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date: 23 March 2017

Korean Phonetics and Phonology

Summary and Keywords

Due to a number of unusual and interesting properties, Korean phonetics and phonology have been generating productive discussion within modern linguistic theories, starting from structuralism, moving to classical generative grammar, and more recently to post-generative frameworks of Autosegmental Theory, Government Phonology, Optimality Theory, and others. In addition, it has been discovered that a description of important issues of phonology cannot be properly made without referring to the interface between phonetics and phonology on the one hand, and phonology and morpho-syntax on the other. Some phonological issues from Standard Korean are still under debate and will likely be of value in helping to elucidate universal phonological properties with regard to phonation contrast, vowel and consonant inventories, consonantal markedness, and the motivation for prosodic organization in the lexicon.

Keywords: phonation contrast, vowel inventory, vowel merger, diphthongization, assimilation, neutralization, prosodic hierarchy

1. Phonation Contrasts in Consonants

There is a controversy on the nature of laryngeal contrast in the Korean obstruent system, from the structuralist formulation of Martin (1951, 1954), through the SPE accounts of Kim (1965) and Kim-Renaud (1974), and post-generative analyses of Cho (2011). There is a general consensus that there are three types of phonation in Korean stops and two types in fricatives on the surface, as illustrated by (1).

(1) Korean consonantal phoneme inventory

Labial

Coronal

Post-Alveolar

Velar

Glottal

Plain1 Stop

p

t

c

k

Aspirated Stop

ph

th

ch

kh

Tense Stop

p’

t’

c’

k’

Plain Fricative

s

h

Tense Fricative

s’

Nasal

m

n

ŋ

Liquid

l

The tense series (also termed as “fortis” consonants) is characterized by “laryngeal tension,” whose precise phonetic characterizations are quite complex (e.g., glottal opening, the muscular tension [e.g., stiffness] of the vocal folds, tension of the pharynx and the walls of the vocal track, high oral pressure, and the heightened subglottal pressure) (Ahn, 1999; Dart, 1987; Han & Weitzman, 1970; Hardcastle,1973; Hirose, Lee, &Ushijima, 1974; Kagaya, 1974; Kim, 1965; Kingston, 1985; Shin, 2015; Silva 1992). Also it should be noted that Korean tense consonants (and aspirated consonants) induce a much higher F0 in the following vowel in contrast to plain counterparts.

The minimal triplets in (2) justify the phonation type contrast for the stops shown in the consonant inventory in (1).

(2) Korean laryngeal contrast in minimal triplets

pul

‘fire’

tal

‘moon’

ca-ta

‘to sleep’

koŋ

‘ball’

phul

‘grass’

thal

‘mask’

cha-ta

‘to kick’

kh

‘bean’

p’ul

‘horn’

t’al

‘daughter’

c’a-ta

‘to be salty’

k’oŋ

‘frozen’

The two fricatives (s and s’) behave differently than the stops, as there is no comparable minimal triplet (e.g., sal ‘flesh’; s’al ‘rice’; *shal). This forces Iverson (1983) to conclude that s is lax in phonology but aspirated in phonetics. The lax nature of s is clearly supported by such phenomena as Post-Obstruent Tensing and the consonant correspondences in sound symbolism, but its phonetic behavior is less clear. On the other hand, Cho, Jun, and Ladefoged (2002) arrives at the conclusion—that even phonetically, s is better characterized as lenis rather than aspirated, on the strength of the observation that it is unaspirated medially (in contrast to its initial manifestation) and sometimes undergoes gradient voicing in a parallel fashion to stops. (See Chang, 2013 for a recent treatment of the coronal fricative.)

Plain consonants are produced with slight aspiration in word-initial position, while aspirated consonants are heavily aspirated. In addition, plain obstruents undergo systematic changes in medial positions. They become voiced between voiced segments within a phonological phrase, except for s, and are realized as tense consonants after any obstruent.2 In syllable-final position, all obstruents are unreleased and, as a result, there are no laryngeal features of any kind, as exemplified in (3).

(3) Syllable-final laryngeal neutralization

iph

ip

‘leaf’

soth

sot

‘pot’

pak’

pak

‘outside’

puəkh

puək

‘kitchen’

Whereas voicing and aspiration are cross-linguistically common laryngeal features for obstruent systems, having a three-way distinction involving aspiration and tenseness (but not voicing) within one language is a quite unusual phenomenon. This rare tripartite pattern has motivated arguments against the tense contrast in Korean, or, in more radical cases, both features of the laryngeal contrast are explained away, leaving no underlying phonation type contrast (Han, 1996; Jun, 1994). Not only tense but aspirated consonants are treated as geminates, and their phonetic properties are derived from the structural configuration rather than from inherent phonetic features. (See Cho, 2011 for a detailed comparison between singleton and geminate accounts, where ample evidence is laid out for treating laryngeal consonants, both tense and aspirated, as singletons.)

Given the complex array of articulatory and acoustic characteristics, it comes as no surprise that no consensus was reached for the selection of the feature defining the tense series. The distinctive features for tense consonants employed for these studies are often general features such as [+tense] (Ahn, 1985; Kim, 1970, Kim-Renaud, 1974, Kohler, 1984) and [+constricted glottis] (Cho, 1990; Chomsky & Halle, 1968; Lombardi, 1994; Sohn, 1987). As noted in Martin (1954, p. 39), however, Korean tense consonants are not glottalic in the sense of ejectives or implosives; rather, “the effect is a clear-cut ‘popping’ release similar to that of glottalized consonants, but with no separately heard glottal release (unlike the glottalized consonants of North American Indian languages).” For this reason, Han (1996) uses [+constricted glottis] as a shorthand for the combination of [+constricted glottis] and [+stiff vocal cords], utilizing the features advocated in Halle and Stevens’s system (1971). More recently, Ahn and Iverson (2004, p. 13) point out the two differences between typical ejectives and Korean tense consonants: a) Korean in-phase constriction versus persisting glottal closure of ejectives; and b) a raising effect on the pitch of the following vowel by Korean tense consonants, as opposed to a lowering effect of ejectives (Kingston, 1985).

The diachronic emergence of laryngeal obstruents seems to be reflected in the debate of laryngeal contrast in Korean. The proto-Korean consonant system lacked phonemic aspiration and tenseness (Poppe, 1965; Starostin, Dybo, & Mudrak, 2003), and the aspirated series emerged by early Middle Korean (MK), as evidenced by the way Chinese aspirated consonants were adopted into Middle Korean (Park, 1996). By early Modern Korean, tense consonants emerged from consonant clusters resulting from vowel deletion and the ubiquitous addition of the linking/s/between morphemes in compounds (K.-M. Lee, 1972).

