1 A/an, the, allomorphy and phonology

The English a/an alternation can be described as follows: an is used if the immediately following word starts with a vowel; otherwise a is used.

    1. (1)
    1. a.
    1. an apple, an interesting book
    1.  
    1. b.
    1. a book, a very red apple

Despite the apparent simplicity of this generalization, the a/an alternation has been notoriously difficult for linguists to understand, and has often been featured as a problematic case study in discussions of the phonology-morphology interface (see e.g. Rotenberg 1978; Kaisse 1985; Zwicky 1986; Hayes 1990; Spencer 1991; Mascaró 1996b; Joseph 1997; Asudeh & Klein 2002; Yang 2004; Lee 2009; Nevins 2011). A/an presents a paradox: it is restricted to a single morpheme, which suggests that it is a morphological phenomenon (viz. allomorphy), yet it depends crucially on information about the following word, and thus cannot be characterized as a strictly word-internal process (Spencer 1991: 127–129). While it is possible to derive a/an phonologically, by either /n/-insertion or /n/-elision (Hurford 1972; 1974; Perlmutter 1970; Venneman 1974), the obvious weakness of such an approach is that it requires postulating a special phonological rule that applies to only one morpheme.1 More recent analyses have therefore treated a/an allomorphically, and have taken care of the non-word-boundedness paradox either by having a(n) cliticize to the following word (as proposed here; see §3), or by admitting some kind of “phrasal” or “external” allomorphy into the grammar (e.g. Hayes 1990; Mascaró 1996b; Asudeh & Klein 2002).

Here I look at a/an alongside a strikingly similar but far less studied phenomenon from English: the alternation between /ði(j)/ and /ðə/ in the definite article (henceforth the). The distribution of the alternants is almost identical to that found with a/an (albeit somewhat less regular):2 use /ði(j)/ if the immediately following word starts with a vowel; otherwise use /ðə/ (Ladefoged 1975: 91–92).3

    1. (2)
    1. a.
    1. /ði/ apple, /ði/ interesting book
    1.  
    1. b.
    1. /ðə/ book, /ðə/ very red apple

Like a/an, the cannot be derived by an across-the-board phonological rule; word-final prevocalic /i/ alternates with preconsonantal /ə/ only in the, not in lovely, happy, agenda, etc.:

    1. (3)
    1. a.
    1. /ði/ apple ~ /ðə/ book
    1.  
    1. b.
    1. lovel/i/ apple ~ *lovel/ə/ book
    2. part/i/ animal ~ *part/ə/ time
    3. *agend/i/ item ~ agend/ə/ change

Should the then be analyzed allomorphically on par with a/an? There has not to my knowledge been a formal analysis that addresses this question head-on. Given their structural and distributional similarities, a unified treatment of a/an and the seems desirable; correspondingly, some previous studies simply adopt the terms allomorphy and allomorphs to refer to the (e.g. Jurafsky et al. 1998: 3; Newton & Wells 1999: 74; Britain & Fox 2009: 180ff). A unified allomorphic treatment might be especially appealing in the context of a theory of allomorphy as the emergence of the unmarked (TETU) (Mascaró 1996a; b; 2007). Both a/an and the appear to be hiatus-avoiding alternations (4), and this kind of phonological optimization can be directly explained by theories where allomorph choice is determined by surface constraints like ONSET and NO-CODA (see §4). Analyzing the in this way would imply, of course, that the was also an allomorphic alternation.

    1. (4)
    1. a.
    1. a egg / (*VV) vs. an egg (V.CV)
    1.  
    1. b.
    1. th/ə/ egg / (*VV) vs. th/ij/ egg (V.CV)

Nevertheless, this paper argues that the is phonological, not allomorphic, in nature – specifically, the /ðə/ variant of the definite article is derived by phonological vowel reduction. Vowel reduction is also responsible for weak/strong alternations in other English function words, e.g. for, have, can; to explain why this otherwise word-internal rule appears to apply across a word boundary in e.g. the dog, I propose that English articles cliticize to the following word. I furthermore argue that article cliticization is what enables allomorphy in a/an (as suggested in passing in Spencer 1991: 128). In the serialist architecture adopted here, a/an is derived in three steps:

  1. article cliticization;
  2. allomorphy (insertion of either /e/ or /æn);
  3. then phonological vowel-reduction – notably, the same vowel-reduction that derives /ðə/ in the definite article – which derives the weak variants /ə/ and /ən/ from the strong variants /e/ and /æn/ (respectively).

The weak/strong distinction in the indefinite article is not widely recognized in previous work, and presents a complication for proposals that treat a/an as uniformly allomorphic. I show that the distribution of the four alternants (/e/, /æn/, /ə/, /ən/), and their very regular parallels with other weak/strong function-word alternations, are best explained in a hybrid, multi-step model where a/an involves both allomorphy and phonology and the involves only phonology.

The analysis has at least two important theoretical consequences. First, it underscores the need for at least some “special” phonology (in this case, word-internal phonology) – meaning that the fact that an alternation does not apply across-the-board cannot in itself be taken as evidence that the alternation is allomorphic. Second, if it is true that allomorphy strictly precedes phonology as in the model adopted here, then allomorphy cannot have direct access to the surface phonological structure (contra TETU-based approaches). In §4 I show that a/an is not always phonologically optimizing on the surface; an is sometimes selected even when its /n/ syllabifies as a coda (e.g. an /ʔ/ápple), and a is sometimes selected even when it is immediately followed by a vowel (e.g. I want a um…). Implications of these findings for theories of the phonology-morphology interface are discussed in §4.4 and §6.

The paper is laid out as follows. In §2 I review some criteria for distinguishing allomorphy from phonology and show that there are non-trivial differences between a/an and the. In §3 I lay out my analysis of a/an and the (briefly sketched above). In §4 I present evidence that neither a/an nor the is uniformly phonologically optimizing. An account of inter- and intraspeaker variability in a/an and the is given in §5, and §6 concludes the paper.

2 Criteria for distinguishing allomorphy from phonology

In this section I review some well-known criteria for distinguishing allomorphy from phonology and hold up a/an and the individually to these criteria. We will see that, despite initial appearances, there are non-trivial differences between a/an and the that would present problems for a uniformly allomorphic treatment of either alternation.

Throughout this paper I use the term allomorphy to refer to a situation where a single morpheme has two or more distinct phonological forms, each of which is memorized and stored (i.e. where neither form is derived from the other). Since allomorphy involves storing distinct forms, it is most clearly at work when (i) the alternants in question have very different pronunciations, and (ii) the alternation is restricted to a single morpheme. English go/wen(t), for example, is an obvious candidate for an allomorphic treatment by both measures: /ɡo/ and /wɛn/ are so dissimilar that it is certainly easier to store them separately than to learn the series of rules that would be needed to derive one from the other phonologically – especially since these rules would have to be restricted to a single morpheme, the light verb vgo.

The alternation between /ætəm/ and /æɾəm/ in the (American) English word atom, on the other hand, is uncontroversially a case of phonological “tweaking” rather than allomorphy: unlike with go/wen(t), (i) the alternants are nearly identical phonetically, and (ii) the distinguishing segments (/t/ and /ɾ/) alternate not just in the word atom but in virtually any context that meets the conditions for Flapping (Nespor & Vogel 1986: ch8, among many others), even across XP boundaries (e.g. We gave the fruitba[ɾ] a shower;Kaisse 1985: 26). It is obviously far less burdensome to learn a phonological rule of Flapping than to memorize a variant pronunciation for every word with a potential t~ɾ alternation (along with its conditioning contexts).

