The phoneme inventory of Arapaho is rather small, for all vowels, consonants and tonemes. Arapaho has a rather unusual four-vowel inventory of ɛ, ɔ, i, u, characterised by the lack of a phonetic low vowel (13). Length is a contrastive phonemic feature on plain vowels as well as on diphthongs. In the following, I will follow Cowell & Moss (2008) and Arapaho orthography and represent the vowels as e,o,i,u, and length by doubling.

The consonant inventory is quite small as well, with only twelve consonants (14). It is important to introduce the consonantal system, because the traces that the Duke-of-York epenthetic vowel leaves behind will manifest themselves mostly through consonantal changes. In addition, the quality of adjacent consonants bears an influence on the quality of the epenthetic vowel.

The distribution of /i/ and /u/ is almost allophonic, as [u] can be analysed as a rounded /i/ in almost all instances. The round vowel is restricted to a position preceded by dorsal consonants, and the unrounded high vowel to syllables with non-dorsal onsets. Between a dorsal onset and a palatal glide however, there is free variation (15).

A preceding /o/ induces rounding (or blocks derounding) of an /i/ across velar and glottal consonants, but also across underlying /θ/ which dorsalises to [x] in this case (16).9

There are two contrasting level tones in Arapaho, low and high (17). Since Cowell & Moss (2008) regard Arapaho as a pitch accent language, following Algonquianist traditions, they define the high tone as “accented” and the low tone as “normal pitch”. I argue that there is evidence that even the low tone is indeed (at least potentially) an underlying tone and not just the phonetic realisation of tonelessness. High tone is marked with an acute, and low tone with the lack of marking. Both tones can appear in any position of the word, but words not containing at least one high tone are extremely rare (17).

A long syllable – a syllable that contains a long vowel or a diphthong, even a short one – can be level low, level high or have a falling contour (18). The fall is marked with an acute on the first mora. There are no tautosyllabic rises, a high tone is always left-aligned to the syllable.

The position of high tones is generally free, but severely constrained by two conditions. A single high tone can maximally span a syllable (two morae), and as said above, minimally the first mora. In addition, a strong OCP prohibits adjacent high tones. There must be at least one low toned mora between them. If a sequence of two high toned syllables arises through concatenation, the left high tone deassociates from the adjacent mora if it is on a long syllable. This process accounts for most but not all falling tones. If the left high tone is associated to a short syllable, the tone is displaced and shifts to the left (19).10 It can only shift on morae belonging to the same morpheme as itself (Zimmermann 2011), and if there is no such mora available, the tone is deleted.

Some morphemes, roots as well as affixes, are lexically specified as containing a floating high tone. This floating tone can never land on the morpheme it belongs to but instead docks to an adjacent morpheme (20).11 I will represent this floating tone with a superscript H as shorthand for the autosegmental structure (21).

If docking of the floating tone creates a sequence of two consecutive high tones, the underlyingly linked tone deassociates forming a falling contour, shifts onto another syllable or deletes (22)12 – the expected OCP pattern. If a floating high tone docks to a syllable which is already high-toned, nothing happens at the surface. The first syllable of such floating tone bearing morphemes is always phonetically low.

A floating high tone normally attaches to the morpheme left of its morpheme of origin. However, there is at least one morpheme that triggers a high tone on the morpheme to its right (23). In (23-b), the high tone of the third morpheme deletes because it cannot shift inside the same morpheme. Delinking of the high tone from the second mora is also ruled out, since this would create a rising tone.

As I have mentioned above, Cowell & Moss (2008) and also Zimmermann (2011) assume, at least implicitly, that the phonetic low tone is nothing but the realisation of phonologically toneless TBUs. This assumption leads mostly to correct predictions, there is however some evidence for floating low tones as well. Some morphemes “repress” a high tone, either on a preceding or on a following morpheme. This pattern is not exactly parallel to the floating high tones, because the floating low tone does not land on the closest mora, it lands on the closest high tone bearing mora.13 If a high tone is replaced by a floating low tone, it does not seem to be able to shift, the evidence for this however is scarce. The deletion of the high tone in the first example of (24) can neither be due to the OCP (see Section 5.1 for more on the OCP) nor general tone rules: those would predict that both high tones of the second morpheme shift to the right.

The floating low tone can force underlyingly associated high tones to deassociate, but it loses against floating high tones if they compete for the same TBU. However, even though it fails to associate, the floating low tone leaves a trace, see (25) and the autosegmental representation in (26). A clash of two high tones on two adjacent TBUs becomes licit if a floating low tone intervenes between them.

These data suggests that the OCP in Arapaho does not target adjacent syllables that are associated to a high tone, but the high tone-mora combinations that are adjacent on both the tonal and the moraic tier.

