/ (negative) (Martin Reference Martin2011: chs 29–31), shown in (28). The OS also includes agent agreement suffixes and /iː/ (durative), which encodes event structure, modality, subject-oriented properties and nominalisation (Martin Reference Martin2011: §28.5). I assume, with Johnson (Reference Johnson2019a), that agent agreement is CP phase (AgrAgt) and patient agreement vP phase (AgrPat), and, with Guekguezian (Reference Guekguezian2020), that durative is also CP phase.

1. (28)

   

(29) gives a syntactic structure that derives the descriptive template in (28). Again, the specific height and labels are not crucial.

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I claim that nouns, unlike verbs, are built in a single phase. Nouns have only a few affixes, shown in (30); while the possessive agreement prefixes (patient and dative) can appear on most nouns, the suffixes /-aki, -taːki/ (plural), /-oʧi/ (diminutive) and /-alki/ (group plural) only appear on some, mainly animate (Martin Reference Martin2011: chs 12–13).

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While the nominal domain is biphasal in some languages, like Bangla (Syed & Simpson Reference Syed and Simpson2017), similar to the Muskogee verbal domain, Muskogee nouns provide no evidence for a word-internal phase head. Since nouns are spelled out at one phase, their single ω (§3.1) falls out from their morphosyntactic structure, similar to biphasal verbs with two recursively layered ω's. As with verbal clitics in C, I assume that clitics on nouns are outside ω_max, as in (22b), and encode the higher phase head D.

3.3 Mismatching inner domains

Muskogee verbs consist of two domains in morphosyntax – the vP and CP phases (§3.2) – and phonology – ω_min and ω_max (§3.1). Muskogee verbs present another case where word-internal phases correspond to phonological domains; see e.g. Marvin (Reference Marvin2002) for English and Slovenian, Newell (Reference Newell2008) for Cupeño, Ojibwe and Turkish, Samuels (Reference Pylkkänen2010) for Basque, Windsor (Reference Windsor2017) for Blackfoot, Miller (Reference Miller2018) for Kiowa and Ojibwe, Crippen (Reference Crippen2019) for Tlingit and Fenger (Reference Fenger2020) for Turkish and Japanese. (31) illustrates phase-to-ω mapping in Muskogee.

1. (31)

   

In (31), the inner morphosyntactic and phonological domains, vP phase and ω_min, are roughly coextensive, but not isomorphic: the final consonant /k/ of the vP phase material is parsed outside of ω_min. This onset undermatch of a vP-final consonant is the general case in Muskogee. For instance, in (32), the vP-final consonants [j] and [p] are parsed outside the ω_min's [wana] and [hom] to form the onset to the syllables [ja] and [pas], which contain CP-phase material (/-áɬiː/, /-as/).

1. (32)

   

Onset undermatches like (32) are driven by syllable phonotactics in conjunction with the phonological shape of verbal morphemes. In Muskogee, a CV sequence is always syllabified [.CV], not [C.V] (Martin Reference Martin2011 : 70–71). Verb roots and vP-phase suffixes always end in consonants, while CP-phase suffixes always begin with vowels. Therefore, the juncture between the two phases is /…C/_{v P}-/V…/_CP, which must be syllabified [[…]_ωC-V…], due to phonotactics (not to any special property of vP-phase-final consonants).Footnote ⁴

Syllabification of /…C/_{v P}-/V…/_CP is [[…]_ωC-V…], not *[[…C]_ω-V…]: in formal speech, Muskogee does not allow coda clusters or long vowels preceding coda sonorants (Martin Reference Martin2011: 64–65, 70–71). Such syllables are actively avoided: for example, when the root /ɬaːm/ is in one syllable, the vowel shortens, as in (33).

1. (33)

   

Assuming general Muskogee phonotactics apply at the end of ω_min, the words in (34) have the vP-phase-final consonant outside of ω_min, in order to avoid a complex coda ([mp]) in (a) or a long vowel + coda sonorant ([oːj] from /apoːj/ ‘set’) in (b).