The two criteria we have been considering are summarized below:

    1. (5)
    1. Allomorphy or phonology?
    2. Criterion Allomorphy Phonology
      A. Degree of phonetic resemblance Very little resemblance (e.g. go/wen(t)) Very close resemblance (e.g. t/d/ɾ)
      B. Degree of lexical/structural restrictedness Restricted to one morpheme (e.g. go/wen(t)) Potentially across the board (e.g. atom, at ’em,…)

I have intentionally begun with very obvious examples. What makes them so obvious is that they are oriented at the opposite endpoints of both the Criterion A scale and the Criterion B scale. But it is important to keep in mind that these criteria do involve scales, not binary choices, and that many (perhaps most) cases fall somewhere in the middle of one or both scales. Different kinds of French liaison, for example, are situated at different points along the Criteria A/B scales and have been analyzed both allomorphically and phonologically with varying degrees of success (see Tranel 1990 for a review; see Hayes 1990; Pak 2008; Siddiqi 2013 and §4 for additional cases and discussion). A/an and the are also both in-between cases, and since they are so similar to each other in basic respects (same language, same morphosyntactic category, same phonological conditions), any differences in terms of where on each scale the alternations are situated will be particularly informative.

Let’s consider how a/an measures up with respect to Criteria A and B.

With respect to Criterion A (degree of phonetic resemblance), a and an are more similar than /ɡo/ and /wɛn/, and it is possible to derive one from the other phonologically via a single rule.4 However, as pointed out by Rotenberg (1978: 27ff), this rule would need to be a rule of /n/—insertion (aan) rather than the more phonologically natural /n/—elision (ana) (pace Perlmutter 1970; Hurford 1972). This is because a, rather than an, is the form that appears in “elsewhere” contexts like (6), where the indefinite article is structurally separated from its nP complement.

    1. (6)
    1. a.
    1. I had a (silence) oh, what do you call it, an epiphany.
    1.  
    1. b.
    1. I’d like a, um, a large coffee and a croissant.
    1.  
    1. c.
    1. [This is] a, although I hate to admit it, very silly idea. (Rotenberg 1978: 39)

So while a phonological analysis of a/an is possible, it would require an unnatural rule arbitrarily inserting /n/ before a vowel (Ø → n / __#V).5

With respect to Criterion B (degree of lexical/structural restrictedness), a/an is an isolated case, applying to only one morpheme. In this respect it is similar to go/wen(t).

Now let’s see how the measures up.

With respect to Criterion A, /ði/ and /ðə/ are identical except that one has a full vowel /i/ where the other has /ə/. It is possible to derive /ðə/ from /ði/ phonologically via unstressed-vowel reduction, which (unlike /n/-insertion) is a cross-linguistically well-established phenomenon (Crosswhite 2004).

With respect to Criterion B, as well, the is closer to the phonological end of the spectrum than a/an. While it is true that word-final /i/ and /ə/ do not alternate in happy, party, agenda, etc. (as noted in §1), V~ə alternations are found in many word-internal contexts in English. For example, affixation and other word-formation processes yield well-known alternations between full vowels and /ə/ ((7)a) (Chomsky & Halle 1968; Marvin 2002). Furthermore, there is both inter- and intra-speaker variation in the pronunciation of unstressed vowels in behave, eleven, and other words beginning with orthographic re-, de-, e-, be-, pre- ((7)b) (Wells 2008; Nádasdy 2013). Finally, many monosyllabic function words – including the – have a “strong” (stressed) full-vowel variant as well as a “weak” (stressless) variant with /ə/ or a syllabic consonant ((7)c) (Selkirk 1995; Jurafsky et al. 1998 among others).

    1. (7)
    1. More V~ ə alternations in English:
      1. a.
      1. Word-formation: beaut/i/~beaut/ə/ful, /ə/xpl/e/n~/ɛ/xpl/ə/nation
    1.  
    1. b.
    1. Stylistic variation: believe, behave, relax, emergency, eraser, eleven
    1.  
    1. c.
    1. Monosyllabic function words:
      1. You c/ǽ/n finish early, but you won’t. ~ You c/ə/n dó it.
      2. I voted f/ɔ́/r it, not against it. ~ I voted f/ə/r Jóhn.
      3. John wrote th/í/ paper on Lincoln. ~ John wrote th/ə/ páper.

So while both a/an and the are “in-between” cases with respect to Criteria A and B, the is closer to the phonological end of both scales than a/an. In the remainder of this paper I pursue the hypothesis that these differences, while not extreme, are nevertheless significant, pointing to a fundamental difference in the grammatical status of a/an and the. As shown in the next section, the can be wholly subsumed under a phonological analysis involving unstressed-vowel reduction, while a/an calls for allomorphy in addition to vowel reduction.

There are at least two additional preliminary indications that the should be analyzed phonologically. First, the phonological conditions for the are very similar to those for V~ə alternations in word-formation: just as the vowel in the (usually) does not reduce before vowels (/ðə/ book, /ði/ apple), the vowel at the end of a root or “stem” does not reduce before a vowel-initial suffix (beaut/ə/-ful, beaut/i/-ous) (Chomsky & Halle 1968: 111). This parallel suggests that the might be produced by the same (word-internal) phonological rule(s) as the alternations in (7)a. If we treated the allomorphically, the fact that the /ðə/ “allomorph” shows up in just those contexts where /ə/ is generally allowed in English (unstressed, before consonants) would be a mere coincidence.

Interestingly, there is also some evidence that children acquire the earlier than a/an. Table 1 shows results from a study of 36 North American 3- to 7-year-olds and their adult caregivers in the CHILDES corpus (MacWhinney 2000). In contexts where the definite article was prevocalic (e.g. the apple), children in this study used the expected form /ði/ 49% of the time, but in contexts where the indefinite article was prevocalic (e.g. a(n) apple), children used the expected form an only 38% of the time (see §5 for more details; see Newton & Wells 1999 for similar results from an experimental study). This apparent lag in the acquisition of a/an is particularly striking given that the adult caregivers showed the opposite pattern, using the expected prevocalic form less frequently with the than with a/an (see Healy et al. 1998; Raymond et al. 2002 for further evidence that adults have more variability with the than a/an).6

Table 1

Frequency of prevocalic an and /ði/ in 36 North American 3- to 7-year-olds and their adult caregivers in CHILDES.7

% an an/(a+an) % ði ði/(ðə+ði)

children 38% 133/347 49% 457/935
adults 96% 1952/2033 90% 773/863

One possible explanation for this contrast is directly related to the proposal advanced here: that the is one reflex of a more general vowel-reduction rule in English. The idea would be that children are noticing at least some of the other V~ə alternations in (7) and making connections among these alternations, the, and phonological vowel reduction, whereas with a/an they have no such precedent and must acquire the alternation as an isolated case (see §§5–6 for further discussion).8 This line of explanation rests on the assumption that the is a phonological alternation between V and /ə/ rather than an allomorphic alternation between /ði/ and /ðə/. If /ði/ and /ðə/ were allomorphs, they would be stored independently and inserted as atoms, just as e.g. /ði/ and /ma/ would be, and any parallels with other V~ə alternations in the grammar would have to be seen as coincidental rather than potentially informative for acquisition.

3 Analysis

For clarity of exposition, I will first lay out an analysis of a/an and the that assumes that both alternations are categorical (contrary to fact). Then, in §5, I will show how this analysis can be incorporated into a competing-grammars framework to account for various kinds of attested inter- and intraspeaker variation.