The syllable structure is simple and basically CV, however there are two exceptions. Word-final codas are allowed and any consonant can be in the word coda. In contrast to onsets, coda consonants are not restricted by the preceding vowel (27). The glottal fricative /h/ is a licit coda even word internally and may form a coda cluster word finally (28). Other clusters are ungrammatical.14

Arapaho thus avoids (word-internal) codas with place features, which is a typologically common restriction on codas (O’Brien 2012). If, however, a word internal coda arises through concatenation, the unwanted configuration is not resolved by debuccalisation, but by epenthesis.15 The quality of the epenthetic vowel is inserted by default, and it is – typologically not unexpected – the high front vowel [i] (29). It rounds to [u] under exactly the same circumstances as morphemic /i/ does, preceded by the low, rounded vowel if no non-dorsal consonant intervenes.

Epenthesis appears to be restricted to configurations where consonant clusters co-occur with a floating high tone (30).

If there is no floating high tone, instead of an epenthetic vowel it is a consonant cluster that is realised (31).

These data look strikingly like a case of floating tone induced epenthesis, as defined in Section 2. A major difference is, that in the case of Arapaho tone cannot be the only trigger of epenthesis, since there is no epenthesis when the coda condition is not violated. In that case the floating tone is shifted onto the adjacent morpheme, as seen in (20). Epenthesis is thus a possible operation if it breaks up a coda and can host a floating tone.

As mentioned in Section 4, OCP violations in the tonal domain are dispreferred (Zimmermann 2011). A high tone span is maximally tautosyllabic, encompassing two morae, and there are no adjacent high tone spans. If concatenation creates a high tone clash, the furthest tone to the left deassociates, deletes or shifts, as shown in (39), repeated from (19).

Floating high tones are, just like non-floating high tones, responsible for the same OCP related processes (40), repeated from (22). However if, a floating high tone lands on an already high toned syllable, there is no visible effect on the surface (41).

The data point crucial for the argumentation is the combination of a floating high tone that follows a high toned syllable with a coda (42).

Now, there are two logical possibilities about what is happening. If epenthesis is due to the demand to keep the tonal quality constant, as assumed above, we expect no epenthesis. The floating tone should be able to dock onto the high tone that is already there. This, however, is not what happens (43).

The epenthetic vowel is realised and attracts the tone. This would create a clash, violating the OCP. The high tone on the prefix, though, behaves like any other high tone in a configuration violating the OCP on adjacent high tones. In the case of (43), it deassociates from the second mora. As we see, epenthesis is actually enabling tonal unfaithfulness, not preventing it. An analysis where epenthesis is partially triggered by tonal faithfulness, like the one laid out in the previous subsection, makes thus wrong predictions and fails to derive the correct output (44). The telephone symbol indicates the candidate that wins in the actual language. The concrete implementation of the OCP is not relevant, since neither of the candidates in (44) violates it.

This problem can be avoided if the constraint in (32) is redefined as referring to tokens of tone. If this assumption is adopted, whatever we do leads to a violation of the constraint – the original high tone is either replaced by a low tone or by another high tone. In order to avoid a violation of the constraint conjunction, an epenthetic vowel must be inserted. This however yields a hardly natural generalisation: epenthesise in order not to change the tone, or if the tone changes anyway.

Another, and probably stronger, argument that tone is not a co-trigger of epenthesis in Arapaho comes from consonantal processes. There are two types of consonant-vowel interactions in the context of (high) front vowels and, as already mentioned, the epenthetic vowel is one of those. The first process is a palatalisation-like process that I will call develarisation, and the second one is a rather unusual chain shift that I will refer to as dental sonorisation. The important aspect of these processes is that they affect every word-internal coda that would be followed by an epenthetic [i], if a floating high tone were available.

Develarisation is a productive and general process that affects all velar consonants /k,x,w/ to different degrees. These consonants are fronted if they precede a front vowel /e, i/ following the scheme in (45). It is not an instance of palatalisation because not all segments turn into a palatal/coronal.

Examples for each change are given in (46).18 Just like the front vowels, the palatal glide triggers develarisation, unlike them it is deleted in the process (46-c).19

Develarisation is blocked by high vowel rounding, compare example a. in (16), repeated in (47). Develarisation of /k/ and /x/ is also blocked if they follow an /o/ and precede an /e/, the glide /w/ however is develarised in this position (48). Develarisation induced by /j/ is never blocked, see (46-c).

The three triggers of develarisation, i, e, j, are thus not completely identical. Develarisation triggered by [i] is always blocked by a preceding low round vowel, feeding the rounding of the potential trigger, while develarisation caused by [e] is partially blocked by a preceding /o/, this blocking though does not result in rounding of the low front vowel. The palatal glide on the other hand triggers develarisation regardless of the context.