1. (34)

   

Moreover, there is no evidence for a left-edge ω boundary between vP-phase and CP-phase material, unlike the two members of a compound (§3.1, Martin Reference Martin2011: 70–71). A glottal stop never intervenes between the phases at the /…C/_{v P}-/V…/_CP juncture, and vP-final plosives are always voiced between voiced segments (Martin Reference Martin2011: 62, Jack Martin, personal communication). These two pieces of evidence show that the vP-final consonant is in the onset of the following syllable; if it were the coda of the preceding syllable, glottal stop epenthesis would be possible and the plosive would remain unvoiced (Martin Reference Martin2011: 62, 71). The vP-final C is always resyllabified: [[…]_ω C-V…].

While onset undermatches are the general case, verbs with odd-parity vP material have rhyme overmatches: the first vowel (and any following coda) of CP material is parsed inside ω_min. Odd-parity vP-phase material cannot be exhaustively parsed into iambic feet without including following CP-phase material (§2.1).

For example, the vP phases /a-wanaj/ and /homp-ak/ in (35) are odd-parity and cannot be exhaustively parsed into iambic feet by themselves: *[(a.wa).na.j], *[(hom).pa.k]. The following CP-phase material is recruited to form the second syllable of another foot with the final light vP syllable: [(a.wa).(na.jiʧ)], [(hom).(pa.ka)]. The first rhyme of the CP-phase material, [iʧ] in (a) and [a] in (b), is overmatched into ω_min, the phonological domain mapped from the vP phase.

1. (35)

   

Without the rhyme overmatch, odd-parity vP phases such as (35) cannot be exhaustively footed. An odd-parity vP phase like /homp-ak/, with an onset undermatch, would require a phonologically illicit process or structure: a unary foot (36b), vowel lengthening (c), leaving ω_min material unfooted (d) or undermatching entire syllables (e). The isomorphic phase-to-ω mapping in (f) requires violation of syllabification constraints. Instead, the attested form is a rhyme overmatch of the CP vowel [a] in (a).

1. (36)

   

As with onset undermatches, rhyme overmatches are determined by general Muskogee phonology and a verb's phonological shape. Any verb with odd-parity vP-phase material has a rhyme overmatch, provided it is in zero grade: since overt grade morphology makes all vP-phase material even-parity (§2.3), all graded verbs have an onset overmatch. Any verb with even-parity vP-phase material has an onset undermatch. Phase-to-ω mismatch or misalignment in Muskogee is predictable from the shape of phonological material spelled out at each phase.

Under- and overmatches are insensitive to other properties. The final consonant of an even-parity vP (or graded odd-parity vP) is always undermatched, whether it belongs to the root (37a–c) or a suffix (d), whether vP-phase material ends in one (b–d) or two consonants (a), whether CP-phase material begins in a lexically toned vowel (a, d) or not (b, c), or whether there is one CP-phase suffix (b) or more (a, c, d).

1. (37)

   

Similarly, with an odd-parity vP-phase, the CP-initial rhyme is always overmatched, whether in a light (38b–d) or heavy (38a) syllable, whether the vowel has lexical H tone (a–c) or not (d), or whether the vP phase ends in a root (a, c, d) or suffix (b).

1. (38)

   

When CP-phase material has only one vowel, the overmatch yields a single ω, simultaneously ω_min and ω_max, as in (39) (see Ito & Mester Reference Ito and Mester2007, Reference Ito, Mester, Grijzenhout and Kabak2009 on defining minimal and maximal prosodic units). The domain of iambic footing, ω_min, is coextensive with the domain of downstep, voicing, s-clusters and the pronounceable unit, ω_max. In (39), the InflP suffix /-as/ is overmatched into ω_min with the odd-parity vP-phase /homp-ip/ (a), and /a-wanaj/ (b), resulting in a single ω.

1. (39)

   

4.1 Parallel mapping, Align and Match

This section investigates how verbal material spelled out at the two phases is mapped to the unbalanced ω-recursive structure in (23a). Following Cheng & Downing (Reference Cheng and Downing2016), I model this mapping in a parallel OT grammar that ‘waits’ to operate until all phases are spelled out from syntax. The input to phonology comprises the spell-outs of every phase, using Align constraints to map one edge of a morphosyntactic constituent to one edge of a phonological constituent, like Align-R(X,ω) in (41).