3.1 The as a phonological alternation

I assume an architecture in which surface phonetic forms are derived by a strictly ordered series of operations in a post-syntactic PF component (Halle & Marantz 1993, among others). PF operations include linearization, vocabulary insertion (i.e. insertion of the phonological content of functional heads, including allomorphically alternating heads), limited structural readjustments (e.g. certain kinds of “cliticization,” or local dislocation), and phonological rules of various kinds (see Embick & Noyer 2001 et seq.) (Figure 1).

Figure 1 

Distributed Morphology architecture.

Consistent with much recent work in Distributed Morphology, I assume that morphosyntactic structures – including internally complex words – are spelled out in chunks (or cycles) instead of all at once (Marvin 2002; Embick 2010 see also note 15). Furthermore, I assume that phonological rules apply as these chunks of increasing size are spelled out and linearized, and thus have access to different kinds of information (Marvin 2002; Pak 2008).

In §2 we reviewed a number of facts suggesting that the is just one reflex of a more general vowel-reduction process in English. The analysis laid out here therefore advances the following hypothesis:

    1. (8)
    1. the is derived by the same (vowel-reduction-based) phonological analysis as other V~ə alternations in English (e.g. (7)a, (7)c).

An initial challenge to such a unified analysis, as noted in §1, is that the appears to be an exception to the strictly word-internal nature of vowel-reduction: /i/ does not usually reduce word-finally (Chomsky & Halle 1968: 111).

    1. (9)
    1. *lovel/ə/ book, *part/ə/ time, *carr/ə/ babies, *craz/ə/ kids
    2. th/ə/ book, th/ə/ time, th/ə/ babies, th/ə/ kids, beaut/ə/ful

Informally speaking, the “acts like part of the following word” for the purposes of vowel reduction. Accordingly, I propose that English D[±def] is part of the following word, by virtue of Local Dislocation (Embick & Noyer 2001; Embick 2010) – a post-syntactic (PF) operation that takes two linearly adjacent words9 and turns them into a single word by adjoining (or “cliticizing”10) one to the other. Local Dislocation has also been argued to apply to the definite article in French (Embick 2007: 328ff; 2010: 87ff), where its effects are manifested in the phonology as irregular vowel deletion.

    1. (10)
    1. a.
    1. l’arbre ‘the tree’ (*le arbre), l’école ‘the school’ (*la école)
    1.  
    1. b.
    1. le chien ‘the.MASC dog’, la fille ‘the.FEM girl’

A Local Dislocation rule for English D[±def] is given in (11). This rule takes as its input two linearly adjacent words spelled out in the same cycle, where the first is D[±def] and the second is any word X, and yields a single word (in square brackets) with D[±def] adjoined to X.

    1. (11)
    1. English Article Local Dislocation: D[±def] ͡ X → [D[±def] [X]]11

Unlike syntactic head-movement, Local Dislocation does not require that one word be the head of the complement of the other; this is why English D[±def] can adjoin to an adverb in e.g. (12). On the other hand, there must be some word X spelled out in the same cycle as D[±def] in order for Local Dislocation to apply; if this condition is not met, as in (13) (see also (6)), Local Dislocation does not occur and D[±def] remains an independent word.

    1. (12)
    1. a.
    1. {ði/an} unusually large baby
    1.  
    1. b.
    1. {ðə/a} surprisingly large baby
    1. (13)
    1. I’d like {the/a}…I don’t know…

By effectively making D[±def] word-internal, Article Local Dislocation allows /ði/~/ðə/ to be potentially subsumed under the same phonological analysis as beauty~beautiful and other word-internal V~ə alternations, consistent with (8). To illustrate how such a unified approach might work, I use a slightly modified version of Chomsky & Halle’s (1968: 111ff) analysis of word-internal vowel reduction. To the extent that SPE-style approaches to vowel reduction have been revised in subsequent work (e.g. Rhodes 1996; Marvin 2002), the current proposal could also be revised without introducing any problems that I am aware of. The important point here, again, is to show that the can be analyzed as one reflex of a more general vowel-reduction rule.

The basic form of the definite article is assumed to be /ðɪ/, inserted by the Vocabulary Insertion rule in (14):

    1. (14)
    1. Vocabulary Insertion: D[-def] ↔ ðɪ

The /ði/ ~ /ðə/ alternation is then produced by two word-internal phonological rules, Tensing and Vowel Reduction:12

    1. (15)
    1. a.
    1. Tensing (cyclic): V[-low -stress] → [+tense] / __{V,#}
    1.  
    1. b.
    1. Vowel Reduction (non-cyclic): V[-stress -tense] → ə

The rules work together roughly as follows: the final vowel in the, crazy, happy, beauty, etc. is underlyingly [-tense] and [-stress]; it becomes [+tense] by rule (15)a if it is prevocalic or final, as in beaute-ous and beauty, which in turn makes it immune to Vowel Reduction (15)b. If the vowel precedes a consonant (as in beauti-ful) then Tensing has no effect and rule (15)b subsequently reduces the vowel to /ə/. The need to specify Tensing as cyclic and Vowel Reduction as non-cyclic will be explained shortly (see (18)-(21) and surrounding discussion, including footnote 17).

Let us see how the proposal works with some sample derivations. Consider first the DP the crazy kid, in a grammar where there is a reduced vowel in the but not in crazy.13

    1. (16)
    1. [DP [D the] [nP crazy kid]] /ðə krezi kɪd/

Within the nP, the words crazy and kid are individually spelled out, and the rules of Tensing and Vowel Reduction apply within each word. The vowel at the end of crazy becomes [+tense] by rule (15)a; this [+tense] feature then prevents the vowel from undergoing reduction (rule (15)b).

On the DP cycle, the definite article (D[+def]) is introduced. First D[+def] cliticizes to crazy by Article Local Dislocation (11), then D[+def] is spelled out as /ðɪ/ by the Vocabulary Insertion rule in (14), and then the phonological rules in (15) apply. The context for Tensing is not met by the vowel in the here, because this vowel is preconsonantal. Therefore, the vowel remains [-tense] and subsequently undergoes Vowel Reduction.

    1. (17)
    1. a.
    1. Article Local Dislocation (11):
    2. D[+def] ͡  [a [√CRAZY] Ø] → [D[+def] [a [√CRAZY] Ø]]
    1.  
    1. b.
    1. Vocabulary Insertion (14): D[+def] ↔ ðɪ
    1.  
    1. c.
    1. Tensing (15)a: NA (because of following /k/)
    1.  
    1. d.
    1. Vowel Reduction (15)b: ðɪ → ðə

In the ugly kid, the DP-cycle derivation proceeds exactly as in (17) except that since ugly is vowel-initial, the context for Tensing is met. The vowel in the becomes [+tense] and thus immune to Vowel Reduction, so the final pronunciation is /ði/ ugly kid.

Now consider the individual words beauty, happy, beautiful and happiness. For many speakers,14beauty and happy both end in /i/, but while this vowel reduces to /ə/ in beautiful, it is a tense /i/ in happiness. How can we account for this contrast?

In the spirit of Marvin (2002) I take this contrast as a sign that beautiful and happiness have different internal structures. Beautiful is spelled out in a single cycle (-ful attaches directly to the root (18)), while happiness is spelled out in two (word-internal) cycles: first the root √HAPPY combines with a null category-defining a(dj) head; then this derived adjective combines with [n-ness] (19):15

    1. (18)
      1. Cycle 1:
      1. [a [√BEAUTY ] -ful]
    1. (19)
      1. Cycle 1:
      2. Cycle 2:
      1. [a [√HAPPY] Ø]
      2. [n [a [√HAPPY ] Ø] -ness]

Since beautiful is spelled out on a single cycle,16 Tensing “sees” that the /ɪ/ in √BEAUTY is followed by a consonant, and accordingly does not apply. Once all word-internal content has been spelled out (in this case, after Cycle 1), the non-cyclic rule of Vowel Reduction applies.

