Dynamics and Transparency in Vowel HarmonyUltrafest, U. of Arizona, 4/15/05

Stefan BenusSpoken language processing group, Dept. of Comp. Science, Columbia University

Outline

Basic facts of transparent vowels in Hungarian vowel harmony (”Phonology”)

Experimental methods and Results (“Phonetics”)

Dynamic model of transparency -- a bridge between the continuous “Phonetics” and the categorical “Phonology”

Front Back [–Round] [+Round] [–Round] [+Round]

High i[i] í[i:] ü[y] ű[y:] u[u] ú[u:]

Mid é[e:] ö[] ő[:] o[o] ó[o:]

Low e[] á[:] a[](Ringen & Vago 98) transparent

Hungarian

Regular palatal vowel harmony: stem V determines suffix VStem Dative Adessive

ház 'house' ház-nak ház-náltök 'pumpkin' tök-nek tök-nél

Hungarian: main challenges The trigger and the target back vowels agree despite

intervening TV(s): papír-nak, aszpirin-nak, kávé-nak This agreement is gradient and affected by:

lip rounding of the intervening Vs: [+round] vowels do not allow this agreement: parfüm-nek

height of the intervening Vs : the lower the vowel, the less likely is this agreement allowed: Józef-nek, hotel-nek/nak

the number of intervening TVs: the more TVs between the trigger and the target, the less likely is the agreement allowed: mam-i-nak, mam-csi-nak, but mam-i-csi-nak/nek

TVs can trigger both front and back suffixes: víz-nek vs. híd-nak

TVs allow vacillation: hotel-nak/nek, mam-i-csi-nak/nek

Previous analyses Traditional: TVs are excluded from participating in vowel

harmony (papír-nak, aszpirin-nak, kávé-nak) (e.g. Ringen 75, Clements 77, Vago 80, Anderson 80, Hulst & Smith 86, Archangeli & Pulleyblank 88, Smolensky 95, Ní Chiosáin & Padgett 97, McCarthy 98, Ringen & Vago 98, Kiparsky & Pajusalu 02).

? the number of intervening TVs affect the choice of the suffix

? generalizations related to the nature of the TVs and the differences among them are difficult to express

Phonetically-based: perceptual features of TVs motivate their phonological behavior (e.g. Ohala 94, Kaun 95, Baković & Wilson 01).

Improve on the traditional analyses but do not capture all aspects of the Hungarian data.

Proposal Hungarian TVs are not excluded from participating in

palatal vowel harmony. Rather, the [±back] harmonizing feature is manifested on the TVs by systematic phonetic differences in the horizontal position of the tongue body.

Fine degree of articulatory backness in the stem-final vowel is phonologized in that it participates in determining the [±back] form of the suffix.

Nonlinear dynamics operating with gestural parameters provides a formal language for linking the qualitative alternation in suffixes to the small continuous changes in tongue body constriction location of the preceding vowel.

Experiment: TVs in [±back] context

Stimuli: Back context Front context 3-syll. [kabitom] ‘daze’ [repitm] ‘let fly’

[bulival] ‘party’ [bilivl] ‘pot’

[bodetol] ‘hut’ [bidetl] ‘bidet’ … 22 pairs, 8 repetitions

1-syll. [] ‘whistle’ [tsm] ‘address’ [tsel] ‘aim’ [sel]

‘wind’ … 8 pairs, 4 repetitions

Methodology: EMMA (3 subjects), Ultrasound (1 subject) Measured: maximal advancement of the tongue, quantified

with 3 independent variables

EMMA: horizontal position of lingual receivers

Determine the value at the peaks of the time functions

representing the kinematic trajectories of the TB and TD receivers (Tiede et al. 1999)

Ultrasound: edge-tracing Determine the frame with the most extreme front position Edge tracing: B-spline snakes (Iskarous 2004), TT on the right!

Area between two curves Determine the area between the curves from the same environment (front-front,

back-back) vs. the area between the curves from different environments (front-back) Pair-wise (bilivel vs. bulival), control for the curves’ lengths Environment affects the position of the tongue if the curves from the identical

environment are more similar (have smaller area) than the curves from the opposite environments.

F F

B B

Same

Diff.