Treating tense consonants as phonologically geminate versions of the corresponding plain consonants is motivated by a desire to do away with an unusual phonation contrast, the coexistence of aspiration and tensity within one system, but it does not explain why we should interpret surface tension as a phonetic property of length contrast derived from the geminate property, which is not justified in Korean phonology in general. Laryngeal contrast is only robust in word-initial position, and neutralized completely (as lax consonants in syllable-final positions) and partially in word-medially positions (lax consonant as voiced in inter-voiced environments and as tense in word-medial post-obstruent environments). One unorthodox position is Kim and Duanmu’s (2004) categorization of lax stops as voiced stops, and tense stops as regular voiceless unaspirated stops, attempts to abolish the tense feature altogether and to account for the consonant–tone correlation. Kim and Duanmu’s classification assumes that true features manifest themselves in medial position but not in initial position; the lax stop devoices and its [voice] shifts to the following vowel, which is realized with a low tone. If the Korean laryngeal contrast is reanalyzed as having voiced, voiceless, and aspirated consonants, as proposed by Kim and Duanmu (2004), the two puzzles could be solved. First, with the two features of [voice] and [aspirated] universally available, an economically tighter prediction emerges with a four-way distinction based on [+/–voice] and [+/–aspirated], while introducing a third feature, [tense], would yield an unwarranted eight possibilities that are not instantiated by the data. Second, the natural consonant–tone correlation of voiceless-high and voiced-low is observed in Korean. However, this position has not been generally accepted.

A more comprehensive phonetic studies by H. Kim (2002, 2005) and Kim, Honda, and Maeda(2005) argue that articulatory patterns (in addition to often-observed acoustic intensity and aerodynamic considerations), such as closure duration, linguopalatal contact, tongue movement, and glottal position, associated with glottal tension all point to the three-way laryngeal contrast in Korean. The phonological features employed here are [+/–spread glottis] and [+/–tense], rather than [+/–constricted glottis], whereby both aspirated and tense consonants are characterized by [+tense], while only aspirates are marked for [+spread glottis]. Kim’s unusual feature organization has different implications for Korean phonology, which have not been fully explored. The phonetic studies discussed above demonstrate that phonetic characteristics could be classified into different patterns depending on one’s view of tensity and aspiration. It is also very likely that laryngeal features associated with segments are being reanalyzed as tonal features. Shin (2015, p. 11) observes that rather than the expected voice-onset time (VOT) differences, the major phonetic cue for lax versus non-lax in initial position is F0 (high tones for non-lax consonants), while aspirated and tense obstruents are distinguished by the quality of the following vowel (breathy for non-tense consonants and creaky for tense consonants). It is also observed by some that contemporary Seoul Korean may be developing a tonal system in lieu of laryngeal contrasts; Silva (2006), Wright (2007), and Lee, Cho, and Liberman (manuscript under revision, “An Interaction Effect Between Tonogenesisi and Prosodic Focus in Seoul Korean”) have shown that Seoul speakers have shown a dramatic change in their use of VOT to mark the distinction among lax, tense, and aspirated stops. While VOT differences between lax and aspirated stops have decreased, the mean F0 for words beginning with tense or aspirated stops has become significantly higher, enough to assume a newly emerging tone genesis.

In the discussion of laryngeal contrasts, Korean Post-Obstruent Tensification (POT)3 is quite relevant, as tense stops emerge in medial positions as part of laryngeal neutralization. Plain obstruents in Korean undergo tensification immediately after another obstruent (Inkelas & Cho, 1993; Kim-Renaud, 1974), as illustrated in (4a).4 The obstruents in (4b) are not subject to POT since they are not preceded by an obstruent.

(4)

a.

Post-Obstruent Tensification (POT)

maktε‎

makt’ε‎

‘stick’

kak + ca

kakc’a

‘each’

kiph-ta

kipt’a

‘it is deep’

k’och-kwa

k’otk’wa

‘flower and’

b.

Intersonorant Voicing

aka

aga (*ak’a)

‘baby’

anc-a

anja (*anc’a)

‘sit down’

POT applies not only in heterorganic clusters but also in geminates, whether derived by assimilation or by a morphological process. Korean allows “real” geminates, both monomorphemic (e.g., əmma ‘mom’; molla- ‘not to know’) and hetero-morphemic (e.g., tot + ko→ tokk’o ‘rise and’; kot + palo → kopp’alo ‘straight’). However, the independent nature of POT with regard to gemination illustrates that tense stops cannot be analyzed away as underlying geminates.

I conclude this section on phonation contrast by citing generalizations summarized in Cho (2011). First, having both tense and aspiration in one obstruent system is so unusual that some researchers (Han, 1996) attempt to do away with tense consonants in phonology by treating them as geminates, thus eliminating the distinctive feature(s) referring to tenseness (and aspiration in some cases) in phonology and obtaining the phonetic manifestation of tenseness as a byproduct. Others fit the Korean contrast along the voice–aspirated system (Kim & Duanmu, 2004). Second, phonetic details are quite complicated: glottal width, laryngeal tension, VOT, F0, medial closure, effects on neighboring vowels, tongue contact position, etc. play a role in making the three-way distinction. Further research is needed to identify relevant phonetic and phonological features.

In sum, I believe Korean obstruents manifest a three-way distinction that cannot be further reduced, thus refuting the evidence from historical evolution and phonetic idiosyncrasy. When a three-way laryngeal distinction is maintained, the simple onset structure of Korean syllables can be maintained without further stipulation. In a geminate account, the economy gained at laryngeal contrast needs to be compensated by additional complications in syllabification.

2. Consonant Markedness/Unmarkedness

One of the most prominent features of Korean phonology is consonantal assimilation, in which a sound takes on the feature(s) of an adjacent consonant. There are several types of assimilations, both in place and manner (e.g., nasalization, lateralization, and spirantization).

First, let me examine place assimilation of the coronal coda, as illustrated in (5). Both the coronal nasal and the oral stop assimilate to the place features of the following consonant.