    1. (20)
    1. Cycle 1: bjutɪ fʊl
    2. Tensing: NA (because of following /f/)
    3. Word-level:
    4. Vowel Reduction: ɪ → ə (and ʊ → ə)

Since happiness is spelled out on two cycles, on the other hand, Tensing never “sees” the /ɪ/ in happy and the /n/ in -ness at the same time. Tensing is a cyclic rule, applying once on each word-internal cycle. When Tensing applies on the first cycle, the only material available is the adjective happy; since nothing follows the /ɪ/ in happy at this point, Tensing assigns [+tense] to it, thus making it immune to (non-cyclic) Vowel Reduction.17

    1. (21)
    1. Cycle 1: hæpɪ
    2.     Tensing: ɪ → i (because nothing follows happy at this stage)
    3. Cycle 2: <hæpi> nɛs
    4.     Tensing: NA
    5. Word-level:
    6.     Vowel Reduction: ɛ → ə (but /i/ does not reduce because it is [+tense])

3.2 Vowel reduction also applies in a/an

One advantage of viewing the as a phonological alternation is that it allows us to understand certain aspects of a/an as well. While a/an is often implicitly assumed to be a two-way alternation, many adult speakers actually have four surface variants: /ə/, /ən/, e(j) and either /æn/ or /ɛn/ (see also Bloomfield 1935: 186; Jurafsky et al. 1998; Asudeh & Klein 2002; Clark & Fox Tree 2002: 102). The full-vowel variants /ej/ and /æn-ɛn/ are used in careful speech, as citation forms, or when they bear nuclear sentence stress (e.g. (22)) – all of which, plausibly, are contexts where D[-def] bears at least some stress. Notice that in these contexts, only the /æn-ɛn/ variant is used prevocalically.

    1. (22)
    1. a.
    1. Not a /ej/ house, but the house.
    1.  
    1. b.
    1. Not an /ɛn/ uncle, but her uncle. (Bloomfield 1935: 186)

Putting these observations together, we can conclude that a and an each have a “strong” form with a full vowel and a “weak” form with /ə/, distributed in the same way as the other monosyllabic function-words pairs we saw in §2 – including, of course, the.18

    1. (23)
    1. a.
    1. You c/ǽ/n finish early, but you won’t. ~ You c/ə/n dó it. (repeated from (7)c)
    1.  
    1. b.
    1. I voted f/ɔ́/r it, not against it. ~ I voted f/ə/r Jóhn.
    1.  
    1. c.
    1. John wrote th/í/ paper on parentheticals. ~ John wrote th/ə/ páper.
    1. (24)
    1. Strong/weak function-word pairs in English
    2. can for to D[+def] D[-def]
      __V else
      strong kæn fɔr tu ði æn-ɛn e
      weak kən fər ðə ən ə

In the previous subsection I used two word-internal rules, Tensing and Vowel Reduction, to derive /ði/ and /ðə/ in the definite article. As expected under the unified-analysis hypothesis in (8), Tensing and Vowel Reduction can be used to derive the other alternations in (24) as well.19 In contexts where the function word bears at least some stress, it will automatically be immune to Vowel Reduction ((15)b). The fact that vowel-final function words (the, a, to) surface with tense vowels when stressed can be attributed to an additional tensing rule (Tensing 2), which assigns [+tense] to a stressed morpheme-final vowel;20 Tensing 2 also applies word-internally and cyclically, and is responsible for the absence of English words ending in stressed lax vowels (*pɛ, *stæ, *kɪ, etc.).

    1. (25)
    1. Tensing 2:21 V[+stress] → [+tense] / ___ ]xo

In contexts where a function word is stressless, the Tensing and Vowel Reduction rules from (15) derive the weak forms, as shown with the following derivations.

On the DP cycle of of a book (with unstressed a), Article Local Dislocation, Tensing and Vowel Reduction all apply exactly as in the crazy kid (17). The main difference between a/an and the involves step (b), Vocabulary Insertion: for a/an, there is an allomorphy rule that inserts /æn/ (or /ɛn/) before vowels and /ɛ/ elsewhere.

    1. (26)
    1. Derivation of a book (DP cycle):
      1. a.
      1. Article Local Dislocation (11):
      1. D[-def] ͡  [n [√BOOK] Ø] → [D[-def] [n [√BOOK] Ø]]
    1.  
    1. b.
    1. Vocabulary Insertion:
       
    1. D[-def]
       

    1. æn /__V
      ɛ elsewhere
    1. (/ɛ/ inserted here because the following segment is the consonant /b/)
    1.  
    1. c.
    1. Tensing (15)a: NA (because of following /b/)
    1.  
    1. d.
    1. Vowel Reduction (15)b: ɛ → ə

I also assume that a Diphthongization rule applies sometime after step (c), inserting a front glide /j/ after a tense front vowel (ði → ðij, e → ej).

In the DP an apple (with unstressed an), the derivation proceeds exactly as in (26) except that since apple is vowel-initial, the /æn/ allomorph is selected at step (b). Once /æn/ is inserted, it behaves exactly like can, for, and other monosyllabic function words with lax vowels in closed syllables – i.e., it escapes Tensing and undergoes Vowel Reduction.

    1. (27)
    1. Derivation of an apple (DP cycle):
      1. a.
      1. Article Local Dislocation (11):
      1. D[-def] ͡  [n [√APPLE] Ø] → [D[-def] [n [√APPLE] Ø]]
    1.  
    1. b.
    1. Vocabulary Insertion:
       
    1. D[-def]
       

    1. æn /__V
      ɛ elsewhere
    1. (/æn/ inserted here because the following segment is a vowel)
    1.  
    1. c.
    1. Tensing (15)a: NA (vowel in /æn/ is followed by a consonant)
    1.  
    1. d.
    1. Vowel Reduction (15)b: æn → ən

This analysis captures the observation that /e(j)/~/ə/ are similar to each other in the same way as /æn/~/ən/ and /ði(j)/~/ðə/ – specifically, each /ə/ form can be derived from a full-vowel form by Vowel Reduction. At the same time, this analysis captures an important difference between a/an and the, apparent in (24) and also schematized in Figure 2: While the is a two-way alternation that can be attributed to phonology alone, a/an is a four-way alternation that involves both phonology and allomorphy.22

Figure 2 

Two-tiered analysis of a/an and the.

If we wanted to pursue instead a single-tiered, uniformly allomorphic treatment of a/an (see e.g. Asudeh & Klein 2002), we would have to adopt something like Figure 3: four-way allomorphy for a/an, with spellout rules that insert full-vowel forms when [+stress] and /ə/ variants elsewhere – but leave this correspondence unexplained.

Figure 3 

Uniform “flat” allomorphy for the English indefinite article (rejected).

    1. (28)
    1. D[-def]
    2.  
    3.  
    4.  
    1.  
    2.  
    3.  
    1. æn / ____V if D[-def] is [+stress]
    2. e if D[-def] is [+stress]
    3. ən / ____V
    4. ə

In the two-tiered approach I have proposed, which makes crucial use of phonological vowel reduction, the systematic correspondences between [±stress] and V~ə alternations is explained. Furthermore, this treatment takes care of the for free. Thus, we have yet another piece of evidence that the is a phonological rather than allomorphic alternation.