1. (41)

   

I give the input word the neutral label ‘X’, and assume that an X is formed by some postsyntactic operation after each phase, rather than by head movement in narrow syntax, which is unformulable (Chomsky Reference Chomsky2020). The details of this operation lie outside the scope of this paper. What is crucial is for an X to be spelled out at each phase, so that biphasal verbs consist of two Xs: one with material spelled out at the vP phase (by Asp) and another with material spelled out at the CP phase. ω-recursion falls out from this input – two Xs from two phases – using the particular Align constraints relevant to the Muskogee mapping.

(42) show two possible accounts for unbalanced recursion in (40a); I find no Muskogee-internal reason to commit to one of them. Without head movement in narrow syntax (Matushansky Reference Matushansky2006), the verbal X spelled out at the CP phase consists of only InflP-level morphemes: /wanaj/ and /as/.

First, Align can be parameterised to lexical words, i.e. Xs containing a lexical category such as a verb or verbalised root. The left edge of each ω in (42a) must be aligned with the lexical X /wanaj/. The unbalanced recursive-ω output (i), the attested structure (modulo onset resyllabification of [j]), satisfies Align-R(X,ω) and Align-L(ω,X_Lex). In the balanced recursive structure (ii), the left edge of the ω [as] is not aligned to /wanaj/_Lex, and so violates Align-L(ω,X_Lex).Footnote ⁵

1. (42)

   

Second, an economy constraint like *ω in (42b) also favours unbalanced ω-recursion (i) over balanced ω-recursion (ii), as the latter has more prosodic structure than the former. In this case, Align-R(X,ω) dominates *ω, to eliminate the single-ω candidate (iii).

I now turn to Align-R and the mismatches between the right edges of the vP-phase X and ω_min. Following reviewers’ suggestions, I propose that Align-R(X,ω) does not care about consonant resyllabification, i.e. it cannot force an output to violate general syllabification rules. I formulate Align-R in (43), using Mester & Padgett's (Reference Mester, Padgett, Merchant, Padgett and Walker1994) alignment schema, where violations are counted by the number of specified phonological units by which morphosyntactic and phonological units are misaligned.

1. (43)

   

Align-R is violated gradiently for every syllable that intervenes between the right edge of an X and an ω. I adopt de Lacy's (Reference de Lacy2002) concept of Designated Terminated Element, where the Designated Terminated Element of a syllable is its nucleus. Every syllable nucleus intervening between the right edges of an X and some ω adds a violation to Align-R (the edgemost segment defines but is not included in the edge). Align-L in (42a) above can be formulated analogously to Align-R in (43) without any difference in constraint rankings, since it is never violated by a winning output. The Muskogee data do not motivate multiple versions of Align parameterised by the misalignment unit (the syllable in (43)). All that is crucial is that Align can be violated gradiently.Footnote ⁶

(44) illustrates the violation profiles of Align-R for different outputs of /homp-ak–áɬiː-is/. The onset undermatch, (a), does not violate Align-R, because the misaligned right edge is the onset [k], which does not count as a syllable. The rhyme overmatch, (b), violates Align-R once: the misaligned right edge [a] counts as a syllable as the Designated Terminated Element of [ka]. The larger undermatch, (c), also violates Align-R once for the misaligned syllable [pa], while onset [k] does not add a violation.

1. (44)

   

For example, with the odd-parity vP-phase /homp-ak/, undermatching the final consonant [k] does not violate Align-R for the ω_min *[hompa]. Such onset undermatches are impossible in Muskogee: odd-parity vP-phase material cannot be exhaustively parsed into binary iambic feet. *[hompa] violates either FootBinarity (FtBin) for *[(hom)(pa)], Exhaustivity(ω_min,σ) (Exh (ω_min,σ); see Ito & Mester Reference Ito, Mester, Grijzenhout and Kabak2009 and Elfner Reference Elfner2012 for indexing constraints to prosodic subcategories) for *[(hom)pa] or Dep(μ) (Morén Reference Morén1999) for lengthening the vP-final vowel in a non-grade form *[(hom)(paː)]. (Graded forms lengthen the vP-final vowel when phonotactically permissible; I assume Dep(μ) cannot eliminate such a form, so Align-R correctly predicts onset undermatches in graded verbs; see (11b) and (12)). (45) illustrates how the higher-ranked constraints favour the attested rhyme overmatch [[(hom)(paka)]liːs], which violates Align-R once.

