## 1 Introduction  
This study was motivated by a desire to eventually control a voice simulator with inputs related to perception. Aside from vowel perception, a sound can be represented in terms of pitch, loudness, and timbre [1]. Timbre is the quality of the sound that differentiates one sound from another when pitch and loudness are the same [2]. In a first attempt, it can be divided into two components, brightness and roughness [3]. Acoustically, the four perceptual features can be quantified with fundamental frequency, sound pressure level, spectral content, and aperiodicity. Neglecting additive noise from air turbulence (breathiness or aspiration in a vowel), it is believed that these four perceptual or acoustic features contain many of the characteristics of a given vowel sound [4]. Quantifying fundamental frequency and sound intensity is well described in the literature. The fundamental frequency of a sound can be measured directly from the oral pressure signal using standard algorithms such as autocorrelation, zero-crossing rate or with more advanced algorithms such as the Yin algorithm [5] or SWIPE' [6]. Sound pressure level, the logarithmic expression of relative sound intensity, can be computed from the radiated pressure signal according to acoustic standards [7]. Brightness is much more abstract and has no agreed-upon standards for calculation on the acoustic signal. Some acoustic features that represent brightness are the total harmonic distortion [8] and the normalized spectral centroid [2; 9]. Roughness also has no standard definition in the literature other than it being attributed to the component of the sound that is not regular (periodic) [10; 11]. However, even periodic sounds can be perceived as rough if multiple harmonics are contained in a critical band [12]. Measures of aperiodicity roughness are jitter and shimmer [13], while a measure of lack of roughness is the cepstral peak prominence (CPP) [14; 15; 16]. Non-linear dynamic metrics such as correlation dimension [17; 18] and various entropy measures [18; 19] are also being studied to accurately quantify aperiodicity. In this study, roughness is considered to be related to the power in the sound that is not part of the fundamental and its harmonic series. Subharmonics and sideband frequencies are included in the quantification of roughness. If the vocal tract configuration (vowel) is kept constant during phonation, all variations in the four perceptual features depend on changes in the vocal source, but the interaction with the vocal tract may vary with fundamental frequency [20]. The laryngeal configuration, and specifically the vocal fold posture, depend on the laryngeal muscle activations [21]. Vocal fold oscillation then depends on the amount of lung pressure available to set the vocal folds into motion. In this study, we focused on the interrelationship between the throarytenoid (TA) and cricothyroid (CT) muscle activations to achieve these four specific physical attributes of a sound as well as vocal fold posturing (setting) features. While our computational model includes postural mechanics derived from five intrinsic muscles (lateral cricoarytenoid (LCA), interarytenoid (IA), and posterior cricoarytenoid (PCA) in addition to CT and TA), preliminary results showed that random combinations of five muscle activations and lung pressure produced too complex relationships to comprehend easily. Hence, a heuristic approach was taken to constrain the LCA, IA, PCA, and lung pressure (P\({}_{\text{L}}\)) for the purpose of targeting self-sustained oscillation. Future studies with computational learning strategies will address the more intricate relations with all the muscle activations. The vocal tract configuration remained constant throughout the phonations (an /\(\alpha\)/ vowel). The posturing variables included are vocal fold length (L) and tissue fiber stress in the superficial layer of the lamina propria (\(\sigma_{SLLP}\)), ligament (\(\sigma_{llg}\)), and TA muscle (\(\sigma_{mus}\)).