Before moving on, notice that the fact that a/an tends to yield unmarked syllables (an before vowels and a before consonants, rather than the other way around), is not “explained in the grammar” under my analysis – i.e., the analysis accounts for the pattern but does not incorporate a principled reason for it. This is not necessarily problematic, since the pattern likely has a historical explanation: a/an started out as phonological /n/-elision and was reanalyzed over time as an allomorphic alternation with a as the default (see note 5). As we will see in the next section, a/an does not always yield optimal syllables in any case.

4 Rule-ordering effects

In the previous section I used a two-tiered model – allomorphy, then phonology – to explain the distribution of the various surface realizations of the English definite and indefinite articles. This approach is clearly at odds with a TETU-based analysis of a/an (e.g. Mascaró 1996b), where allomorphy can “see” the surface phonological structure and be influenced by surface well-formedness constraints. Mascaró’s (1996b) analysis of a/an works as follows: a and an are listed as allomorphs, both of which are considered as potential candidates for insertion wherever the indefinite article is used. Since a and an are equally faithful candidates, the choice between them is determined by the low-ranked constraints ONSET and NO-CODA.

    1. (29)
    1. TETU analysis of a/an (Mascaró 1996b)
    1.  
    1. {a,an} book ONSET NO-CODA
      ☞a.book * *
      an.book * **!
    1. {a,an} egg ONSET NO-CODA
      a.egg **! *
      ☞a.n egg * *

The idea is that even though English generally allows codas and onsetless syllables, a preference for unmarked CV.CV structures “emerges” in just those contexts where there are multiple, equally faithful underlying forms for a single vocabulary item.

An advantage Mascaró claims for his approach is that it explains why so many cases of (apparent) external allomorphy appear to involve hiatus avoidance or some other kind of phonological optimization (see (30) for a sample of cases cited in the literature).23 As noted in §1, since tense vowels are diphthongized in English, the could be easily incorporated into Mascaró’s framework, and might even be viewed as an additional source of support for a theory of allomorphy as TETU (31).

    1. (30)
    1. Other proposed cases of allomorphy as TETU (Mascaró 1996a; b; 2007; Lee 2009)
      1. a.
      1. French bo __C vs. bɛl __V (beau mari, bel enfant ‘good-looking husband/child’) (also nouveau/nouvel ‘new’, ce/cet ‘this’, ma/mon ‘my’, etc.)
    1.  
    1. b.
    1. Catalan personal definite: ən __C vs. l __V (en Wittgenstein, l’Einstein)
    1.  
    1. c.
    1. Northwest Catalan lo __C vs. l __ V (lo pá, l ámo, ‘the owner/bread’)
    1.  
    1. d.
    1. Ribagorçan Catalan ésto/ íʃo __C vs. ést/ íʃ __ V (ésto ʎiβre, ést ɔme ‘this book/man’)
    1.  
    1. e.
    1. Moroccan Arabic C__ -uvs. V__ -h (ktab-u, x a-h ‘his book/error’ (also i/ja in 1SG)
    1.  
    1. f.
    1. Korean C__ -ivs. V__ -ka (sok-i ‘inside-NOM’, so-ka ‘cow-NOM’) (Lee 2009)
    1.  
    1. g.
    1. Basque N__ du, else tu (ilun-du ‘darken’, argi-tu ‘clear up’) (also dar/tar, ko/go, tik/dik)
    1. (31)
    1. TETU analysis of the (to be rejected)
    1.  
    1. {ðə, ðij} book ONSET NO-CODA
      ☞ðə.book *
      ðij.book **!
    1. {ðə, ðij} egg ONSET NO-CODA
      ðə.egg *! *
      ☞ði.j egg *

In Mascaró’s (1996b) analysis, an is selected iff its /n/ is syllabified as an onset on the surface. This idea is unformulable in the architecture I adopt in §3. Since Vocabulary Insertion (allomorphy) strictly precedes phonological rule application in this model (see Figure 2), there is no way for an allomorphy rule to “see” the final phrase-level syllable structure – or, more specifically, for the /n/ in an to “know” that it will ultimately be syllabified as an onset. On the other hand, the model I adopt allows for a different kind of scenario: one where, after allomorph insertion, the phonology renders additional changes to D[-def] and surrounding material, possibly enough to disrupt the expected optimal syllable structures. The following subsections provide evidence for exactly this kind of post-allomorphic phonological meddling. First I show that the /n/ in an is not always syllabified as an onset on the surface (§4.1). Then I show that an sometimes fails to be selected even when it is followed by a vowel on the surface (§4.2–§4.3).

4.1 Emphatic glottal stops

It is well-known that vowel-initial words in English are frequently pronounced with an initial glottal stop. Whether or not /ʔ/ appears depends on a number of factors; it is more likely to be inserted before a stressed vowel at the beginning of an utterance, but it is also possible in connected speech if the vowel-initial syllable has special “prominence” or “emphasis” (Borroff 2007: 166; Garellek 2012; 2013: ch5).

    1. (32)
    1. a.
    1. He’ll fall asleep /ʔ/ánywhere.
    1.  
    1. b.
    1. She’s from /ʔ/Óregon, not Washington.
    1.  
    1. c.
    1. I haven’t seen John in for/ʔ/éver.

I will refer to the glottal stop in examples like (32) as Emphatic Glottal Stop, in order to distinguish it from the (optional) glottal stop in e.g. Tuscaloosa /ʔ/Alabama, which seems to serve as a hiatus-breaker, but this distinction is not crucial to my analysis.

Notably, emphatic glottal stop can occur between the an variant of D[-def] and its complement:

    1. (33)
    1. a.
    1. That’s an /ʔ/éxcellent idea.
    1.  
    1. b.
    1. What an /ʔ/ídiot.

Examples like (33) are by no means odd or unnatural; in our CHILDES corpus study, for example, 25% of adults’ connected-speech utterances of an + V had an emphatic glottal stop before the vowel.24 But under Mascaró’s (1996b) TETU-based analysis of a/an, these utterances present a problem. The /n/ in an here must be a coda, since English does not allow [nʔ] onsets. But if allomorph choice is truly determined by surface syllable well-formedness, /an.ʔidiot/ should always be beaten by either /a.ʔidiot/ or /a.n idiot/, which have fewer NO-CODA violations:25

    1. (34)
    1. ONSET NO-CODA
      an.ʔidiot ** **
      a.n idiot ** *
      a.ʔidiot ** *

A similar problem would arise under a TETU-based analysis of the, since /ði(j)/, like an, can be followed by /ʔ/. In our CHILDES corpus study (see §5), for example, 21% of adults’ prevocalic /ði(j)/ (161/773) were followed by /ʔ/, and Keating et al. (1994: 137) and Todaka (1992: 46) report /ʔ/ after 30% of prevocalic /ði(j)/ in the TIMIT corpus. Before other consonants, however, unstressed /ði(j)/ is much less frequent (Todaka 1992: 41).

    1. (35)
    1. a.
    1. That was /ði(j) ʔ/óther guy.
    1.  
    1. b.
    1. Turn on the /ði(j) ʔ/áir conditioner.
    1. (36)
    1. ?* He’s walking /ði(j)/ dog.