1. (45)

   

The rhyme overmatch also beats the larger undermatch *[[hom]pakaɬiːs], which undermatches the vP-phase material /pak/. The attested overmatch and the hypothetical undermatch tie on Align-R, with one violation. The overmatch parses two more syllables into the ω or ω_max than the larger undermatch. The single-ω output in (46a.iii) parses all its syllables into a ω, but has two violations of Align-R.

1. (46)

   

On the other hand, a single-ω output is correctly predicted if CP-phase material is only a single rhyme, like /-as/ in (46b), completely parsed inside ω or ω_min in the rhyme undermatch [(hom)(pipas)] (cf. (4a)). An onset undermatch *[[hompi]pas] violates one of the higher-ranked constraints Exh(ω_min,σ), Dep(μ) and FtBin; to save space, I only show Exh(ω_min,σ) in (46b). The rhyme overmatch is chosen over a larger undermatch by the low-ranked general constraint Exh(ω,σ).

The constraint ranking in (47) models the footing generalisations: material within ω_min is exhaustively footed, while material outside ω_min is not. The vP-phase material is aligned to ω_min, and can be minimally misaligned to satisfy other constraints, but not to exhaustively foot the whole word.

1. (47)

   

Align-R accounts for the Muskogee mismatch pattern because it is gradiently violated. McCarthy (Reference McCarthy2003) argues against gradient Align as in (43); however, he argues that gradient Align predicts unattested word-internal mismatches: ‘prosodic constituents that come close to but don't perfectly align with morphological constituents’ (Reference McCarthy2003: 88–89). In the hypothetical example in (48) (adapted from McCarthy Reference McCarthy2003), when Onset prevents a perfect match between morphology and phonology, gradient alignment prefers a slight mismatch over a lack of match.

1. (48)

   

The Muskogee mismatch patterns are exactly what McCarthy (Reference McCarthy2003: 88–89) states is unattested. Overmatches, with material outside the vP phase inside the internal ω, correspond to candidate (48a). Undermatches, with material inside the vP phase outside the internal ω, correspond to (b). The Muskogee pattern is a counterexample to McCarthy's claim that gradient alignment is typologically unsupported. Therefore, the Muskogee pattern provides evidence for gradient Align.

Moreover, categorical morphosyntax–phonology mapping constraints like Match constraints in Match Theory (Selkirk Reference Selkirk2009, Reference Selkirk, Goldsmith, Riggle and Yu2011) have difficulty accounting for the Muskogee mismatches, because they do not distinguish different-sized mismatches or lack of match. The two main formulations of Match are Selkirk's (Reference Selkirk, Goldsmith, Riggle and Yu2011: 17) edge-based version and Elfner's (Reference Elfner2012: 28) terminal node-based version; following Elfner, I refer to her formulation as ‘Match_T’ (for ‘terminal node’) and Selkirk's as ‘Match_E’ (for ‘edge’).

In Selkirk's (Reference Selkirk, Goldsmith, Riggle and Yu2011: 17) Match_E formulation in (49), the edges of a syntactic constituent must correspond to those of a relevant prosodic constituent (syntax–prosody; S-P faithfulness) or vice versa (P-S faithfulness); the formulations in (49) are modified from the general Match constraints in Selkirk (Reference Selkirk, Goldsmith, Riggle and Yu2011: 17) by replacing ‘constituent of type α’ with ‘word’ and ‘constituent of type π’ with ‘ω.’ I take ‘edge’ in (49) to be the leftmost or rightmost segment, so MatchWord assigns a violation mark for each X (a) or ω (b) whose edgemost segments do not correspond.

1. (49)

   

Elfner's (Reference Elfner2012) Match_T formulation demands that syntactic and phonological units dominate the same material. Elfner defines MatchPhrase, an S-P constraint, in (50a). Edge alignment falls out from exhaustive domination: if a prosodic constituent contains all and only the terminal elements of its matched syntactic constituent, then the edgemost terminal elements of both constituents correspond. Elfner's MatchWord (S-P) and Matchω (P-S) are based on Selkirk's (Reference Selkirk2009) correspondence-based definitions (2012: 243–244), though Elfner states that terminal node-based versions are possible. I propose the P-S constraint Matchω_T in (50b), based on Elfner (Reference Elfner2012: 28).