(5) Place assimilation (Cho, 1990; Jun, 1995; Kim-Renaud, 1974; Sohn, 1987)

a.

a. Coronals take on the place of the following non-coronal consonant places (labials, postalveolars and velars).

pat-ko

pakko

‘to receive and’

kot+palo

koppalo

‘straight’

kot+caŋ

koccaŋ

‘right away’

han-kuk

haŋguk

‘Korea’

man-pal

mampal

‘full bloom’

b.

Labials and postalveolars assimilate to velars5.

kam+ki

kaŋki

‘a cold’

nac+ko

nakko

‘to be low and’

əp+ko

əkko

‘to carry on the back and’

Coronal assimilation (especially of the nasal coronal) is very well attested cross-linguistically (English, Japanese, Catalan, Sanskrit, etc.), but it is noteworthy that Korean place assimilation is much more pervasive as it allows non-coronals to assimilate. Labials and postalveolars assimilate to velars, but velars remain intact, and there is no interaction between labials and postalveolars. This asymmetrical behavior has been handled in various frameworks in generative phonology, starting with an SPE-style account of Kim-Renaud (1974), to Sohn’s (1987) and Cho’s (1990) underspecification account, and most recently, as interaction among perceptual and articulatory constraints under the framework of Optimality Theory (Jun, 1995).

In addition to place assimilation, there is an array of manner assimilation: Nasalization, spirantization, and lateralization, shown in (6).

(6) Manner assimilation

a.

Stop nasalization

nap-nita

namnita

‘sprout-VE’

kath-ni

kanni

‘is it the same?’

ak+moŋ

aŋmoŋ

‘nightmare’

b.

Spirantization

kut-so

kusso

‘to harden-VE’

mit-saopnita

missaomnita

‘to believe-VE’

c.

/t/-lateralization

tikɨt+liɨl

tikɨlliɨl

‘the letters t and l

d.

/n/-lateralization (bidirectional)

wən+lε‎

wəllε‎

‘originally’

kal+nip

kallip

‘reed’

sin+la

silla

‘Shilla Dynasty’

sol+nip

sollip

‘pine needle’

All coda obstruents obligatorily nasalize to a following nasal consonant (6a), while /t/ also assimilates to the continuant and lateral features of the following consonants. Labials and velars do not undergo manner assimilations other than nasalization, and thus do not yield non-phonemic labial or velar fricatives or laterals.

Most manner assimilations can be accounted for by a sort of syllable contact constraint whereby the coda consonant is stipulated as more sonorant than the following onset consonant (with the sonorant hierarchy defined as lateral > nasal > fricative > stop). Lateralization of /n/, however, is different from /t/-lateralization in its directionality. The latter assimilates only regressively (/t+l/ → [ll], but not /l+t/ → /ll/), but a sequence of two coronal sonorants (/n+l/ or /l+n/) is not allowed regardless of their syllabic positions, resulting in bidirectional lateralization.

Korean consonantal assimilation cannot be discussed without mentioning coda neutralization, which interacts closely in the feeding order with assimilation. Neutralization involves manner, laryngeal and place simplification; the fricatives /s/ and /s’/ and the glottal approximant /h/ all neutralize to the unreleased [t]. The prepalatal affricates lose their continuant feature as well as their place features, again resulting in [t]. All laryngeal codas surface as lax counterparts, as shown in (7c).

(7) Coda Neutralization

a.

Continuants (/s/ and /h/) are neutralized to stops.

kas

kat

‘mustard green’

nas

nat

‘sickle’

kas’-ta

katt’a

‘went-Verb Ending’

hiɨh

hiɨt

‘the letter /h/’

b.

Prepalatals are neutralized to dentals.

nac

nat

‘day’

cəc

cət

‘milk’

nach

nat

‘face’

c.

Laryngeal features do not surface.

pak’

pak

‘outside’

aph

ap

‘front’

toch

tot

‘sail’

In Korean consonantal phonology, the special status of /t/ has been noted for a wide range of processes, as listed in (8).

(8) List of special behaviors of /t/ in Korean (Cho, 1990)

  1. a. Assimilation: /t/ assimilates completely to a sonorant following it, and takes on the place features of a following obstruent.

  2. b. Neutralization: All coronal obstruents (alveolars and postalveolars), regardless of their place and manner features, neutralize to [t] in the syllable coda position.

  3. c. Simplification: In clusters, coronal obstruents are deleted regardless of their position.

  4. d. Tensification: There is coronal-specific tensification (il-pun, il-kyək vs. il-t’o, il-c’əŋ, ils’u).

Different theories have arisen over the past four decades to explain why only certain types of change are allowed and under what conditions such processes take place. In particular, the asymmetrical behavior of coronal and non-coronal stops is noted across languages and gives rise to the Underspecification Theory (Archangeli, 1984). The unmarked status of coronal place in Korean is captured either by the underspecification of /t/ (Cho, 1990) or by a hierarchy of perceptually motivated faithfulness constraints, crucially ranking faithfulness to non-coronal features in an unreleased position over a coronal feature (Jun, 1995).

Although it works for neutralization and assimilation, it is very difficult to assume that /t/ is the least-marked of all consonants when processes have to specifically refer to its features to the exclusion of the other place features. In underspecification accounts, it is not possible to refer to the set of coronal features, as they are assumed to be not specified—they are absent, as shown in (9). Alveolars assimilate to the other places as they lack underlying place features, while Labials assimilate to Velars as the former are less marked than the latter.

(9) Place Features in Underspecification Theory (Cho, 1990)

Labial: [-coronal]

Alveolar:

Postalveolar: [-anteria]

Velar: [-coronal], [-anteria]

Similarly, when a hierarchy of faithfulness features is involved, there is no way to isolate coronal features alone without also involving non-coronal features, aside from a class of cases identified as “the emergence of the unmarked” (McCarthy & Prince, 1994).

Kang (2000), however, argues that even though coronal unmarkedness is a default situation that covers all context-free cases, cross-linguistic generalizations call for a markedness constraint hierarchy to account for the special behavior of coronals. As support for coronal unmarkedness, she cites the four cases in (10).

(10) Coronal Unmarkedness cases (Kang, 2000, p. 110)

  1. a. Inventory favors coronal over non-coronal consonants.

  2. b. Epenthetic consonants are more likely to be coronal.

  3. c. Coronal consonants are often immune to the OCP.

