# How Much Does the Dynamic F0 Curve Affect the Expression of Emotion in Utterances?
## 4 Discussion
### Discrepancies with Previous Literature
This elevated pitch in sadness may convey a sense of emotional weight or poignancy, distinguishing it from the more neutral or relaxed state of calm. While both emotions are low in arousal, sadness typically carries a negative valence, whereas calm is generally neutral or slightly positive. This difference in emotional valence might be subtly reflected in the acoustic properties, such as the slight elevation in pitch for sadness. As illustrated in Figure 8, the left panel displays the fitted pitch contours for calm (red line) and sadness (blue line) over 500 samples. Both contours demonstrate a similar downward trend, but the pitch level for sadness remains consistently higher than that of calm. The shaded areas represent the confidence intervals excluding random effects, showing the reliability of these observations. The right panel of Figure 8 presents the estimated difference in the F0 between the calm and sad conditions, with the shaded area indicating the confidence interval of the difference. The fact that the confidence interval does not cross zero throughout the entire time window (0 to 525 samples) suggests that the difference in pitch level between calm and sadness is statistically significant across the utterance. These findings highlight the similarities between calm and sadness in terms of pitch contour shape: both exhibit a downward slope indicative of low arousal. However, the differences in the overall pitch level provide an acoustic cue for distinguishing between the two emotions. The higher pitch in sadness may reflect a slight increase in emotional intensity or a different emotional valence compared to calm. In our study, the pitch contours of happiness and surprise display distinct characteristics that aid in differentiating these emotions acoustically. The pitch contour of happiness begins at a mid-level pitch and exhibits a steeper downward slope compared to other emotions. This pattern aligns with previous research suggesting that happiness involves increased pitch variability and dynamic intonation patterns, reflecting a cheerful and expressive vocal demeanor. In contrast, the pitch contour of surprise is notably distinctive. As illustrated in Figure 9, surprise shows significant fluctuation throughout the utterance and features an elevated pitch towards the end, surpassing even other high-activation emotions like anger and fear. This elevation in pitch at the conclusion of the utterance may mirror the suddenness and heightened intensity typically associated with surprise. The dynamic rise in pitch could be indicative of an exclamatory expression, which is characteristic of how surprise is often vocally manifested. The left panel of Figure 9 demonstrates the fitted pitch contours for both emotions. While both happiness and surprise start at similar pitch levels, their trajectories diverge significantly over time. Happiness maintains a relatively steady pitch before descending sharply, whereas surprise exhibits considerable fluctuation and culminates in a pronounced pitch increase at the end. The right panel of Figure 9 highlights the estimated difference in the F0 between the two emotions. The areas where the confidence interval does not cross zero indicate time windows where the difference in pitch is statistically significant. These differences suggest that listeners may rely on the distinctive pitch patterns, particularly the end-of-utterance elevation in surprise, to differentiate it from happiness. Figure 8: Comparison of pitch contours between calm (red) and sad (blue) speech samples. The **left panel** displays the fitted pitch values in semitones over 500 samples, with shaded areas representing the confidence intervals, excluding random effects. The **right panel** shows the estimated difference in the F0 (fundamental frequency) between the calm and sad conditions, with the shaded area indicating the confidence interval of the difference. Figure 9: Comparison of pitch contours between surprise (red) and happy (blue) speech samples.