Same

F

B

Effect of environment: vs.

γ

O

γ

O

Degree of dorso-pharyngeal constriction

Determine the distance between the fixed point on the line and the point where the line intersects the tongue surface

10mm

fixed reference points

Tongue Tip

intersection points

D

54

21

3

Main results - overview

TVs in front harmony contexts were less retracted than in back harmony contexts.

This effect was robust and highly significant for all 3 subjects and both methodologies with trisyllabic words.

With monosyllabic words, the effect was less robust but still significant for some measurements.

3-syll words: EMMA

Dependent var.: TD, TB2, TB1

MD = MAX (R, TV) back – MAX (R, TV)front

Factors: Environment (Env), T. vowel (TV), L. pair (P)

Env, TV, P, Env*P: significant for both subjects and all three receivers

Env*TV: significant for ZZ, /é/ is the most advanced in the front env. and the most retracted in the back env.

/i/ /í/ /é/ All Front Back MD Front Back MD Front Back MD MD

TD -48.27 -49.26 -0.99* -48.50 -49.07 -0.56* -47.28 -48.57 -1.29* -0.95* TB2 -39.45 -40.98 -1.53* -39.16 -39.73 -0.59* -37.39 -39.41 -2.01* -1.39*

ZZ

TB1 -24.31 -25.70 -1.39* -23.53 -23.84 -0.31 -22.42 -24.63 -2.22* -1.32* TD -43.53 -43.89 -0.37 -42.80 -43.15 -0.36* -42.99 -43.45 -0.46* -0.4* TB2 -31.40 -31.91 -0.51* -30.64 -31.03 -0.38* -30.55 -31.43 -0.88* -0.59*

BU

TB1 -22.20 -22.53 -0.34 -21.15 -21.43 -0.28* -21.63 -22.19 -0.56* -0.4*

3-syll. words: Ultrasound

Area: environment significantly affected the tongue shapes Direction: TVs in back env. (buli-val) were significantly

more retracted than in the front env. (bilivel). Env*TV: the two /i/ vowels were significantly more

advanced in the front env., and more retracted in the back env. than /é/.

MD = DFront – DBack AREA Block Vowel

Line-1 Line-2 Line-3 Line-4 Line-5 Total Same Different /í/ 1.4 2.34 2.79 2.35 1.24 2.03 734.3 1022.8 288.5

/i/ 1.34 1.97 2.19 2.12 1.03 1.73 700 994.3 294.3 1

/é/ 0.69 0.87 0.74 0.36 -0.09 0.51 686 872.4 186.4

/í/ 1.92 2.68 3.05 2.94 2.07 2.53 684.1 1209.1 525

/i/ 1.48 2.27 2.92 2.7 1.69 2.21 799.8 1245.6 445.8 2

/é/ 1.31 1.54 1.5 1.34 0.97 1.33 764.7 1058.8 294.1

Effect of environment on individual vowels

Palatal area (EMMA):/e/ > /i/ Dorso-pharyngeal area (Ultrasound): /i/ > /e/ Possible explanation: retraction of high vowels causes

flattening in the palatal area => the tongue volume re-distributes partly to the font, which decreases the degree of retraction

/í/ /é/

Tip Tip

pal. dors-phar.

pal. dors-phar.

Ultrasound imitates EMMA

The results from lines 3-5 are more similar to the EMMA results than from lines 1-2

The actual values, however, are different (different placement of the lines, separate sessions, US higher measurement error)

10mm

fixed reference points

Tongue Tip

intersection points

51

34

2

MD = DFront – DBack Block Vowel Line-1 Line-2 Line-3 Line-4 Line-5

/í/ 3.33 2.95 0.51 0.5 0.47

/i/ 2.68 2.52 0.58 0.41 0.37 1

/é/ 0.83 0.48 1 0.62 0.43

/í/ 3.79 3.36 1.24 1.14 1

/i/ 3.53 2.77 0.76 0.57 0.49 2

/é/ 1.88 1.86 1.23 1.06 0.87

Summary of trisylabic words

Transparent vowels in back harmony domains are produced further back than in front harmony domains.

Individual vowels are affected by harmonic environment to a different degree depending on the part of the tongue.