  4. d. Coronal consonants may participate in vocalic spreading.6

As for coronal markedness, Kang (2000) cites Korean Consonant Cluster Simplification (CCS; (11)) as a case of coronal markedness: The Korean coda allows only one consonant, and “when both consonants are obstruents or both are sonorants, it is always the coronal consonant that is deleted” (pp. 59–60).

(11) Consonant Cluster Simplification (when combined with consonant-initial suffixes)

/kaps/

‘price’:

kaps-i

but

kap-kwa, kap-to

/salm/

‘life’:

salm-i

but

sam-kwa, sam-to

/halth-/

‘to lick’:

halth-a

but

hal-t’a

The marked status of/t/in deletion is treated as a markedness phenomenon by Kang (2000), since/t/needs to be singled out. She concludes that the fact that Korean does not contrast sub-coronal places supports her claim that/t/-deletion in Cluster Simplification is a case of coronal markedness. Within her account, coronal markedness is universally tied with the absence of sub-coronal place contrasts.

However, postalveolar affricates in Korean are coronals that are marked by [+coronal, –anterior], being distinct from coronals marked [+coronal, +anterior]. Moreover, in many dialects and in certain phonetic contexts, Korean affricates are pronounced as dentals (Kim, 1999). Therefore, the inventory-based argument is quite arbitrary for Korean coronals.

In (12), the first consonant wins unless the second is a non-coronal. The clusters in (12a), the second consonants (s, c, h, th) all neutralize to [t] due to Coda Neutralization, so in both (a) and (b) non-coronals are syllabified. When both consonants are coronals, the first consonant surfaces (as in/nc/, /nh/, /lh/, and /lth/), which is a clear case of coronal unmarkedness. I believe that CCS in Korean nominal and verbal stems can be obtained by the mechanism of syllabification; that is, the first consonant wins unless the second one is a non-coronal consonant (see Cho, 2015) for a detailed analysis of CCS). Given a generalization like this, there is no need to refer to the marked status of/t/. Rather, non-coronals are more marked and take precedence over coronals as coda consonants, which is in accordance of the distribution facts of coda consonants in Korean (Shin, Kiaer, & Cha, 2013, p. 131); the four consonants /ŋ, n, l, k/ are 5% of the codas in the dictionary while /n, ŋ, l, m/ are over 90% in speech. In both purviews, /t/ makes up less than 2% of the total distribution.

(12) Consonant Cluster Simplification (Cho, 2015; Martin, 1992,)

a.

The first C surfaces

b.

The second C surfaces

/ks/→ k

/ps/→ p

/lk/→ k

/nc/→ n

/lm/→ m

/nh/→ n

/lp/→ p

/lh/→ l

/lph/→ p

/lth/→ l

Another noteworthy point is the frequency of /t /in Korean in any position. Contrary to the expectation, /t/ is one of the least frequent sounds among non-laryngeal consonants (The five consonants /k, n, ŋ, l, c/ make up over 50% of the total consonantal distribution in the dictionary, while the four consonants /n, k, l, m/ do so in speech.) This is in stark contrast with English: in the dictionary /t/ is the most frequent, followed by /s/, /n/, /l/, /r/, /k/, /d/, /z/; in speech, the order is /n/, /t/, /d/, /s/, /l/ (Shin, Kiaer, & Cha, 2013, pp. 121–142). While /t/ in Korean behaves as unmarked in neutralization and assimilation, the distribution does not support its unmarked status.

Another coronal coda mystery involves the preference of/s/over/t/as a stem-final consonant. Many nouns tending in a laryngeal consonant have been reanalyzed to a lax form in the same fashion as a cluster in noun stems has been simplified. More mysterious is the fact that stem-final coronal obstruents in nouns are generally in variation with [s], as shown in (13).

(13) Stem-final coronals are in variation with [s] in the prevocalic position.

pic

~

pis

‘debt’

nac

~

nas

‘day’

cəc

~

cəs

‘milk’

pich

~

pis

‘light’

k’och

~

k’os

‘flower’

mith

~

mis

‘below’

soth

~

sos

‘pot’

Recent studies (Albright, 2008; Jun, 2010; Kang, 2003a) argue that these alternations are analogically motivated rather than phonetically or phonologically driven. The distribution of lexical obstruents in noun stems determines relative preference among variants. In addition, high-frequency words tend to be more resistant to the innovative/s/or lax-stop pronunciation than low-frequency words that have already undergone reanalysis. The paradigm in (14) shows that the accusative –ɨl and the nominative –ka often allow the innovative/s/or the lax form; the locative –e tends to preserve the conservative form, which clearly argues against completely reanalyzing the underlying form in favor of innovative consonants.

(14)

/path/

‘field’

/mith/

‘below’

pasi, pasɨl, pathe

misi, misɨl, mithe

The mixed paradigm in (14) agrees with Albright’s (2008, pp. 163–171) observation that “noun paradigms are being rebuilt on the basis of unsuffixed (isolated) forms, even though these forms suffer from drastic coda neutralization.” The fact is that unmarked forms are much more frequent than suffixed forms in nouns due to frequent ellipsis of case markers, but the form with the locative suffix (/-e/) reveals the old underlying form. From over 40,000 nouns in the Sejong Project corpus (Kim & Kang, 2000 via Albright, 2008), the following distribution facts emerge: 42% end in a sonorant consonant, 39% end in a vowel, but only 18% of all Korean nouns end in an obstruent. Also, a severe asymmetry is observed among obstruents: among labials and velars, lenis stops make up more than 95%, while among coronals almost 80% of the stems end in /s/ or /ch/, but not /t/.

The innovative /s/ as a default coronal is firmly established in loanword phonology. As shown in (15a), English /t/is adopted as /s/ when the vowel is short, and the resulting form requires a vowel-initial suffix (e.g., makes-i ‘market-Nominative’). When the syllable is heavy, the epenthetic vowel is inserted at the end (15b).

(15) Korean adaptation of English /t/ and /d/ in coda position

a.

English /t/ as Korean /s/

market

makes

helmet

helmes

racket

rakes

jacket

cakes

internet

intənes

hot

has

robot

robos

out

aus

b.

English /t/ as Korean /thɨ/

chart

chathɨ

report

riphothɨ

right

raithɨ

date

teithɨ

boat

pothɨ

part

pathɨ

nest

nesɨthɨ

hint

hinthɨ

c.

