# How Much Does the Dynamic F0 Curve Affect the Expression of Emotion in Utterances?
## 1 Introduction  
The modulation of vocal elements, such as pitch, loudness, duration, and voice quality, across syllables in an utterance conveys both linguistic information--such as prominence and prosodic phrasing--and non-linguistic information, notably the speaker's emotional state [1]. Emotional states are psychological conditions indicated by neurophysiological changes, being typically associated with thoughts, feelings, and behavioral responses [2]. These states are communicated not only through facial expressions but also through vocal expressions in both linguistic and paralinguistic contexts [3]. When speaking, individuals inherently transmit their emotional status alongside linguistic content. Two prevailing theories attempt to explain how emotions influence behavior and expression: the dimensional theory and the discrete emotion theory [4]. The dimensional theory, proposed by [5] and further developed by [6], suggests that emotionscan be distinguished along two primary dimensions: valence (the positivity or negativity of the emotion) and arousal (the intensity of the emotion). According to this perspective, basic emotions are defined within this two-dimensional emotional space. In contrast, the discrete emotion theory, initially devised by [7] and extensively developed by [2], posits that there are specific biologically and neurologically distinct basic emotions. [PERSON]'s research supports the view that emotions are discrete, measurable, and physiologically distinct, and certain emotions are universally recognized across cultures. These basic discrete emotions typically include happiness, sadness, anger, fear, disgust, and surprise. Acoustic features play a critical role in the analysis and recognition of emotional speech [4; 8]. Features such as the fundamental frequency (F0), variability (pitch), voice intensity (energy), and Mel-Frequency Cepstral Coefficients (MFCCs) are commonly used in automatic emotion recognition tasks. MFCCs capture the human auditory frequency response and represent the signal more effectively than raw frequency bands [9; 10; 11]. However, some studies have reported poor emotion classification results using MFCCs, possibly due to the embedded pitch filtering during cepstral analysis that may obscure important pitch-related emotional cues [8]. Despite the availability of rich acoustic data, challenges remain in accurately classifying emotions based on speech. This is partly due to the complexity of emotional expression and the limitations of analytical methods that often simplify dynamic vocal data, potentially overlooking intricate patterns indicative of specific emotions [12]. For instance, previous research suggests that some acoustic features are associated with general characteristics of emotion rather than specific emotional states, supporting the idea that grouping emotions by activation levels (e.g., high-activation emotions like anger and joy) can improve recognition performance [13; 14]. However, distinguishing between emotions within similar activation levels remains challenging. Intonation, particularly pitch contour patterns, has been recognized as important for expressing emotional states [15; 16; 17; 18; 19]. Previous works [15; 16; 17; 18; 19] have made significant contributions to enhancing our understanding of the role of F0 in emotional speech. However, previous studies often used simplistic intonation parameters, which may contribute to lower classification rates of emotional types based on acoustic features [8]. Simplifying dynamic data can reduce the data size and make traditional statistical methods easier to apply, but it may also lead to the loss of potentially interesting patterns [20]. Some studies, such as [15; 19], have modeled F0 dynamics in emotional speech. But the previous approaches had a limitation in allowing us to evaluate not only the general trends of F0 contours but also their interaction with speaker-specific variability and temporal effects.