One might try to save the TETU account of a/an by proposing that the glottal stop does not really count as a consonant, or that it is somehow “outside of the grammar” altogether. However, while it is certainly debatable whether glottal stop is a phoneme, segment, feature or gesture (see Borroff 2007 for discussion), the problem here has to do with the distribution of emphatic /ʔ/, which is highly systematic and clearly grammar-internal. Consider the following contrasts:

    1. (37)
    1. That’s /ənʔo/.
      1. a.
      1. ✔That’s an ‘O.’
    1.  
    1. b.
    1. *That’s a ‘no.’
    1. (38)
    1. a.
    1. an ʔapple, Joan ʔAllen, %unʔethical, %inʔoperable
    1.  
    1. b.
    1. *banʔana, *anʔalysis, *connʔection, *menʔorah, *internʔational

The relevant generalization seems to be that emphatic /ʔ/ must be syllable-initial, and therefore can occur between a consonant C and a vowel V́ only if C is morpheme-final and thus potentially syllable-final. In other words, emphatic /ʔ/ needs to “see” that the /n/ in an apple can be a coda, unlike the /n/ in analysis, and it is not clear how this information would be accessible if the emphatic /ʔ/ were not part of the same system as the regular phonology and morphology. Under a TETU account, the problem is that the /n/ in an apple is crucially not supposed to be a coda.

Under my proposal, the fact that an and /ði/ show up before emphatic /ʔ/ can be straightforwardly explained as a rule-ordering effect: emphatic /ʔ/ is inserted relatively late, after Vocabulary Insertion, Tensing and Vowel Reduction have applied, and therefore does not count as a consonant for the purpose of a/an or the.

    1. (39)
    1. a.
    1. Vocabulary Insertion
    1. /æn/ idiot
    1. /ðɪ/ idiot
    1.  
    1. b.
    1. Tensing / Vowel Reduction
    1. /ən/ idiot
    1. /ði/ idiot
    1.  
    1. c.
    1. Emphatic /ʔ/ Insertion (optional)
    1. /ən ʔ/idiot
    1. /ði ʔ/idiot

At the stage when Emphatic /ʔ/ is added, the /n/ in an is still a coda (by virtue of being morpheme-final) and the first syllable of idiot is onsetless. (This VC.V syllable structure is what enables Emphatic /ʔ/ Insertion in an. /ʔ/a.lley but not in *a.n/ʔ/a.ly.sis.) Resyllabification does not apply until after Emphatic /ʔ/ Insertion, and in (39) the resyllabification of /n/ in an is blocked by the epenthesized /ʔ/.

Resyllabification in turn precedes other PF processes. Flapping, which has been independently treated as a late-stage phenomenon in various serialist models,26 applies post-resyllabification and, as expected, turns out to behave very differently from a/an with respect to whether it “sees” an epenthesized emphatic /ʔ/. Flapping applies only if /t/ or /d/ is immediately followed by a vowel on the surface, with no intervening segment or silence – which in turn suggests that the flap must surface as an onset (Kaisse 1985; Bermúdez-Otero 2007). Notably, an emphatic /ʔ/ that intervenes between /t/ and a vowel blocks Flapping:

    1. (40)
    1. (41)

Flapping “sees” and is blocked by emphatic /ʔ/ while a/an is blind to it. This contrast is unexpected under Mascaró’s (1996b) analysis of a/an; if allomorph choice were directly guided by surface syllable well-formedness, then an should be blocked by an emphatic /ʔ/ just as Flapping is. In the current model, however, this contrast follows automatically from the way the relevant operations are ordered: emphatic /ʔ/ is inserted after the early rules of allomorphy and Tensing/Vowel Reduction, but before the late rules of resyllabification and Flapping.

4.2 /h/ dropping

A similar solution can be applied to data described in Hurford (1972; 1974).27 Hurford reports that older Cockney speakers who otherwise have categorical prevocalic an will use a if the following word starts with a “dropped” /h/. The resulting forms have non-optimal (hiatus) syllable structures, so it is unclear how they would surface in a TETU-style approach:

    1. (42)
    1. a.
    1. a half [əɑːf], a heart [əɑːʔ]
    1.  
    1. b.
    1. an artist [*əɑːtɪst], an office [*əɔfɪs]

In the current model, we can propose that this dialect has a rule of /h/-Deletion that applies after Vocabulary Insertion. Since the /h/ in half is still present when Vocabulary Insertion applies to D[-def], a is inserted rather than an. Later, /h/-Deletion applies, producing the forms in (42)a.

(43) a. Vocabulary Insertion /ɛ hɑːf/
  b. Tensing / Vowel Reduction /ə hɑːf/
  c. /h/-Deletion /ə ɑːf/
       

4.3 Pause-fillers

Recall that a/an is actually a four-way alternation for many speakers, with the full-vowel strong variants /e(j)/ and /æn/ as well as their reduced-vowel weak counterparts /ə/ and /ən/ (rsp.). In §3.2 I argued that the default allomorph of D[-def] is /ɛ/, and that /ɛ/ either becomes tense and diphthongized /ej/ (when stressed) or is reduced to /ə/ (otherwise).

Interestingly, D[-def] surfaces as /ej/ not only in [+stress] contexts like I want /éj/ book, not two books, but also in contexts like (44) – with little or no stress, before the vowel-initial pause-fillers uh/um, often with no intervening silence. This is also a context where /ði(j)/ is used (Fox Tree & Clark 1997; Clark & Fox Tree 2002).

    1. (44)
    1. a.
    1. I’d like /ej/ um… a large coffee and a croissant.
    1.  
    1. b.
    1. This is /ej/ uh… part of a trailer truck. (Braunwald ale33)
    1. (45)
    1. And from the-uh /ðijə/ spectator point of view it looks like airplanes going in all directions…We-um have a-uh /ejə/ pyro-techniques team. (Clark & Fox Tree 2002: 103)

If allomorph choice were driven by surface syllable well-formedness, the question would be why we find /ej/, rather than an, in contexts like (44)–(45). Put slightly differently, why would an be chosen before e.g. umbrella but not before uh/um?28

    1. (46)
    1. a.
    1. I’d like {/ej/, ?*an} um…
    1.  
    1. b.
    1. I’d like {*/ej/, an} umbrella.

In a serialist model like the one assumed here, on the other hand, it is possible to follow the intuition that pause fillers like uh and um are structurally exceptional, with a fundamentally different status in the grammar from words like umbrella. Arguably, pause-fillers are not present in the syntax at all, but are inserted post-syntactically during the PF derivation (see Roternberg 1978; Kaisse 1985 for precedent for this idea). If this proposal is on the right track, it suggests an explanation for the contrast in (46).

Recall that Article Local Dislocation can apply only if there is something right-adjacent to D[±def] for D[±def] to cliticize onto. If pause-fillers are not yet present, this condition will not be met (there will be no statement D[±def] ͡ [X…] to provide the necessary input for rule (17)) and D[±def] will remain an independent word, triggering insertion of the elsewhere allomorph.

    1. (47)
    1. Derivation of I’d like /ej/ um… (DP cycle):
      1. a.
      1. Article Local Dislocation (11): NA; nothing follows D[-def] at this stage
    1.  
    1. b.
    1. Vocabulary Insertion:
       
    1. D[-def]
       

    1. æn /__V
      ɛ elsewhere
    1. (/ɛ/ inserted here because nothing follows D[-def] word-internally)
    1.  
    1. c.
    1. Tensing (15)a: ɛ → e (because nothing follows D[-def] word-internally
    1.  
    1. d.
    1. Vowel Reduction (15)b: NA because /e/ is [+tense]

For the purposes of this analysis, the pause-filler could be inserted at any point in PF after step (a) Article Local Dislocation. Once Article Local Dislocation fails, nothing outside of D[±def] can be visible for the word-bounded rules of Vocabulary Insertion, Tensing, or Vowel Reduction, so D[-def] will surface as /ej/ (after Diphthongization). The larger question of when and how exactly pause-fillers are inserted in PF – if, for example, different kinds of pause-fillers might be inserted at different points or by different mechanisms – remains open for future investigation.

