Tuesday, August 26, 14. Articulatory Phonology

Transcription

1 Articulatory Phonology

2 Problem: Two Incompatible Descriptions of Speech Phonological sequence of discrete symbols from a small inventory that recombine to form different words Physical continuous, context-dependent variation in many articulatory, aerodynamic, acoustic parameters What is the relation between the two?

3 Combinatoric Units Discrete Context-independent Time-invariant Low Dimensionality Physical Measurements Continuous Context-dependent Time-varying High Dimensionality

4 Responses Cognitive vs. Physical Hockett s Easter Egg analogy: no systematic relation Mutual reciprocity: Cognitive and physical structures of speech constrain each other. Hallmark of self-organized systems Cognitive and physical properties of systems cannot in general be satisfactorily described independently of one another. Feature Theory (Jakobson, Halle, Stevens) First serious attempt to unify these descriptions Same features employed in both domains But problems remain e.g. generalizations of articulatory timing and its variation

5 Self-organization

6 Evidence for mutual reciprocity in speech? Local, microscopic constraints on global pattern: classical phonetic explanations for sound patterns Ohala Stop systems often missing [g] Rarity of voiced fricatives Solé incompatibility of fricative-trill sequences

7 Evidence for mutual reciprocity in speech? Global constraints on local, microscopic interactions V-V coarticulation (Manuel) Shona and (Southern) Sotho are related Bantu languages, spoken in the same area in Zimbabwe. Shona has 5 vowels, Sotho has 7. Sotho exhibits more constrained V-V coarticulation Denser vowel space inhibits variability in vowel production

8 Evidence for mutual reciprocity in speech? Global constraints on local, microscopic interactions: Variability in coronal stop production System-related constraints on tongue tip position Distribution of Tongue-Tip constriction locations in running speech in Hindi vs. English

9 Hindi English TTx TTx mm from teeth mm from teeth

10 Self-organization: BZ Reaction Text 5

11 Self-organization: Termite nests 9

12 Self-organization: Termite nests 10

13 Self-organization: Termite nests 11

14 Self-organization Simple local rules Emergence of macroscopic structure No architect, no blueprint Mutual reciprocity

15 Key components of AP approach to phonological-physical Dynamical representation Articulatory representation Synergy Coordination and Overlap

16 Dynamical Representation I Dynamical systems originated (Newton, Leibnitz) to describe the motion of objects. I But today, they are widely employed to understand (and model) an enormous variety of phenomena. I I I I I I I population growth and decay weather neural changes during learning locomotion chemical reactions economic growth and decline brain circuits

17 What is a dynamical system? I Equation (or set of equations) that quantitatively describes the change in something over time. I Two parts: 1. State of the system (quantity whose change is being described) I amount of money in the bank I number of individuals in a population I volume of water in a bathtub I activation level of a neuron I the concentration of Sodium in a solution I the speed of tra conthe101 I the temperature in a room 2. Rule for how the state changes, depending on the current state. Current state predicts the state at the next instant in time. I System is constant, even while state is changing.

18 Example Dynamical System I State: Amount of water in bathtub (x) I Rule for change: Change in x = 1 2 x Time H Water in bathtub Time

19 Example Dynamical System I Alternative rule for change: I Rule for change: Change in x = Water in bathtub How do you know that this isn t right for emptying bathtub? Time

20 Initial Conditions I Suppose the bathtub has 40 units of water at time 1. I Same rule for change: Change in x = 1 2 x Water in bathtub Time Same rule for change produces very di erent functions over time.

21 Goal or Point Attractor I With this rule for change, all initial conditions wind up at 0. I We can call this a goal of this system. 100 Water in Bathtub Time

22 More initial Conditions I Same rule for change: Change in x = 1 2 x I Suppose the state being modeled is the amount of money in your bank account. I Balance can be positive or negative I Suppose you begin with a negative balance of $ Money in Bank Time

23 Goal I Same rule for change: Change in x = 1 2 x I All initial conditions, positive, negative, zero, result in the same goal value, Money in Bank Time

24 Setting the Goal I Suppose we are trying to model a system in which the goal is not 0? I Keep your bank account at $40. I Production of segment like /s/, in which the tongue tip does not quite touch the alveolar ridge. I Alternate rule for change: Change in x = 1 2 x + 20 Time x change Money in Bank Time

25 Setting the Goal I The new goal will also be reached from any initial condition, positive or negative. I Rule for change: Change in x = 1 2 x Money in Bank Time

26 Rate of Goal Attainment I The rate at which a system approaches its goal can be adjusted by changing the 1 2 to a di erent fraction, e.g.,.25,.75,.95. I This parameter is sometimes referred to as k. I Rule for change: Change in x = kx I The higher the value of k, the faster the goal is attained. Money in Bank Time

27 Bifurcations What happens when k<1? Qualitative change in behavior k= 1.04 k=.95

28 When k < 1, system has an attractor (goal) at 0. All initial conditions result in P = 0. Even if the system is perturbed, end state is the same. When k > 1, no attractor System grows indefinitely Effect of initial conditions (or perturbations) is always there. When k = 1 Fixed point Neutral stability Dependence on initial conditions and perturbations.