1. (50)

   

Match_E and Match_T cannot account for Muskogee mismatches, since they both assign one violation whenever syntactic and phonological units are mismatched. Fatally, P-S Match constraints favour unattested single-ω outputs without ω-recursion when an exact match is impossible. For example, for the input vP-phase X /a-wanaj/, all the outputs in (51) violate Match_E(X,ω) (49a) once, since the right edge of input vP-phase material /j/ does not correspond to the right edge of any output ω_min's. (51a–d) also all violate MatchWord_T once: in the undermatches in (a, b), ω_min does not exhaustively dominate all vP-phase input segments /a-wanaj/, while in the overmatch (51c) and lack of match (51d), ω_min does not exhaustively dominate only vP-phase input segments.

1. (51)

   

Partial mismatches, (51a–c), violate the P-S constraints more than the lack of match, (51d). ω_min in (a–c) violates Match_E(ω,X) once, since its right edges do not correspond to the right edge /j/ of an input X, e.g. /a-wanaj/. In (a–c), ω_min violates Matchω_T in (50b) once, since /a-wanaj/ does not dominate only ω_min segments in (a, b), nor all ω_min segments in (c). On the other hand, the entire ω [awanajijaɬiːs] lacks a matching input X based either on edges or dominated morphemes, violating Match_E(ω,X) and Matchω_T respectively. While a single-ω output [awanajijaɬiːs] incurs a violation of Match(ω,X) and Matchω_T, the recursive-ω outputs incur an additional violation for ω_min, so that P-S Match constraints prefer the single-ω to the recursive-ω. As (52) shows, the single-ω output harmonically bounds the attested recursive-ω output in terms of the relevant constraints.

1. (52)

   

(52) shows a ‘sour grapes’ problem (Padgett Reference Padgett, Suzuki and Elzinga1995): because no output of an odd-parity vP can be a perfect match (modulo resyllabified consonants) and satisfy Dep(μ), FtBin and Exh(ω,σ), the grammar defaults to a single-ω, lack-of-match output that vacuously satisfies P-S Match. Because even a small overmatch violates P-S Match, odd-parity vP-phase material is wrongly predicted not to show morphosyntax–prosody matching. Again, this goes against McCarthy's argument for categorical constraints and against alignment: mismatching is not ‘all or nothing’ (2003: 89).

Reviewers have suggested that calculating MatchWord/ω_T violations based on misaligned morphemes could keep mismatches minimal. MatchWord_T would assign one violation to each mismatched morpheme, i.e. a ‘terminal node … exhaustively dominate[d]’ by a syntactic word but not a phonological word (Elfner Reference Elfner2012). By itself, though, this reformulation is unworkable: without exhaustive domination of terminal nodes, there is no way to ensure that a certain X maps to a specific ω. Defining MatchWord_T to assign violations gradiently to morphemes requires assuming that the X and ω correspond, as in (53). Without the italicised material in (53), different morphemes’ phonological exponents could satisfy MatchWord_T while being in separate ω's.

1. (53)

   

The same problem does not apply to Align-R in (43), which only cares about the edges of Xs and ω's, not their morphological content. Align-R calculates violations based on whichever ω edge is closest to the X edge in question; it is agnostic to the particular ω it counts the distance from (thanks to an anonymous reviewer for raising this question).

In order for Match_T to enforce minimal mismatching by counting morphemes, X–ω correspondence must be enforced as well, presumably by a separate Match-like constraint. Alternatively, as suggested by a reviewer, Match constraints may be evaluated categorically at the interface itself, while the prosodic structure build by Match can then be altered in the phonology proper. Whether either of these two options is viable is beyond the scope of this paper. However, Match Theory requires one of these options to model Muskogee mismatches.

4.2 Cyclic models and phase (in)alterability

Because of the close alignment of morphosyntactic phases and phonological domains in Muskogee, phasal phonological models are well suited to these data. This section investigates a cyclic, Direct Reference account of Muskogee mismatches. In a cyclic model, the output of each phase is evaluated by the phonology in turn (e.g. Marvin Reference Marvin2002, Newell Reference Newell2008, Reference Newell, Newell, Noonan, Piggott and Travis2017, Samuels Reference Samuels2010, Scheer Reference Scheer2012, Šurkalović Reference Šurkalović2015).Footnote ⁷

A key question in cyclic models of both syntax and phonology is whether and to what extent previous cycles are ‘frozen’, or inalterable, in later cycles. Chomsky (Reference Chomsky, Martin, Michaels and Uriagereka2000), for instance, defines the ‘strong’ version of the PIC as in (54).