English /d/ as Korean /tɨ/

lid

ritɨ

pyramid

phiramitɨ

cupid

khwuphitɨ

liquid

rikhwitɨ

slide

sɨllaitɨ

word

wətɨ

land

rε‎ntɨ

As shown in (15c), English /t/ and /d/ behave differently, in that the English /d/ uniformly induces epenthesis and surface as [dɨ] due to productive Intersonorant Voicing of Korean lax obstruents. This is in contrast to non-coronal codas, which show more variability and less regularity in preserving phonemic contrasts (Kang, 2003b).7

In this section, I have discussed the special behavior of Korean /t/ (asymmetry in neutralization and assimilation) and the paradoxical nature of its role (unmarked in phonological processes but extremely marked in distribution). The issue of coronal unmarkedness and markedness is far from resolved, and further research is required to shed light on this interesting phenomena.

3. The vowel inventory

The prescriptive grammar of Standard Korean posits ten vowels, shown in (16). While it is well documented that the front rounded vowels /ü/ and /ö/ were pure monophthongs in earlier stages of Korean, for the past hundred years the diphthongization process has been well underway, drastically limiting the monophthongal realization of these vowels only to certain contexts.

(16) The ten vowels in Standard Korean

Front

Back

Round

Round

High

I

ü

ɨ

u

E

ö

ə8

o

Low

Ε‎

a

Concerning the vowel inventory there are two areas of debate: first, the phonemic status of the front rounded vowels (ü and ö) and second, the ongoing merger of /e/ and /ε‎/. Due to these marginal vowels, some researchers posit only seven underlying vowels for Standard Korean (Shin, 2015; Shin, Kiaer, & Cha, 2013).9

Due to prevalent diphthongization, the front rounded vowels are not pure monophthongs in most contexts. As exemplified in (17), these marginal vowels surface as the corresponding diphthongs [wi] and [we], especially when there is no onset consonant preceding these vowels.

(17) Obligatory diphthongization of front rounded vowels in onset position

/ü-lo/

wiro

‘upwards’

/paü/

pawi

‘rock’

/ö-halməni/

we-halməni

‘maternal grandmother’

/ye-ö/

yewe

‘exception’

I assume that the diphthongal allophones [wi] and [we] are phonologically derived from /ü/ and /ö/, mostly for the sake of expository simplicity because the reverse assumption of monophthongization is harder to conceptualize when we consider variable surface forms that depend on the place and the manner of articulation of the preceding consonant in blocking diphthongization, as shown in (18).

(18) Diphthongization patterns

ü

after labials and coronals (mü, pü, tü, t’ü, cü, sü, nü, rü)

after laryngeal consonants (hü, k’ü)

wi elsewhere (wi, kwi)

ö

after labials and [s, c] (pö, sö, cö)

after laryngeal consonants (k’ö)

we elsewhere (we, twe, kwe, nwe)10

The data in (18) are messy and do not allow neat analyses. The syllable-level OCP, a sort of negative constraint on the sequence of two labial features, can probably account for the lack of diphthongization in the labial context. Moreover, the mid-vowel /ö/ allows a wider context for diphthongization than /ü/, in particular after dental stops. Han (1963), however, observes different contexts for diphthongization: after labials, velars and /h/, /ö/ is realized as [we], while other environments (/t, n, c, s, ph, th, kh, ch/) tend to preserve the monophthongal qualities. Kang, H.-S. (1997) looks at phonological variation in glides and diphthongs, and also concludes that the place articulation of the preceding consonant is one of the important linguistic factors. It is clear that the contexts of diphthongization of the two vowels /ü/ and /ö/ differ from each other, and diphthongization and glide deletion exhibit wide inter-speaker variability with regard to place and laryngeal features, in addition to non-linguistic factors such as register and speech rate. Systematic acoustic studies are called for, as past research seems to focus only on onset positions in (18) and do not examine all post-consonantal environments.

In addition to acoustic and perceptual evidence, there is one clear phonological diagnostic that indicates a clear lack of diphthongization. As is commonly observed, Korean /s/ surfaces as the palatal counterpart [š] before a high front vocoid, without exception. This pattern of /s/-palatalization clearly demonstrates the monophthongal quality of /ü/ before /s/. The examples in (19) illustrate that not only /i/, but also /ü/ obligatorily triggers palatalization. If /ü/ surfaced as [wi], /s/ would not change in anteriority, as [w], as a high back glide, does not trigger /s/-palatalization. Only the high front vowels trigger palatalization.

(19) /s/-palatalization before high front vowels /i/ and /ü/

sip

šip

‘ten’

süp-ta

šüpta

*swipta, *süpta

‘to be easy’

sü-ta

šüta

*swita, *süta

‘to rest’

sul

sul

*šul

‘wine’

su-i

sui

*šui

‘easily’

The second point of contention regarding the vowel inventory involves the merger of the two front non-high vowels, /e/ and /ε‎/. I observe roughly the patterns in (20) in Standard Korean.

(20) Orthographic distinction of /e/ and /ε‎/

Pe

‘hemp’

pε‎

‘pear, boat, stomach’

te

‘place’

tε‎

‘bamboo’

ke

‘crab’

kε‎

‘dog’

ne

‘your’

nε‎

‘my’11

e

‘at’

ε‎

‘child’

Four decades ago, H.-B. Lee (1971, 1973) reported that while the distinction was clear among older speakers of Standard Korean (who were older than 30 years of age at that time), younger speakers did not make any distinction. Hong (1987) confirms Lee’s observation by presenting experiments involving both production and perception experiments. She identifies an age-related correlation: the formant values of the younger speakers overlapped to a greater extent than the older speakers. She also points out the difficulty of making perceptual distinctions as evidence for the complete merger of these phonemes in the younger generation. On the other hand, J.-H. Lee (1995) argues that the much-discussed merger is not a real merger in progress but a near-merger in the sense of Labov, Karan, and Miller (1991). Near-merger is a case where two phonemes keep a small phonetic distance and are not completely identical. It happens when speakers make a distinction in production but not necessarily in perception, thus accounting for the commonly held view of a total merger (Silva & Jin, 2008). More recent studies all seem to point to the completion of the merger (Hwang & Moon, 2005, Shin, 2015).

Whether we assume total merger or near-merger, it is clear that the distinction is tenuous at best, in contrast to the existence of /ü/ and /ö/. The morphological role that is played by the height distinction in vowel harmony is fading out as well. In the Sound Symbolism in (21a), the high vowels /i/and /e/are dark vowels, and their corresponding bright vowel is /ε‎/.