The other process, dental sonorisation, occurs in a similar environment: before the high front vowel [i] and the palatal glide, but not the mid front vowel [e]. Anterior coronal obstruents become gradually more sonorous before front vowels, as in (49). This process takes the form of a chain shift, which by itself is a difficult issue for (parallel) OT (Kirchner 1996; Farris-Trimble 2008). The complications that arise because of the chain shift will be ignored in the following. Examples are given in (50).

The additional process of /θ/ velarisation, which changes underlying /θ/ to [x] between a back and a high vowel, blocks this process, as could be seen in (16), repeated in (51).

In contrast to develarisation, dental sonorisation is a derived environment effect. Monomorphemic /ti/ and /θi/ sequences surface unaltered (52). There are some lexemes which idiosyncratically do not undergo dental sonorisation, even across a morpheme boundary (53).

The epenthetic vowel behaves with respect to develarisation and dental sonorisation just like any other front/front high vowel. Develarisation is triggered unless the epenthetic vowel is preceded by an [o], and dental sonorisation is triggered unless the morpheme is specified as a non-undergoer (54).

These changes also occur in contexts where we would expect an epenthetic vowel due to syllable-structure constraints, i.e. where we have a word internal coda, but the vowel fails to surface due to the lack of a floating high tone (55).

It is not possible to argue that these changes are due to a constraint that forces codas to undergo independently the [i] induced processes independently, since any consonant can be a word-final coda (but the condition on word-final codas might still be different) and changes do not occur if the expected epenthetic vowel would be [u] (56).

A mechanism that forces word-internal codas to undergo exactly the same processes they would undergo if followed by an [i] seems like a redundant duplication of processes in the language. Additionally, word internal codas may arise through a separate process of /o/ deletion, in which case the derived codas do not show any of the effects (57). Furthermore, there is no phonetic motivation for such changes in a coda at all.

These data clearly suggest that the epenthetic vowel is there long enough to influence its segmental surroundings and attract a high tone, and then be deleted. A deletion hypothesis receives further support from different data: every non-final, non-initial low toned high vowel may delete. This deletion is obligatory for epenthetic vowels, except for very deliberate, slow speech, but optional for lexical morphemic vowels. It has been claimed that such patterns should not exist (de Lacy 2006). However, such tone sensitive reduction phenomena are not unattested. For example Stojković (2017) argues that this is exactly what happens in Bosnian: reduction (including deletion) of insufficiently sonorous vowels, in the case of Bosnian they are low toned mid vowels, and all high vowels regardless of tonal quality.

Stratal OT (Kiparsky 2000; Bermúdez-Otero 1999; 2003; Bermúdez-Otero 2011; Trommer 2011) is a serial variant of OT that transfers some major insights from Lexical Phonology (Kiparsky 1982; 1985) into Optimality Theory. The evaluation of outputs is distributed on several levels or strata, normally but not necessarily assumed to be three: stem level, word level and phrase level. Affixes select the stratum in which they concatenate. Between the strata, a re-ranking of constraints is possible, which makes Stratal OT capable of accounting for many cases of opacity. Stratal OT puts no inherent restrictions on the generator.

For the Arapaho case, I assume that the relevant strata are the stem and the word level. There are no very strong reasons that make this assumption necessary, however, there are two arguments in its favour. First, the deletion of the low toned, low sonority high vowels is sensitive to the boundaries of the phonological word: it does not affect last or first vowels of prosodic words. Second, there are a few prefixes that do not trigger vowel epenthesis or show its traces, they also do not block stem-initial [h]-epenthesis, see (59).

The first is an argument for deletion at the word-level while the second is an argument for epenthesis at the stem level. Especially the first argument is weak, as even processes on the phrase level might be sensitive to word boundaries. In addition, the deletion process is optional and optional processes tend to occur rather at the outer-most stratum. To put epenthesis on the stem level and deletion on the phrase level might thus be just as valid.

Almost all of the processes discussed so far apply at the stem level: epenthesis of course, and along with it develarisation, dental sonorisation, docking of floating tones and the tonal displacement caused by the OCP. Re-ranking between strata is possible and the sole constraint responsible for epenthesis, NOCODA, is demoted. At the next stratum, the word level (or potentially the phrase level, skipping the affixation of prefixes like the ones in (59)), low toned, short high vowels are (optionally) deleted. This deletion is again actually a cumulative effect: a vowel is deleted if it does not have a high tone and it has [+high] feature and is dominated by only one mora. Such vowel deletion that depends from multiple factors can either be analysed with Harmonic Grammar, as in Stojković (2017), or with complex cover constraints, as in McCarthy (2008). For the sake of exposition, I employ the latter, here called SYNCOPE and defined as in (60).

Develarisation and especially dental sonorisation are complex on their own and cannot be fully analysed in this paper. I suggest that develarisation is the response to a markedness constraint that penalises [DOR][-back] sequences inside a syllable (61).