Monosyllables with EMMA

All monosyllabic stems F B MD

TD -46.67 -46.93 -0.26 TB2 -36.17 -36.81 -0.64*

ZZ

TB1 -20.35 -20.62 -0.27 TD -42.1 -42.61 -0.51** TB2 -29.58 -30.38 -0.8**

BU

TB1 -20.06 -20.6 -0.54** * p<0.05, **

p<0.001 TVs in stems selecting [+back] suffixes are more

retracted than TVs selecting [–back] suffixes.

Monosyllables with Ultrasound

Area: environment significantly affects the tongue shapes

Direction: environment not significant

Mean Area Vowel df Mean Square F Sig.

Same Diff.

All 1 1342122 8.729 .003 848.690 959.292

Summary & modeling Experiment:

all vowels, including TVs, participate articulatorily in vowel harmony.

a continuous phonetic dimension of stem-final vowel correlates with discrete phonological alternation of the suffix vowel ([±back]).

Proposal Vowel harmony is construed as blending of adjacent vowel

gestures within the limits of (perceptual) recoverability of these gestures.

Degree of tongue body retraction for the stem-final vowel is one result of this blending, and depends on quantal features of these stem-final vowels.

Retraction degree of front stem vowels is phonologized in that it is used to predict the form of the suffix that follows them.

Gestural representation of vowels

V = {CL, CD}

Onset Target Release

audio

TB2 max max [ i [ a

TD max max

1550 1600 1650 1700 1750 1800msecs Time

Monostable landscape V(x) = (x – x0)2

x0 represents the CL target value front or back (Browman & Goldstein 1995, Gafos 2002).

Model of stem-internal blending

Simplest working hypothesis: linear combination of input potentials, αF(x) + βG(x)

α, β - weights of the individual gestures

q = α/β determines the degree of articulatory retraction for F(x)

Degree of retraction R is an output parameter of blending

Model of suffix selection

x = N(x, R) + noise = – dV(x, R)/dx + noise

x is the order parameter, the constriction location of the suffix vowel

R is the control parameter, a function of the retraction degree of the preceding stem vowel

For our purposes:N(x, R) = (3R – 2) + x – x3

dV(x, R)/dx = (2 – 3R)x – x2/2 + x4/4

Transparent vowels: significant retractiona={uvul., wide}

CLa = -2í={pal.,nar.} CLí= 2

V={___, wide}CL = ??(a/e)

‘papír-nak’

V(x,R) = (2-3R)x – x2/2 + x4/4 = - x – x2/2 + x4/4

Opaque vowels: small retraction

a={uvul., wide} CLa = -2

ü={pal.,nar.} CLí= 2

V={___, wide}CL = ??(a/e)

‘parfüm-nek’

V(x,R) = (2-3R)x – x2/2 + x4/4 = .9x – x2/2 + x4/14

Intermediate retraction => bistability As control parameter is smoothly decreased below a certain

critical value, there is a qualitative change in the behavior of the system, from a one attractor landscape to a two attractor landscape (known as a bifurcation).

Noise: a small, random fluctuation force which pushes the position of the ball back and forth randomly.

‘hárem-n{a/e}k’

á={uvul., wide} CLa = -2

e={pal.,wide} CLe= 2

V={___, wide}CL0 = ??(a/e)

V(x,R) = (2-3R)x – x2/2 + x4/4 = .1x – x2/2 + x4/4

Vacillation: intermediate retraction

Support for differences in retraction Transparent vowels are those front vowels that can be maximally retracted while still successfully recovered as front.

Front rounded vowels cannot be retracted to the same degree as /i/ without losing its perceptual identity (Wood 1986).

/e/ is low and somewhat retracted: increased acoustic sensitivity to articulatory perturbations in the horizontal position of the tongue body

Multiple transparent vowels BTT stems are more likely to vacillate or take front suffixes

than BT stems This generalization is predicted by the model: given

participation of all stem vowels in VH, stem-final /i/ in mami is assumed to be more retracted than stem-final /i/ in mamicsi.

a={uvul., wide} CLa = -2

i={pal.,nar.} CLi= 2

V={___, wide}CL = ??(a/e)

i={pal.,nar.} CLi= 2

‘aszpirin-n{a/e}k’

Conclusions It was argued:

Transparent vowels participate in palatal vowel harmony by sub-phonemic retraction of the tongue body.