(21)

  1. a. Vowel alternations in Sound Symbolism (Cho, 2006)12

  2. b. Vowel alternations revised by the merger of two front vowels

Whereas alternations such as kilc’uk/kε‎lc’uk (‘long and slim’) and pisil/pε‎sil (‘weak’) are still robust, the /e/–/ε‎/ alternation, which was once productive, seems to have lost the meaning differences, as in kelkel/kε‎lkε‎l (‘exhausted’) and t’ekul/t’ε‎kul (‘rolling down’). In contrast, both of the two back unrounded vowels /ɨ/ and /ə/ still function as dark vowels in opposition to their bright counterpart /a/: sɨlc’ək/salc’ak (‘secretly’), k’ɨt’ək/k’at’ak (‘nodding’), hɨntɨl/hantɨl (‘breezy’), əlluk/allok (‘motley’), k’əŋchuŋ/k’aŋch (‘jumping’), pənc’ək/panc’ak (‘twinkling’). Also, with the prevalent diphthongization of /ü/ and /ö/ and glide deletion (e.g., k’ücücü/k’öcöcö → k’wicici/k’wecece ‘dirty’), the /ü/~/ö/alternation is not as active as the other vowel alternations.

Another interesting fact about Korean vowels is the co-occurrence restrictions on sub-syllabic units (onset consonant, glide and vowel). First, there are occurrence restrictions holding between a consonant in onset position and the following glide: a labial consonant cannot in general be followed by /w/, while a palatal onset never occurs with /y/ (Martin, 1992). In addition, glides also participate in the G+V distribution, as listed in (22).

(22) Distribution of diphthongs: Gaps in CV sequence

i

wi

*yi

ɨ

*wɨ

*yɨ

u

*wu

yu

e

we

ye

ə

o

*wo

yo

ε‎

wε‎

yε‎

a

wa

ya

The front rounded vowels do not allow any glide to precede them. It is not clear whether it has something to do with their almost ubiquitous diphthongal realization. In addition, Korean has a marginal sequence, /ɨ+i/, as a diphthong. While many claim it is a falling diphthong and the second element is a glide, it is clear that the first vocalic element is a glide, followed by [i]. As first noted by K.-O. Kim (1978), support from prolongation in singing and in emphatic speech clearly demonstrates that only the second vocalic element [i] is subject to prolongation. Glides, as a momentary type of articulation (Catford, 1977), have an extremely narrow aperture at the articulator and cannot be sustained, unlike true vowels and syllabic sonorants. I will exclude this sequence from the discussion of co-occurrence restrictions as (a) it is found only in onsetless initial syllables of Sino-Korean morphemes, exhibiting a marginal distribution; and (b) it is invariably neutralized as a simple vowel in non-formal registers and in most dialects.

The non-occurrence of /wɨ/ and /yɨ/can be accounted for in a fairly natural way: the high back unrounded vowel /ɨ/is the weakest vowel, which is prone to deletion in V+V sequences, assimilation to other vocalic features and insertion in breaking illegitimate consonant clusters, as shown in (23).

(23) Unique behavior of /ɨ/

a.

Deletion

s’ɨ-ə

s’ə

‘to use+Continuative’

ku-ə

kuə

‘to roast+Continuative’

b.

Assimilation

English

Korean

crown

khɨraun

brown

puraun (ɨ → [u] after a labial C)13

church

chəchi (ɨ→ [i] after an alveo-palatal C)14

c.

Insertion

English

Korean

Sprite

sɨphɨraithɨ

Christmas

khɨrisɨmasɨ

By a productive feature assimilation process, the sequences [wɨ] and [yɨ] undergo rounding and fronting, resulting in the ill-formed wu and yi, which are independently blocked by the occurrence restrictions (*[+round][+round], *[+high, –back][+high, –back]). Although there are general tendencies, the OCP restrictions are language-specific (Harris, 1983; Selkirk, 1982; Steriade, 1982). Many languages (Spanish, Klamath, etc.) have restrictions on yi and wu as onset clusters, and Japanese goes one step further and disallows ye as well as yi and wu. The distributional restriction observed in Korean diphthongs can be accounted for simply by invoking two OCP constraints over the feature sets of [+round] on the one hand and [+high, –back] on the other.

In this section I deal with two main issues concerning the changing Korean vowel inventory, namely the status of front rounded vowels and the merger of two front non-high vowels. Despite limited distribution patterns of /ü/ and /ö/, they still surface in well-defined environments, and phonologically, /ü/ participates as a high front vowel in /s/-palatalization. However, /e/ and /ε‎/ are distinct in neither phonetic realization nor the phonology of vowel alternations. Set (24) is a summary of the phonotactic constraints holding in G+V sequences.

(24) Phonotactic constraints on G+V

  1. a. *[+high, -back] (*yi)

  2. b. [+round][+round] (*wu, *wo)

4. Prosodic Hierarchies as Domains of Phonological Processes

In this section I explore the mismatches between morphology and syntax on the one hand, and phonology on the other. As they are unique domains of grammar, the categories needed in phonology are not isomorphic to the morpho-syntactically defined units; each domain of grammar relies on unique properties in its definition, and these properties are not always intersecting. In delving into questions of domain mismatches, four decades of research into lexical and phrasal phonology since the introduction of Lexical Phonology and Morphology (Kiparsky, 1982) leads to the consensus that it is absolutely necessary to divide lexical and postlexical processes as two independent modules.

I assume the following prosodic hierarchies for Lexicon and Post-Lexicon. Whereas the postlexical prosodic hierarchy is universally accepted as an organizing principle of phrasal-level phonetics and phonology (Inkelas, 1990, 2008; Jun, 1996, 2005; Ladd,1997; Nespor & Vogel, 1986; Pierrehumbert, 1980; Pierrehumbert & Beckman, 1988; Selkirk, 1984 ), there has not been enough discussion on sub-lexical prosodic hierarchies. Some even identify the metrical hierarchy (consisting of the foot, the syllable and the mora) as the one governing the Prosodic Word (Jun, 1994).

(25) Prosodic Hierarchies (Universal)

For any discussion of phonological processes, one should stipulate a domain of application, and in order to define meaningful sub-lexical domains, we need two independent notions of “the word” in the lexicon, in the same manner that syntax does not directly map with phrasal categories of phonology, but an intermediary interface between syntax and phonology needs to be formulated.

