Using polynomial equations to model pitch contour shape in lexical tones: an example from Green Mong

Abstract

Tone is usually described by starting height and direction of movement, but in languages with a crowded tonal space, multiple tones can have similar contours. Even in languages with few tones, details of contour shape may be used by listeners for tone identification. This study examines the effectiveness of using coefficients from polynomial equations to explore small differences in pitch contour shape and to convey this information for statistical analysis. Pitch contours for three tones from Green Mong are used as test cases. All three tones have low falling contours, but each has a distinctive phonation type. Using coefficients, large numbers of tokens can be compared to find consistencies in contour shape within tone categories and differences across categories. Discriminant analyses using the coefficients as predictor variables show that all three tones can be identified at levels well above chance using pitch contour shape alone. Quadratic coefficients improve classification rates over linear coefficients. The results also suggest that phonation type plays the largest role in identifying creaky tones in Green Mong. This technique should prove useful for analysis and synthesis of pitch contours. It seems particularly useful for examining details of contour shape in languages with a crowded tonal space.

Using Functional Data Analysis for investigating multidimensional dynamic phonetic contrasts

“…Previous studies of dynamic features have attempted to avoid the need for converting contours into a small set of discrete measurements. Andruski and Costello (2004), Grabe et al (2007), Aguilar (1999) and fit polynomial functions to the sampled trajectories and use the coefficients of these polynomials as numerical data that can be submitted to statistical analysis. Aguilar (1999) hypothesised and verified that the curvature of F 1 and F 2 trajectories would differ between diphthong and hiatus.…”

“…Such details in the f 0 shape may be irrelevant in some context, but crucial in others (Dombrowski & Niebuhr, 2010). An alternative method to code pitch, formant or intensity contours consists in using the coefficients from a polynomial fit (Andruski & Costello, 2004;Grabe, Kochanski, & Coleman, 2007). This may be a good solution for short curves with a single extremum, but it leaves us with the burden of interpreting the coefficients of the polynomial when fitting more complex trajectories.…”

Effects of talker-to-listener distance on tone

“…Polynomial equations were used in Andruski and Costello (2004) to model three lexical tones in Green Mong (Hmong) with different phonation types. The researchers successfully classified tones with similar low-falling pitch contours using these coefficients.…”

Nuclear Pitch Accents in Majorcan Catalan Declaratives: Phonology, Phonetics, Diachrony

“…Quadratic polynomial equations are used to holistically describe curvilinear functions and are therefore applicable to curvilinear pitch contours. A first step in the direction of studying pitch curves with the use of polynomial equations, within the linguistic-phonetic literature, was taken in Andruski & Costello (2004). Andruski & Costello (2004) studied three Green Mong tones that are very similar in shape.…”

“…A first step in the direction of studying pitch curves with the use of polynomial equations, within the linguistic-phonetic literature, was taken in Andruski & Costello (2004). Andruski & Costello (2004) studied three Green Mong tones that are very similar in shape. Among the seven tones of Green Mong, three display a falling configuration.…”