1. (54)

   

A cyclic account of Muskogee verbs requires vP-phase material in the first phonological cycle to be accessed, i.e. altered or deleted, in the second cycle, which includes CP-phase material. The Muskogee data thus cannot be subject to a strong PIC. Either the PIC must be weakened (Chomsky Reference Chomsky and Kenstowicz2001), allowing a phonological cycle to modify the output of the immediately preceding cycle (Samuels Reference Samuels2011), or it must be optional for a given phase head (D'Alessandro & Scheer Reference D'Alessandro and Scheer2015), or it cannot hold in phonology at all (Newell Reference Newell, Newell, Noonan, Piggott and Travis2017). In the latter case, the fact that previous phonological structure in Muskogee is minimally altered would be due to, for example, phonological persistence (Piggott & Newell Reference Piggott and Newell2016) or violable phase-phase faithfulness constraints (Šurkalović Reference Šurkalović2015).

In the cyclic model, vP-phase material goes through the first phonological cycle, which parses iambic feet. No additional metrical parsing occurs in the second cycle, so CP-phase material is generally unfooted. (55) illustrates the cyclic model: the vP-phase material, /a-wanaj-ak/, is exhaustively parsed into iambic feet in the first cycle. The CP-phase material, /-áɬiː-is/, is added in the second cycle, in which no further footing occurs, so the CP-phase suffixes are unfooted.

1. (55)

   

In (55), the vP-phase-final consonant /k/ is resyllabified into the following syllable, [ka], at the CP phase. In general, phasal models of phonology allow for resyllabification of earlier material in a later cycle, as mismatches between cyclic boundaries and syllable boundaries are commonly attested (e.g. Hayes Reference Hayes1995, Marvin Reference Marvin2002, Scheer Reference Scheer2012). As a reviewer notes, resyllabifying across a phase boundary suggests that, in phonology, even the strong PIC cannot be absolute. At the very minimum, a PIC or similar condition must allow for resyllabification as in (55).

I now show that the strong PIC cannot hold in Muskogee, even allowing for resyllabification. The vP-phase material in (55) is even-parity, and can be exhaustively parsed into binary iambic feet in the first cycle. Odd-parity vP-phase material, on the other hand, cannot; to metrically parse all odd-parity vP-phase material into feet, CP-phase material must be incorporated in the second cycle. This creates an intractable problem for the strong PIC, which states that a cycle is immediately frozen once built: the second cycle cannot parse more feet, since CP-phase material is generally unfooted. If the second cycle alters an existing foot built in the first cycle or deletes first-cycle material, the strong PIC is violated, and thus cannot hold in Muskogee.

For instance, in the verb [(aˌwa)(naˈja)ɬiːs] (56), with odd-parity vP-phase material /a-wanaj/, the final odd-numbered light syllable [na] is footed by including the CP-phase vowel [a] of /-áɬiː-/, giving (naˈja). The CP-phase vowel [a] must be footed, since it has H tone rather than downstepped H tone. The remaining CP-phase syllable [ɬiːs] has L tone and must remain unfooted, showing that new feet are not built on the second cycle.

1. (56)

   

With the odd-parity vP-phase /a-wanaj/, the output of the first cycle must have two feet, since no new feet can be built in the second cycle (57). The final foot may be degenerate [(ˈna)], (a), with the final consonant [j] unparsed, a heavy syllable [(ˈnaj)], (b), including the final consonant, or two light syllables [(naˈji)], (c), with a second vowel /i/ not present in the surface form (see Martin Reference Martin2011: 85–87; thanks also to an anonymous reviewer for the suggestion).

1. (57)

   

All three outputs in (57) require alterations of first cycle metrical structure in the second cycle. If the final vP-phase syllable is a single syllable foot in the first cycle (a, b), it has final stress: (ˈna) (58a), (ˈnaj) (58b). Final stress is incorrectly predicted to stay on this syllable in the second cycle ((a.ii), (b.ii)), whether the vP-final consonant [j] is resyllabified (b.ii) or not (b.iii). Altering the second foot to include the following CP-phase vowel [a] violates the strong PIC, which prevents structure built in one cycle from being altered in a subsequent cycle.