29 Sequence of Goal Values I You set the thermostat to 70, the a visitor arrives, who switches the setting to 60. I Rule for change: Change in x = 1 2 x + 35 then Change in x = 1 2 x Temperature Time

30 Towards a solution to our problem... Phonological units as dynamical systems (gestures). Dynamical system is time-invariant, but lawfully produces timevarying state. Change in state is continuous, but change in system is discrete. System is context independent, but gives rise to contextdependent trajectories of the state variable, as a function of initial conditions. Continuous change to parameters can result in discrete change (bifurcation) in system behavior.

31 Example of context dependence 30 /AA/ sod 30 /D/ mm 0 mm /IY/ seed /D/ mm 0 mm

32 Goal-seeking and articulator motion for /d/ I A dynamical system with a goal of 0 can be used to model the distance of the tongue tip from the alveolar ridge over time (time-function). I The same dynamical system will produce the di erent time functions we observe in seed and sod. Change in x = 1 4 x Water in Bathtub Time Distance of TT from alveolar ridge (mm) Time

33 Other initial conditions Distance of TT from alveolar ridge (mm) AA AE IY IH Time

34 Degrees of freedom: Tasks, articulators, redundancy, synergy I How do we use dynamical systems to simulate articulator motion? I Each consonant and vowel can be thought of as a (motor) task to achieve a goal for a particular state variable. I What might be relevant goals and state variables for consonant and vowel tasks? I The change over time of the state can be controlled by a dynamical system with a goal and a sti ness. I The changing state causes changes in the articulators of the vocal tract that can produce those state changes.

35 Degrees of freedom: Tasks, articulators, redundancy, synergy I Performance of any skilled motor task requires cooperation of several independently moveable body parts, which will call articulators. I e.g., reaching for an object on a table I There is large (possibly infinite) set of articulator postures that will achieve the task. This is sometimes called redundancy. I When we learn to perform a task, we learn a pattern of inter-dependency among the articulators specific to the task. This is called a synergy or a coordinative structure. I The synergy allows the task to be performed in di erent ways in di erent environmental contexts. I Di erent actors learn to tune the synergy di erently, resulting in di erent articulator movements for the same task,

36 Harnessing Redundancy

37 Synergies in speech I Tasks in speech are constrictions that form the consonants and vowels. I For example a task that is in common to /p,b,m/ is the closure of the lips. I What articulators are part of the synergy for a lip closure? I I I jaw lower lip upper lip I Di erent people learn to tune the synergy di erently: They employ di erent relative contributions of these articulators. I Relative contributions di er when some perturbing event occur in the world. I Relative contributions di er when the task is produced in the context of other tasks.

38 Speaker differences in Lip Closure synergies back mm 0 mm Speaker A Speaker B UL LL Jaw LA ULy LLy MNIy LA Time (ms) ULy LLy MNIy LA Time (ms)

39 Speaker differences in Lip Closure synergies ship mm 0 mm Speaker A Speaker B UL LL Jaw LA Time (ms) Time (ms)

40 Compensation for perturbation I What happens when the jaw is suddenly perturbed during a lip closure task? I Compensation. Upperlipand lower compensate for jaw perturbation and goal is achieved. I Speed. Compensatory action is extremely fast (20 ms or so). This implicates direct inter-articulator cooperation. I Task-specificity. Ifthesubject is producing /z/, instead of /b/, response is not seen. Mutual dependency among articulators reduces the degrees of freedom

41 Task performance in different I The relative contribution of the articulators in the synergy may di er when the same task is produced in di erent contexts in which one of the articulators may be required for some other task. I I I contexts For example, lip closure in back vs. been. Jaw is recruited to be low in back because of the low vowel (AE) and high in been because of high vowel (IH), More lower lip lowering emerges in back than in been. 18 Upper Lip Height (mm) back been Time in milliseconds

42 Task performance in different contexts We have evidence for constriction invariability in live speech production, without jaw pullers or lip paddles. Context can act as a perturbation. Data /svd/ by 26 speakers of AE (XRMB), 10 V. Measures: TTCD, Tip Height, and Tip Max Velocity as a function of previous V jaw height.

43 Hypotheses For the final /d/ of /svd/, the task is a value of TTCD that is 0 (or negative). This can be achieved with the tongue tip and jaw synergy. The height of the previous vowel can act as a perturbation on the jaw: if the previous vowel is low, the jaw is down, pulling down on the jaw during the /d/, requiring the tongue tip to act independently of the jaw to achieve 0 closure. If the task is achieved, TTCD and TT height should not depend on previous V jaw, but TT upward velocity should increase for low previous vowels.

44 Results