Organizing syllables into groups - Evidence from F0 and duration patterns in Mandarin

Abstract

In this study we investigated grouping-related F₀ patterns in Mandarin by examining the effect of syllable position in a group while controlling for tone, speaking mode, number of syllables in a group, and group position in a sentence. We analyzed syllable duration, F₀ displacement, ratio of peak velocity to F₀ displacement (v_p/d ratio) and shape of F₀ velocity profile (parameter C) in sequences of Rising, Falling and High tones. Results showed that syllable duration had the most consistent grouping-related patterns. In a short phrase of 1-4 syllables, duration is longest in the final position, second longest in the initial position, and shortest in the medial positions. In Rising and Falling tone sequences, syllable duration was positively related to F₀ displacement, but negatively related to v_p/d ratio. Sequences consisting of only the High tone, however, showed no duration-matching F₀ variations. Modeling simulations with a second-order linear system showed that duration variations alone could generate F₀ displacement and v_p/d ratio variations comparable to those in actual data. We interpret the results as evidence that grouping is encoded directly by syllable duration, while the corresponding variations in F₀ displacement, v_p/d ratio and velocity profile are the consequences of duration control.

Keywords: F0 contour; affinity index; duration; peak velocity; second-order linear system; stiffness; stress; syllable grouping; vp/d ratio.

Fig. 1

MeanF₀ curves under the effects of speaking mode and articulatory pressure. Thick line — Mean F₀ curves of all-R, all-F, RF and FR sentences in lecture mode. Thin line — Mean F₀ curves in conversation mode.

Fig. 2

Effects of location in sentence and phrase length on Mean F₀ curves of all-R and all-F sequences. Thin line — sentence final; thick line — non-final.

Fig. 3

Various measures of all-R and all-F sequences as a function of phrase length and tone. (a) Mean up-down cycle duration. (b) Mean up-down cycle duration of the initial syllable. (c) Mean up-down cycle duration of the final syllable. (d) Mean v_p/d ratio. (e) Mean C. (f) Mean maxF₀

Fig. 4

(a) Mean up-down cycle duration at different syllable positions with different phrase lengths. (b) Corresponding mean F₀ displacement. (c) Corresponding mean v_p/d ratio.

Fig. 5

Simple linear regressions of F₀ peak velocity over F₀ displacement for different syllable positions: initial, medial 1 (2nd syllable of 3- and 4-syllable sequences), medial 2 and final (final syllable of all sequences, including monosyllables) positions.

Fig. 6

Scatter plots of F₀ displacement (a), mean v_p/d ratio (b) and mean C (c) as functions of up-down cycle duration.

Fig. 7

Effects of regrouping on Mean F₀ curves of all-R and all-F sequences. Thick line — AB+CD sequences, with y-axis on the left; thin line — A+BCD sequences, with y-axis on the right.

Fig. 8

Up-down cycle duration shown in Figure 4a (white bars), minimum time needed for making the amount of F₀ displacement at each syllable position shown in Figure 4b, computed with equations [3] and [4] (grey bars), and the difference between the two (measured – predicted) (dark bars). The separate bar clusters show values for the 1–4 syllable sequences, respectively.

Fig. 9

(a) Simulated movement trajectories based on a critically damped second-order linear system defined by equation [5]. See text for details about the parameters used. (b) Velocity profiles of the trajectories in (a). (c) Simulated displacements as a function of duration at different stiffness levels indicated by ω_n. (d) Simulated v_p/d ratios as a function of duration at different stiffness levels. (e) Simulated parameter C (peak-velocity/average-velocity) as a function of duration at different stiffness levels.