1. (58)

   

With the third alternative, (b.iii), vP-phase material ends in an abstract vowel /i/, as Martin (as well as an anonymous reviewer) suggests in a theory-neutral account (Reference Martin2011: 85–87). The abstract vowel allows a second, disyllabic foot, (naˈji), to be constructed in the first cycle, and metrical parsing is surface-true. However, the abstract vowel must be deleted and replaced by the following CP-phase vowel in the second cycle, violating the strong PIC (58c).

In a cyclic model with the weak PIC or without the PIC, the first cycle outputs in (57) can be altered on the second cycle to derive [(aˌwa)(naˈja)ɬiːs]. A final foot (ˈna) (58b.i) can be altered on the second cycle to meet binarity: (naˈja). A vP-phase-final consonant [j] (58b) is resyllabified on the second cycle and the final foot expanded to (naˈja). A vP-phase-final abstract vowel [i] (58c) is deleted on the second cycle.

Further evidence that a cyclic model of Muskogee verbs cannot include a PIC comes from right-spreading lgr H tone, which marks eventive aspect. §3.2 assumed that grade morphology is the exponent of an Asp phase head, which spells out the vP phase. The strong PIC cannot hold, no matter whether Asp is in the first or second phonological cycle. If lgr is in the input to the second phonological cycle, the strong PIC cannot account for verbs whose vP-phase material forms multiple feet. The second foot of vP-phase material, (waˈnaː), has downstepped H tone, as in (59).

1. (59)

   

Following Martin (Reference Martin2011: 88–91), lgr H tone is downstepped in forms like (59) because regular H tone precedes it. If lgr tone is in the input to the second cycle, the first cycle output will have H tone, due to footing (60a). On the second cycle, lgr H tone must displace first cycle H tone on the vP-phase-final foot (waˈnaː), and then undergo downstep. The strong PIC incorrectly prevents tone links established on the first cycle from being deleted in the second, predicting the wrong tone pattern in (60b).

1. (60)

   

If lgr H tone is present in the first cycle input, it correctly undergoes downstep. However, it is unclear what motivates lgr tone to spread rightward in the second cycle. In verbs whose vP-phase material comprises a single foot, as in (61), lgr H tone does not undergo downstep, even when spreading onto CP-phase material.

1. (61)

   

The tone pattern of the first cycle output with level lgr H tone will be identical to that of zero-grade and hgr-grade verbs, which lack additional input tone, as in (62a). There will be no way for lgr H tone to spread in the second cycle, since other H tones do not. In fact, the strong PIC should prevent any H-tone link in the first cycle from spreading in the second cycle. On the second cycle, lexically specific information from lgr grade will no longer be present, so the CP-phase syllable [jis] is incorrectly predicted to have L tone (62b).

1. (62)

   

As with the zero-grade forms, a cyclic model of lgr verbs must either use the weak PIC (Samuels Reference Samuels2011) or no PIC at all (Newell Reference Newell, Newell, Noonan, Piggott and Travis2017), or parameterise the PIC in phonology so that it does not apply to the Muskogee phase head Asp (see D'Alessandro & Scheer Reference D'Alessandro and Scheer2015 for Italian). A cyclic model of lgr verbs without the strong PIC allows either second-cycle lgr tone ^!H to displace H tone from the first cycle (cf. (60)) or first-cycle lgr tone to spread in the second (cf. (62)).

4.3 Stems and Stratal OT

Phonological models that make reference to the stem can also account for the mismatch of the inner morphosyntactic and phonological domains. I focus on Stratal OT (Kiparsky Reference Kiparsky2000, Bermúdez-Otero Reference Bermúdez-Otero, Hannahs and Bosch2018), which uses both a stem-level and a word-level grammar. In Muskogee, a Stratal OT account must stipulate that only vP-phase material goes through the stem-level grammar, while the entire word goes through the word-level grammar. Stratal OT avoids the problems of a phase-based phonological model with a strict PIC, since the output of the stem grammar can be altered in the word grammar, modulo faithfulness constraints.