Generalizations for Bi, Bü, Be, and Bii stems converge: more retraction in stem-final vowel correlates with more chances for [+back] suffix.

It was modeled: Stem-internal retraction of vowels as blending of

articulatory gestures A cognitive system of suffix selection as a non-linear

dynamic system in which continuous variation in retraction affects discrete alternation in the suffixes.

And it was proposed: Phonetics-Phonology interface is a single system of two

interdependent levels with different granularities

Thank you

Contact: sbenus@cs.columbia.edu

Selected referencesBeddor, P. S., Krakow, R. A., and S. Lindemann (2001)Patterns of perceptual compensation and their

phonological consequences. In E. Hume and K. Johnson (eds.) The Role of Perceptual Phenomena in Phonology, 55-78. San Diego: Academic Press.

Benus, S. (in prep.) Transparent vowels in vowel harmony. PhD dissertation, New York UniversityFant, Gunnar (1970) Acoustic theory of speech production with calculations based on X-ray studies of

Russian articulations. The Hague: Mouton Fonagy, I. (1966). Iga es ige. Magyar Nyelv: 323-324.Gafos, A. (1999). The articulatory basis of locality in phonology. Garland. (1996 PhD. Dissertation, John

Hopkins University.)Gordon, M. (1999). The “neutral” vowels of Finnish: How neutral are they? Linguistica Uralica1: 17-21.Ladefoged, Peter (2001). A Course in Phonetics, Fourth Edition. Orlando: Harcourt.Ohala, J. (1994). Hierarchies of environments for sound variation; plus implications for “neutral”

vowels in vowel harmony. Acta Linguistica Hafniensia 27(2): 371-382.Perkell, J., M. Cohen, M. Svirsky, M. Matthies , I. Garabieta & M. Jackson (1992). Electromagnetic

midsaggital articulometer (EMMA) systems for transducing speech articulatory movements. JASA 92:3078-3096.

Stevens, K. (1989). On the Quantal Nature of Speech. Journal of Phonetics 17: 3-45.Wood, A.J.S. (1986). The Acoustic Significance of Tongue, Lip, and Larynx Maneuvers in Rounded

Palatal Vowels. JASA 80: 391-401.

Contact information:Stefan Benussb513@nyu.eduNew York University, Dept. of Linguistics, 719 Broadway, 4th floor, New York, NY 10003

Phonetic Basis of Transparency

[i] can be retracted significantly without corresponding acoustic consequences (Stevens 1972, Wood 1979).

[i] is most likely to be followed by a [+back] suffix in B-i stems. Transparent vowels are those front vowels that can be

maximally retracted while still successfully recovered as front.

I

II

III

Degree of Retraction

Front-Back Front, non-low, unrounded vowels

Length of back cavity

Low /e/: medial retraction

The acoustic output of the front unrounded low vowels is more sensitive to articulatory perturbations in the horizontal position of the tongue body than the acoustic output of the non-low vowel.

Support:Välimaa-Blum (1999), and indirectly in Stevens (1989) and Wood (1986)

/e/ is medially retracted /e/ is followed by either [+back] or [–back] suffixes.

BT vs. BTT stems

Given participation of all stem vowels in VH, stem-final /i/ in mami is assumed to be more retracted than stem-final /i/ in mamicsi.

Generalization: BT stems are more likely to trigger [+back] suffixes than BTT stems.

In sum: generalizations for Bi, Bü, Be, and Bii stems converge. More retraction in stem-final vowel correlates with more chances for [+back] suffix.

Optimality theory

How to account for phonological alternations that depend on phonetic information without compromising qualitative and cognitively essential features of discreteness and stability?

OT constraints are defined as dynamic systems that control phonetic dimensions and establish (dis)preferred values of these dimensions.

The evaluation and ranking of such constraints then determines the degree to which individual languages use phonetic details in their phonological systems.

Crucial OT conflict: Ident[front] vs. AgreeCL

Ident[front] AgreeCL

Cand. *!

Cand. **!

cand. *