The derivation of /ði/ uh/um in the definite article works exactly as in (47), except that there is no allomorphy in step (b): 29

    1. (48)
    1. Derivation of I’d like /ði/ um… (DP cycle):
      1. a.
      1. Article Local Dislocation (11):
      2. NA; nothing follows D[+def] at this stage
    1.  
    1. b.
    1. Vocabulary Insertion: D[+def] ↔ ðɪ
    1.  
    1. c.
    1. Tensing (15)a): ɪ → i (nothing follows D[+def] word-internally
    1.  
    1. d.
    1. Vowel Reduction (15)b): NA because /i/ is [+tense]

It is important to recognize that like emphatic glottal stops, pause-fillers are not completely “outside the grammar” even though they are inserted late. Whether or not they count as bona fide words in other respects (see Clark & Fox Tree 2002 for discussion), uh and um are clearly visible for the apparently late-stage phonological rule of Flapping:

    1. (49)
    1. Bu/ɾ/ uh … we think tha/ɾ/ uh …

Again, the fact that pause-fillers are invisible for some rules (allomorphy) but visible for others (Flapping) is taken to be a rule-ordering effect: pause-fillers are inserted after Article Local Dislocation but before Flapping. If a/an were determined by surface syllable well-formedness constraints, however, we would not expect a/an to behave any differently from Flapping with respect to whether its alternating segment could syllabify as an onset onto uh/um.

4.4 Interim discussion

What I have shown in the preceding subsections is that neither a/an nor the can be analyzed as allomorphy as TETU,30 at least not for varieties of English where any of the phenomena discussed here (emphatic glottal stop, /h/-dropping, pause-filler insertion) apply as described. While a/an plays an indirect role in creating many optimally syllabified strings (V.CV), it can also contribute segments that are ultimately syllabified in a non-optimal way (VC.CV). In the current proposal, this is because Vocabulary Insertion operates on whatever information is available early in PF; later phonological processes may then add, delete, or modify segments.

As pointed out by a reviewer, the theory of allomorphy as TETU is not necessarily threatened just because it turns out to be inappropriate for English a/an. Mascaró (2007) does not claim that all phonologically conditioned allomorphy (PCA) is optimizing; rather, he distinguishes optimizing (externally conditioned, regular) PCA from non-optimizing (internally conditioned, lexical, arbitrary) PCA (see also Bonet et al. 2007).31 It could be that English a/an, despite initial appearances and contraMascaró 1996b, is an example of arbitrary PCA and thus would not be expected to yield to a TETU analysis.

However, earlier in the paper I showed that a/an is a best analyzed in a serialist architecture where allomorphy precedes phonology; this approach allows us to account for all four variants (/ej/, /æn/, /ə/, /ən/) in a way that captures the parallels between the strong/weak forms here and in other function words, including the. As noted at the beginning of §4, it is impossible in this model for allomorphy to have access to surface phonology, since Vocabulary Insertion strictly precedes phonology. To introduce a new kind of late-stage, post-phonological, surface-sensitive allomorphy into this model would represent a significant addition. Is this addition necessary? Or, more generally: Do we really need two kinds of allomorphy, or can we get by with just one?

The main argument for TETU-based allomorphy that appears in the literature is that it captures an important cross-linguistic generalization: “[T]he linguistic generalization that the allomorph is chosen because it yields an unmarked structure should be incorporated into grammatical theory, since it rests on an extensive empirical base” (Mascaró 2007: 716). A key question for future research is whether the many proposed cases of optimizing allomorphy from the literature, including those in (30), really are consistently optimizing on the surface. Surface-optimization could be established by testing whether the given alternation interacts with pause-fillers and the output of late-stage phrasal phonology in the expected way (as demonstrated in §§4.1–4.3).32 We have seen that English a/an is not surface-optimizing, even though at first sight it seems like a well-behaved textbook case of allomorphy as TETU.

TETU-based proposals make a strong prediction that the given alternation should “see” exactly what is there on the surface, including pause-fillers and epenthetic segments, much like American English Flapping. What I hope to have shown is that apparent phonological optimization does not always correspond to surface phonological optimization across contexts.

5 Accounting for variation

As noted earlier, neither a/an nor the is a categorical alternation. The goal of this section is to give a slightly fuller picture of the inter- and intraspeaker variation with a/an and the, and to show how the analysis presented in §3 can be incorporated into a competing-grammars approach to account for this variation. I do not make any internal changes to the analysis from §3 here.

Prevocalic a is common in many varieties of British and American English; in fact, some of these varieties have invariant a, prevocalically and preconsonantally (see Gabrielatos et al. 2010 and references cited there). Prevocalic /ðə/ is also a feature of at least some of these dialects (see e.g. Britain & Fox 2009). In fact, prevocalic /ðə/ occurs even in varieties that generally do not have prevocalic a, e.g. “standard” American English (Healy et al. 1998; Raymond et al. 2002), and appears to be becoming more common in younger generations in some regions (Todaka 1992; Keating et al. 1994: 136–138).

Prevocalic a and /ðə/ are also a well-known feature of children’s speech. As shown earlier (Table 1, §2), children in our CHILDES corpus study use the “standard” prevocalic forms an and /ði/ far less frequently than their adult caregivers. Table 2, which includes data from more corpora and breaks down the children’s data by age,33 shows that children’s use of prevocalic an and /ði/ does not reach even 65% frequency until age 6 (see also Newton & Wells 1999).

Table 2

Frequency of prevocalic an and /ði/ in North American children and adults in CHILDES.34

% an an/(a+an) % ði ði/(ðə+ði)

age 3 30% (166/561) 41% (160/388)
age 4 22% (73/326) 38% (109/289)
age 5 36% (32/90) 61% (115/187)
age 6–7 67% (59/88) 77% (94/122)
age 8–9 74% (14/19) (no audio data)
age 10–11 95% (42/44) (no audio data)
adults 95% (2883/3019) 90% (773/863)

Examples of prevocalic a and /ðə/ in a 5-year-old’s speech are given in (50). Notice that a /ʔ/ is inserted after prevocalic a/ðə. This /ʔ/ is also a feature of adult speech (Todaka 1992; Britain & Fox 2009); in our corpus study, for example, 80% (72/90) of adults’ prevocalic /ðə/ had a /ʔ/ between /ðə/ and the following vowel.

    1. (50)
    1. a.
    1. Pretend this was a [əʔ] elevator. (Sawyer 2-26-92)
    1.  
    1. b.
    1. if you don’t want me to take the [ðəʔ] elephant (Sawyer 2-28-92)

The analysis laid out in §3 can be adapted to account for inter- and intraspeaker variation in a/an and the. To see how this might work, consider the mini-grammars in (51)–(52). DEF1 (51) is a mini-grammar for a hypothetical speaker with categorical /ði/ prevocalically and /ðə/ elsewhere (i.e. a condensed version of the analysis in §3.1). DEF2 (52) is a mini-grammar for a hypothetical speaker with categorical /ðə/ in all contexts – i.e., no ði/ðə alternation.

    1. (51)
    1. Grammar DEF1 (/ðə/ book, /ði/ apple)
      1. a.
      1. Article Local Dislocation
    1.  
    1. b.
    1. Vocabulary Insertion: D[+def] ↔ ðɪ
    1.  
    1. c.
    1. Tensing / Vowel Reduction
    1. (52)
    1. Grammar DEF2 /ðə/ book, /ðə/ apple
      1. a.
      1. Vocabulary insertion: D[+def] ↔ ðə

I assume that DEF2 also includes a phonological rule that (variably) adds /ʔ/ between /ə/ and a following vowel; the relationship between this rule and the Emphatic /ʔ/ Insertion rule described in §4.1 remains to be explored.