While the parallel model in §4.1 accounts for the scope of footing by ranking Exh(ω_min,σ) above Exh(ω,σ), a Stratal OT model can do so by changing the ranking between stem-level and word-level grammars. Specifically, in the stem-level grammar, Exh(ω,σ) outranks *Foot. This ranking must be reversed in the word grammar, so that no further feet are constructed. (63) illustrates the onset undermatch [(aˌwa)(naˈja)kaɬiːs] ‘they will tie it to it’ with even-parity vP-phase material /a-wanaj-ak/ ‘dir-tie-pl’.

1. (63)

   

The word-level grammar ranks *Foot over Exh(ω,σ) to prevent further footing, the opposite of the stem-level grammar. As suggested by a reviewer, faithfulness to prosodic structure comes into play at the word level: high-ranking Max(Ft) prevents feet built at the stem level from being deleted at the word level (63b). Since there are no feet in the input to the stem level, Max(Ft) is not relevant in (63a).

To model rhyme overmatches with odd-parity vP-phases, the stem level must build a foot on the vP-final syllable, which thus must be closed by the vP-final consonant to meet FtBin. Odd-parity nouns like [(miːk)ko] in (6b), which go through the stem level as well, do not form a degenerate foot on the last syllable, showing that FtBin outranks Exh(ω,σ) in (64a).

1. (64)

   

At the word level, the final foot (ˈnaj) is altered to include the first CP-phase rhyme, since resyllabifying the vP-final consonant would otherwise result in a degenerate foot. I use Ident(Ft) to penalise altering the foot to (naˈja), while assuming that consonant resyllabification (as in (63b) above) does not violate Ident(Ft). With odd-parity vP-phase material, consonant resyllabification violates FtBin, which therefore dominates Ident(Ft) (64b). Onset and Dep(μ) also dominate Ident(Ft), since foot alteration is preferred to both leaving the CP-initial syllable onsetless (b.iii) and lengthening the vP-final vowel (b.iv). Higher-ranked Max(Ft) prevents vacuous satisfaction of Ident(Ft) by deleting the foot (ˈnaj), as in (b.v).

Recall from §2.3 and §3.3 that verbs with overt grade morphology, e.g. [(aˌwa)(ˈnah)jis], are always onset undermatches. Because grade morphology makes the vP-final syllable heavy, an odd-parity vP becomes even-parity with grades. I assume grade morphemes enter at the word level, which follows if the Asp phase head is not spelled out (though the analysis does not require this). At the word level, vP-final vowel lengthening (or /h/-infixation in the hgr grade) allows the final foot to satisfy FtBin without alteration. I assume that Dep(μ) is not violated in (65), since lengthening is due to lexical specification of an input morpheme, rather than mora epenthesis.

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In nouns, like [(noˌko)(soˈʧi)] in (6a), the domain of footing is the entire word. Therefore, the whole noun must go through both the stem level and the word level. The stem-level grammar, where Exh(ω,σ) outranks *Foot, selects the exhaustively footed output, as in (66).

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For the footing of nouns, then, the word level is superfluous: the stem-level output is already exhaustively footed. High-ranked Max(Ft) prevents feet from being deleted, and there is no material remaining to be footed (67). (The word level is still relevant for obstruent voicing and tonal downstep, which applies to the entire word.)

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The tableaux above show how Stratal OT accounts for the Muskogee mismatch data, which highlight the connection between phases and strata. The stem-level input is the material spelled out at the first phase of the word: the vP phase in verbs and the entire word in nouns (minus clitics; §3.2). The Muskogee pattern thus provides more evidence that word-level cyclic domains go through the stem stratum (see also Giegerich Reference Giegerich1999, Bermúdez-Otero Reference Bermúdez-Otero, Hannahs and Bosch2018, Dolatian Reference Dolatian2020).

The role of prosodic faithfulness constraints like Max(Ft) and Ident(Ft) in Stratal OT merits further investigation. In parallel OT, inputs do not have prosodic structure, and prosodic faithfulness constraints are not possible (cf. serial versions of OT like Harmonic Serialism; McCarthy Reference McCarthy2008). In Muskogee, feet can be altered (Ident(Ft) can be violated), but not deleted (Max(Ft) is always obeyed). In (64), I assumed that consonant resyllabification does not violate Ident(Ft), but inclusion of a following vowel does. What constitutes violation of Ident(Ft) and what other foot faithfulness constraints exist in Stratal OT are open questions.