I define Korean prosodic categories (α‎ and β‎) under the framework of prosodic subcategorization within the framework of Prosodic Lexical Phonology (Inkelas, 1990), which calls for a four-way distinction, as in (26).

(26) Prosodic subcategorization

  1. a. Morphologically-defined ‘m-word’

  2. b. Prosodically-defined ‘p-word’

Morphologically dependent

Not morphologically dependent

Prosodically dependent

Affix

Clitic

Not prosodically dependent

Root15

Stem

Korean morphology needs categories such as the morphologically dependent affix and root on the one hand, and the prosodically independent root and stem, on the other. In particular, morphological constituents such as prefix, root, root-verb, stem-noun, nominal particle, verbal-suffix, etc. are clearly needed. Moreover, there is ample evidence for two independent prosodic domains (α‎ and β‎) in the lexicon.

The following processes are sensitive to the sub-lexical β‎ domain: syllabification (Coda Cluster Simplification, neutralization), Post-Sonorant Tensing, processes in compounding (Sai-Sios, /n/-Ø alternation, palatalization, /l/-alternation, among others. First, let us look at coda neutralization, whereby all laryngeal, manner, and prepalatal place features are neutralized, as shown in (3) and (7). All continuants and laryngeal consonants surface as [t] in the coda position. Coda neutralization does not apply when a vowel-initial suffix follows, but it does apply at a prefix boundary and in compounding, as illustrated in (27).

(27) Domain of syllabification

a.

Noun+suffix

Isolation

C-suffix

Vowel-suffix

/os/ ‘clothes’

ot

ot-t’o

os-i

/cas/ ‘pine nut’

cat

cat-t’o

cas-in

/aph/ ‘front’

ap

ap-t’o

aph-e

/pich/ ‘light’

pit

pit-k’wa

pich-i

/pak’/ ‘outside’

pak

pak-k’wa

pak’-i

b.

Compounds

/os+an/

otan

‘inside clothes’ (clothes+inside)

/path+ilaŋ/

patilaŋ

‘ridge of field’ (field+ridge)

c.

Prefix+Noun

/təs+os/

tətot

‘outer garment’ (cover+clothes)

/us+əlɨn/

utəlɨn

‘elder’ (upper+person)

/chəs+insaŋ/

chətinsaŋ

‘first impression’ (first+impression)

The suffix is prosodically and morphologically dependent, and when it is affixed to a stem as in [os-i] (27a), the resulting combination gets promoted to a β‎ category, which is the domain for syllabification as well as palatalization in Korean. Palatalization (28) is a phenomenon where dental stops /t, th/ are realized as prepalatal affricates [c, ch] when followed by an /i/ or /y/ across a morpheme boundary, one of the prime cases of Nonderived Environment Blocking (NDEB) (Kiparsky, 1973, 1985).16 Palatalization is blocked in underived forms (native words such as əti ‘where’ and candi ‘grass,’ or recent loans such as ratio ‘radio’ and ticithal ‘digital’). We determine that the relevant prosodic category is exactly the same as syllabification, namely within a β‎ in the lexical prosodic hierarchy.

(28) Palatalization

a.

Derivational morpheme boundary

kath-i

kachi

‘together’

same+ ADV

hε‎ tot-i

hε‎ toci

‘sunrise’

sun rise-NONIM

kut-hi-ta

kuchita

‘make it hard’

hard-CAUS-VE

b.

Inflectional morpheme boundary

path—i

pach i

field-NOM

path—ilaŋ

pach ilaŋ

field-COMITATIVE

path—i-ta

pach ita

filed-COPULA

Palatalization is blocked across β‎ boundaries (i.e., compounds) and between larger phrasal units, as shown in (29).

(29) Lack of palatalization across β‎

a.

Compounding

chəs+ insaŋ

chətinsaŋ

‘first impression’

path + ilaŋ

patilaŋ

‘ridge of a field’

b.

Post-lexicon

path ilkwə

pat ilkwə

‘till the field’

At this point, we need to deal with the prefix–suffix asymmetry often observed in Korean (Han, 1993; Kang, 1992). As in many languages, Korean suffixes are grammatical morphemes (derivational suffixes, nominal paradigmatic markers, verbal inflectional suffixes, cross-categorical delimiters, etc.). On the other hand, despite its traditional classification as ceptusa “prefix,” it makes more sense to treat the Korean prefix not as an affix but as a bound root. Korean prefixes carry semantics similar to “content morphemes” (much like the English bound roots cran- and huckle-) and are morphologically dependent and prosodically independent, according to the subcategorization frame of (26).

The sub-lexical prosodic category β‎ is also the domain of another morpho-phonological process, /n/–Insertion (Cho, 1995; Kang, 2004). While there is no alternation within an underived word (e.g., anita ‘not to be’) or between a stem and an affix (e.g., man-ita ‘ten thousand-COPULA’), (30) shows alternations in certain lexical and phrasal combinations.

(30) /n/–Insertion

a.

Lexical combinations

“Prefix”+root

cit + iki-

cinniki-

‘to mash’

hoth + ipul

honnipul

‘single-layer quilt’

Compounding

khoŋ + yət

khoŋnyət

‘bean taffy’

pom + yəlɨm

pomnyəlɨm

‘spring and summer’

b.

Phrasal compound

tε‎hak + yaku → tε‎haŋnyaku, ~ tε‎hak yaku ‘college baseball’

In (30b), the first form with the /n/ inserted is probably a lexical compound, while the latter is a phrasal combination. This optional /n/-insertion occurs only in frequently used compounds in Standard Korean. As noted by Han (1993), Kyengsang Korean exhibits /n/-Insertion in smaller domains than stem-compoundings.

While it is obligatory to have a nasal coda in (30a), in phrasal combinations, only certain frequently occurring combinations (probably due to lexicalization) optionally allow /n/-insertion, as shown in (31).

(31) Phrasal combinations (across phonological words)

a.

Optional /n/-insertion

han il

‘something that is done’

os ip-ta

‘to wear clothes’

səlɨn yəsəs

‘36’

t’ɨkəun yəl

‘hot heat’

s’ɨn yak

‘bitter medicine’

b.

No /n/-insertion in phrasal combinations

sekyecək yumul

‘world-class heritage’

cəŋsincək iyu

‘psychological reason’

sɨmathuhan yuniphom

‘smart-looking uniform’

c.