DEF1 produces 100% prevocalic /ði/ while DEF2 produces 0% prevocalic /ði/. Speakers with intermediate rates of prevocalic /ði/ – including probably most speakers of “standard” English – can be assumed to have access to both DEF1 and DEF2, and to go back and forth between these grammars depending on dialect, register, style, carefulness, and other factors that remain to be explored. I propose that children start out favoring the simpler grammar in DEF2, and over time they learn to use DEF1 more and more frequently until they reach the adult pattern for their particular variety of English.35 The adults in our CHILDES corpus study, for example, who pronounce prevocalic the as /ðə/ 10% of the time (see Tables 12), would be assumed to be using grammar DEF2 10% of the time.

This notion of competing grammars has also been adopted to explain doublets like dived/dove, where an individual speaker seems to have access to two different analyses of a past-tense form (Kroch 1994; Embick 2008). A competing-grammars approach can also help explain intraspeaker variability in presume-tensing (Nádasdy 2013), where either /i/ or /ə/ is used in the unstressed initial syllable of presume, believe, eleven, remember, enormous, etc. (see (7)b). Presume-tensing speakers could have one grammar with underlying tense /i/ in these words, and another grammar with underlying lax /ɪ/ that subsequently undergoes Vowel Reduction.

For the indefinite article, our sample derivations in §3.2 followed the grammar summarized in INDEF1, with four variants (/e/, /æn/, /ə/ and /ən/). As with the definite article, this grammar can be assumed to exist alongside a “non-alternating” grammar with a single invariant form /ə/ (INDEF2).

    1. (53)
    1. Grammar INDEF1 (/ə/ bóok, /ən/ ápple, /é/ book, /ǽn/ apple)
      1. a.
      1. Article Local Dislocation
    1.  
    1. b.
    1. Vocab. Insertion:
       
    1. D[-def]
       

    1. æn /__V
      ɛ elsewhere
    1.  
    1. c.
    1. Tensing / Vowel Reduction
    1. (54)
    1. Grammar INDEF2 (/ə/ bóok, /ə/ ápple, /ə́/ book, /ə́/ apple)
      1. a.
      1. Vocab. insertion: D[-def] ↔ ə

It is likely that many speakers also have a third “intermediate” grammar: one that has the basic /n/~Ø alternation but lacks the full-vowel forms /e/ and /æn/.

    1. (55)
    1. Grammar INDEF3 (/ə/ bóok, /ən/ ápple, /ə́/ book, /ə́n/ apple)
      1. a.
      1. Article Local Dislocation
    1.  
    1. b.
    1. Vocab. insertion:
       
    1. D[-def]
       

    1. ən /__V
      ə elsewhere

As with the definite article, I assume that children initially favor the simple grammar that inserts /ə/ categorically (INDEF2). Over time, they increase their use of INDEF3 (with allomorphy) and/or INDEF1 (with allomorphy and Tensing/Vowel Reduction) until they achieve the adult pattern for their given variety of English. Some adult speakers may alternate between INDEF2 and INDEF3, some between INDEF1 and INDEF3, and some among all three grammars. Again, it is possible that children (and adults) use additional grammars beyond those sketched here.

Among other things, this approach explains why there is intraspeaker variability in the pronunciation of pitch-accented articles:

    1. (56)
    1. a.
    1. This is {ðí/ðə́} book to read on global warming.
    1.  
    1. b.
    1. I said I wanted {éj/ə́} croissant, not two croissants.

When the full-vowel form is chosen, the speaker is using grammar (IN)DEF1. When the /ə/ form is chosen, the speaker is using grammar DEF2, INDEF2 or INDEF3.

6 Concluding thoughts

The question posed in the title of this paper is “How allomorphic is English article allomorphy?” I have answered this question as follows:

  1. the is not allomorphic. It is derived by the same phonological rules – Tensing and Vowel Reduction – as other V~ə alternations in English, e.g. beauty~beautiful, /kæn/~/kən/ in the function word can.
  2. A/an is partly allomorphic. For speakers with the strong forms /e/ and /æn/ as well as /ə/ and /ən/, a/an is best analyzed as involving both allomorphy and phonology: first allomorphy establishes a basic split between /æn/ (before vowels) and /e/ (elsewhere); then the same phonological rules involved in the – Tensing and Vowel Reduction – derive the variants /ə/ and /ən/ in their designated contexts.

Recall that children do not reach adultlike patterns with a/an and the until age 6 or later (Table 2; Newton & Wells 1999). In this respect, a/an and the are very different from some of the other “between-word processes” that have been examined in the acquisition literature, e.g. cluster simplification and assimilation (Newton & Wells 1999):

(57) a. Cluster simplification: just like [ʣʌslaɪk]
  b. Assimilation: one cloud [wʌŋklaʊd]

Cluster simplification and assimilation show no clear developmental trend: the 3-year-olds in Newton & Wells (1999) apply them at roughly the same rates as the 7-year-olds. Newton & Wells speculate that a/an and the, unlike cluster simplification and assimilation, must be gradually learned because they are language-specific and relatively “unnatural” from a phonetic perspective (1999: 74). In a follow-up study, Newton & Wells (2000) look at another between-word process, /r/-liaison in British English (e.g. saw a [sɔɹə]), and show that it is also gradually acquired. This is as expected, since the glide-like behavior of /r/ is a language-specific rather than cross-linguistic phenomenon.

These findings reinforce the point made in §2 that “phonological naturalness” involves degrees on a scale. While I have argued for a phonological treatment of the on the grounds that the is less arbitrary and idiosyncratic than a/an, I have not suggested that vowel reduction is an “automatic” or “low-level phonetic” rule like cluster simplification or assimilation. Some languages do not have vowel reduction at all, while others (like English) impose language-specific constraints on vowel reduction (e.g. word-internal, sensitive to tense/lax distinction), so that children have to learn the rule itself as well as figuring out exactly when it applies.

The current model allows for a wide range of types of phonological rules. Some rules tend towards ease of articulation, and it is expected that these will be easier to acquire than less natural ones (all else being equal). Furthermore, phonological rules are structurally restricted depending on when they apply in PF, so that some rules apply cyclically during word-formation (like Tensing) while others apply over entire utterances (like Flapping), and still others apply at various intermediate stages (see Pak 2008). Under this type of approach, we can view both phonetic similarity (Criterion A) and structural restrictedness (Criterion B) as gradient, rather than binary, measures, and we are not necessarily forced to adopt an allomorphic treatment of an alternation just because it is not a “low-level” or “across-the-board” rule.

Another contribution of this paper has been to call attention to the question of what it means for allomorphy to be phonologically optimizing, and how (or whether) phonological optimization should be explained in the grammar. In §4 I used evidence from emphatic glottal stops, /h/-dropping and pause-fillers to show that despite initial appearances, English a/an is not always phonologically optimizing on the surface (e.g. an/ʔ/ápple, I wantaum….). In the model I adopted in §3 to analyze a/an and the, this result is unsurprising: since allomorphy strictly precedes phonology, it is not expected to be able to “see” the surface syllable structure. The question I posed at the end of §4 is whether other proposed cases of allomorphy as TETU really are demonstrably surface-optimizing, using diagnostics similar to those I use in §§4.1–4.3.

It has not been my intent to argue for a phonological treatment for every ambiguous case that has been cited in an “allomorphy vs. phonology” debate. I have, however, laid out an analysis of English a/an and the whose ingredients may be involved in many of these other cases. As we have seen, opening up the possibility for a phonological treatment allowed us to recognize a number of important similarities and differences between a/an and the, which would have gone unexplained in a uniformly allomorphic treatment.