# Machine Learning with Evolutionary Parameter Tuning for Singing Registers Classification
## 1 Introduction  
Behind the apparent simplicity of the sound of the human voice lies an intricate interplay of resonances that both mold and define the unique quality of each voice. According to [1], the human phonation system is made up of three parts: (I) the respiratory system, (II) the pair of vocal folds, and (III) a system of cavities, i.e., the vocal tract. Since the respiratory system performs the function of a compressor by compressing the air stored in the lungs, only the last two mentioned parts contribute directly to the formation of thevocal timbre. Indeed, the pair of vocal folds are responsible for generating sound through vibrations that interrupt the airflow from the lungs in a sequence of air pulses. The vocal tract includes the oral and nasal cavities, the pharynx, and the larynx, which contains the vocal folds. In particular, the larynx is divided into glottis, supraglottis, and subglottis. Moreover, the vocal tract plays the role of a resonance chamber or filter that molds the sound generated by the vocal folds. Figure 1 illustrates the latter voice production process in detail. The air coming from the lungs provides the energy needed for the vocal folds to vibrate. This periodic vibration generates a spectrum of fundamental and harmonic frequencies. The vocal tract then filters the excitation signal produced by the vocal folds. The interaction between the spectrum of the sound source and the transfer function of the vocal tract produces the spectrum of the radiated sound, which is the sound actually perceived by the listener (speech signal). The relative amplitudes of the different frequencies in the radiated spectrum determine the acoustic characteristics of the sound, such as timbre and intensity. Relying on the above-described process, it is possible to adjust the formation of vocal acoustics. Indeed, the act of altering the shape of the vocal tract, known as articulation, makes it possible to control the formants of speech since the movement of the articulators can modify the acoustic resonances of the vocal tract (with articulators, it is referred to the structures used to organize the shape of the vocal tract in different ways, namely: pharynx, velum, tongue parts, and lips). Similarly, specific kind of adjustments can be made by activating the laryngeal muscles, which, in a way, can control the geometry and mechanical properties of the vocal folds, thus making it possible to control or modify the voice itself [1; 3]. Figure 1: The source-filter model of speech production consists of the glottis as the excitation source and the vocal tract (nasal and oral cavities) as the filter. Furthermore, the temporal and spectral representations of the source, vocal tract, and resulting speech signal are represented. Reprinted from [PERSON] et al. [2], Copyright (2023), with permission from Elsevier. Vocal folds, in turn, exhibit a non-linear, anisotropic shape and viscoelastic behavior. In particular, the stress-strain curve shown in Figure 2 illustrates the non-linear mechanical behavior typical of the anteroposterior direction of vocal folds. The above-reported behavior provides a means for regulating the stiffness and tension of the vocal folds by lengthening or shortening them, which plays an important role in controlling the fundamental frequency (\(f_{0}\)) or pitch of voice production. In particular, the two laryngeal muscles involved in regulating the length of the vocal folds are the cricothyroid muscle (CT) and the throarytenoid muscle (TA), whose activation also alters the shape of the medial surface of the vocal folds and the geometry of the glottal canal [3]. In addition, [PERSON] and [PERSON] [4] stated that the vocal folds are adducted at their posterior portion by the inter-arytenoid muscle (IA), abducted at their posterior portion by the posterior cricoarytenoid muscle (PCA), and adducted at their posterior portion by the lateral cricoarytenoid muscle (LCA), which also controls \(f_{0}\), intensity, and register. Figure 3 shows all the latter muscles involved in voice production.