No /n/-insertion across higher categories in the Prosodic Hierarchy

acu coha-hanun #yaku-sihap ‘the baseball game I like a lot’

nae-ka cincca cincca coha-hanun #yaku-sihap ‘the baseball game I really like.’

The historical evolution of /n/–Ø alternation looks like Synchronic Rule Inversion, as it started as /n/-deletion before a high front vocoid starting in the 18th century. Now it applies equally to both etymologic /n/ and non-etymologic /n/, as shown in (32).

(32) /n/–Ø alternation

a.

Etymologic /n/

əkɨm+ni

əkɨmni

‘molar’

b.

Non-etymologic /n/

pam+il

pamnil

‘night work’

sε‎k+yuli

sε‎ŋnyuli

‘colored glass’

The process is captured straightforwardly by Sonorant Juncture Constraint (SJC) under the Optimality Framework (Anttila & Cho, 1998; Cho, 1995). SJC will select the form that has /n/, whether it involves an etymologic /n/ or a non-etymologic /n/.17

(33) Sonorant Juncture Constraint (SJC):

A sonorant consonant followed by a high front vocoid across a prosodic-word boundary is ill-formed: *Son][i/y__

More recent studies (Hong, 2006; Jun, 2015) attempt to derive variability in /n/-Insertion in terms of lexical stratification and Korean-specific syllable-affiliation constraints, but it remains undisputed that its domain is limited to a sublexical prosodic category, namely, β‎.

In this section, I have demonstrated the existence of sub-lexical prosodic categories in Korean that are derived from the prosodic and morphological subcategorization framework, as delimited by Syllabification (27) and Palatalization (28). A number of phonological processes (Syllabification, Palatalization, and /n/–Insertion)18 clearly require the Lexical Prosodic Hierarchy of (25a).

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Notes:

(1.) Plain consonants are also called “lenis” or “lax” consonants.

(2.) Phonetically Intervoiced Slackening of fricatives might be considered the same process as Intersonorant Voicing (Cho, Jun, &Ladefoged, 2002); the same slackening process in the voicing environment may be also responsible for the relatively newly emerged obligatory disappearance of intersonorant h, as in /coh-a/ → [coa] ‘to be good-continuative suffix.’

(3.) POT is different from morphologically sensitive tensing, such as Post-Nasal Tensing in verbal morphology (e.g., /an-ta/ → [ant’a] ‘to sit-verb-ending’) and Post-Lateral Coronal Tensing in the Sino-Korean vocabulary (e.g., /il-ca/ → [ilc’a] ‘one word’).

(4.) Contemporary tense consonants are derived from Middle Korean consonant clusters such as sp, sk, pt, pc, pst, etc., which lends support to the hypothesis that the Modern Korean tense series resulted from a historical POT process.

(5.) There is no direct evidence for the postalveolar assimilating to the following velar, as the postalveolar invariably neutralizes to [t] in the coda position, and the process can be subsumed under the coronal target.

(6.) The data are not clear due to prevalent dialect mixing, but in Korean umlaut (vowel fronting), non-coronals participate in vocalic spreading but not coronals (aki → ε‎ki ‘baby’; əmi → emi ‘mother’; api → ε‎pi ‘father’; but no changes in əti ‘where’; kaci ‘eggplant.’)

(7.) Korean loanword phonology has yielded many interesting insights into the role of perception in adaptation of foreign sounds (De Jong & Cho, 2012; Kang, 2003a; Kenstowicz, 2005), which deserves a separate entry.

(8.) The mid back vowel is not the schwa of other languages that tends to weaken in prosodically weak positions, and it is sometimes transcribed as /ʌ/ or other phonetic symbols ( Shin, 2015). However, I follow the general practice of using the symbol /ə/, even though the phonetic studies find this vowel to be quite back and lower-mid, on the basis of a common practice in Korean historical phonology, where the symbol /ʌ/ is reserved for the Arae-A vowel of Middle Korean that was lost in Modern Korean (except in Cheju Island).

(9.) Non-standard dialects exhibit smaller vowel inventories; for example, the Kyengsang system has six symmetrical vowels (i, e, ə, a, u, o), and Pyengan dialect has no distinction between /ə/ and /o/ (Lee & Ramsey, 2000).

(10.) The C+glide clusters [Cwi] and [Cwe] undergo massive [w]-deletion in casual speech, as in [kwi] → [ki] and [twe] → [te].

(11.) As expected, the confusion caused by the vowel merger in question is particularly problematic for the pronouns ne and nε‎. These morphemes are not only possessive pronouns (‘your’ and ‘my,’ respectively), but also the allomorphs of and na, respectively, before the nominative suffix –ka, as in ne-ka (‘you-nominative’) and nε‎-ka (‘I-nominative’). As a result, a new form ni has emerged and is currently used in all contexts other than in writing, where the graphemic distinction is still maintained between the two vowels.

(12.) According to the received view of Korean Vowel Harmony, Vowel Shift (K.-M. Lee, 1964, 1972) was assumed to bring about the change from Middle Korean palatal (front–back) harmony to Modern Korean height harmony. However, Ko (2012, 2013) convincingly demonstrates that Mongolian loanwords, the primary philological evidence for the Vowel Shift, are not tenable because both Old Mongolian and Middle Korean had an RTR (Retracted Tongue Root) contrast-based vowel system, not a palatal vowel system.

(13.) Orthographically it is <pɨ>, and [pɨ] is a possible, but not a natural pronunciation.

(14.) While one can posit /i/ as an epenthetic vowel after an alveo-palatal consonant, such a move would beg a question as to why /i/ here, while /ɨ/ is the universal epenthetic vowel.

(15.) Bound roots in English include -ert, -placable, -ept, -mit, -couth, cran-, etc., which are idiosyncratically found in words like inert, implacable, inept, transmit, uncouth, cranberry.

(16.) Anttila and Cho (1998) and Cho (2009) account for NDEB cases such as Korean palatalization and Sanskrit ruki by interaction between markedness and faithfulness constraints within Optimality Theory (McCarthy & Prince, 1993; Prince & Smolensky, 1993).

(17.) While many phonologists attempt to do away with processes that stipulate the information on junctures by subsuming juncture rules under domain-span and domain-edge rules, Korean /n/–Insertion is a true juncture phenomenon. Kang’s (2004) account relies on CRISP-EDGE, which requires crisp alignment between morphological and prosodic categories.

(18.) There are additional processes, in particular the nasal–lateral alternation, that demonstrate the existence of prosodic categories α‎ and β‎.