The velar obstruents /k/ and /x/ are then associated with an epenthetic feature [COR], turning them to [t∫] and [s]. The glide /w/ on the other hand has an additional labial feature from the beginning and thus does not need to insert a new one. It just loses its [DOR] feature and becomes a labial, [b].20

Dental Sonorisation is even more problematic, mostly because it is a derived environment effect and a chain shift and hence comes along with all the associated difficulties. For the time being, it will be derived by the ad hoc constraint D(ENTAL)S(ONORISATION), given in (62).

Future research should address an in-depth analysis of these two intriguing processes and especially put them in relationship to other vowel-consonant interactions triggered by front vowels. While the OCP and the changes related to it constitute an argument against a tone-triggered analysis, they do not give a good argument for a Duke-of-York analysis either: every time tones get unexpectedly shifted in front of an epenthetic vowel, that epenthetic vowel has received a high tone and is thus not deleted. In other words, the derivation stops at the EDC stage. This is a regular feeding interaction. I will therefore leave the OCP cases out of the following discussion.

Let us now turn to the technicalities of the derivation. At the stem level, NOCODA outranks (DEP) and SYNCOPE, a ranking that enables epenthesis. I assume that the insertion of a [-high] vowel is ruled out due to a higher ranked (DEP) constraint. It has long been noted in the literature, that the vowels which tend to be epenthesised and the vowels which tend to be deleted are very often the same, see e.g. Lombardi (2002). The tableau in (63) illustrates the stem level computation of an input with a coda but without a floating tone. In this particular case, the coda consonant is the dental fricative /θ/. Candidate a. is faithful and consequently violates the high ranked NOCODA. Both candidate b. and c. satisfy this constraint by epenthesising an [i], but candidate c. fails to undergo dental sonorisation making b. the winner.

A stem level derivation for an input with a coda consonant and a floating tone does not look very different (64). The faithful candidate a. does not satisfy NOCODA. Candidates b. to d. are ruled out because they fail to land the floating tone or to develarise the glide /w/ or both. Candidate e. is the winner: it epenthesises, avoiding a violation of NOCODA, develarises and attaches the floating tone. Candidate f. does this too, but it lands the floating tone on the prefix instead of the epenthetic vowel. This candidate is here ruled out by the low ranked ID.T because a TBU does not surface with its underlying tonal specification.

After the stem level has been computed, its output serves as the input for the word level. At this stratum, the constraint ranking has changed. The formerly high ranked NOCODA is now lower ranked, while SYNCOPE has gained importance. In the case without the floating tone, in tableau (65), this becomes crucial. The faithful candidate a. contains a low toned short high vowel, which violates SYNCOPE. The winner is thus candidate b. which deletes the vowel that has just been inserted at the last stratum.

In the case of t∫ebísee (66), the high tone protects the epenthetic vowel from deletion. It does not fall under the scope of SYNCOPE any more.

Stratal OT, due to its ability to have both intermediate representations and re-ranking, is thus able to account for the Duke-of-York epenthesis in Arapaho.

A central argument in favour of HS is that it allows and presupposes intermediate representations, and can therefore derive patterns that are impossible to derive for parallel OT, exactly because parallel OT lacks such representations (Elfner 2016). The intermediate representation is necessary for Arapaho, too, but HS still fails to derive it, because it does not allow for re-ranking.

Cases of (optional) deletion of underlying high vowels that have triggered segmental changes are also not unproblematic since they constitute an instance of counterbleeding, see McCarthy (2016) for an analogous problem. However, there are several ways out for HS – for example, SYNCOPE can be defined in such a way, that it becomes active only after DS has been satisfied (see Elfner 2009; 2016 for similar approaches to opacity in HS). Extending such an analysis to the cases of visible epenthesis, a high ranked NOCODA is needed to enforce epenthesis in the first place. This constraint will prove to be fatal for this account, but it derives data like t∫ebísee correctly, as is shown in the derivation from (67) to (70). The ordering of docking the floating tone and changing the consonants and hence the ranking of *[DOR][-bk] and *FLOAT is arbitrary.

The HS approach, (71) to (73), however cannot account for the deletion of epenthetic vowels, even if it satisfies SYNCOPE. The epenthetic vowel is per definition toneless. Its introduction therefore always violates SYNCOPE. It follows from this that the epenthesis triggering constraint NOCODA must outrank SYNCOPE. At a later step, though, NOCODA must be outranked by SYNCOPE, so that the epenthetic non high-toned vowel can be deleted. A re-ranking of the two constraints in the middle of the derivation is however not a possibility in the framework of HS.

After the consonant has been modified, the derivation converges on the wrong candidate (73). The winner of the actual language is marked with the telephone symbol (73-a), it can never be optimal in this derivation because NOCODA is so highly ranked.