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Singing voice is a human quality that requires the precise coordination of numerous kinetic functions and results in a perceptually variable auditory outcome. The use of multi-sensor systems can facilitate the study of correlations between the vocal mechanism kinetic functions and the voice output. This is directly relevant to vocal education, rehabilitation, and prevention of vocal health issues in educators; professionals; and students of singing, music, and acting. In this work, we present the initial design of a modular multi-sensor system for singing voice analysis, and describe its first assessment experiment on the 'vocal breathiness' qualitative characteristic. A system case study with two professional singers was conducted, utilizing signals from four sensors. Participants sung a protocol of vocal trials in various degrees of intended vocal breathiness. Their (i) vocal output, (ii) phonatory function, and (iii) respiratory behavior-per-condition were recorded through a condenser microphone (CM), an Electroglottograph (EGG), and thoracic and abdominal respiratory effort transducers (RET), respectively. Participants' individual respiratory management strategies were studied through qualitative analysis of RET data. Microphone audio samples breathiness degree was rated perceptually, and correlation analysis was performed between sample ratings and parameters extracted from CM and EGG data. Smoothed Cepstral Peak Prominence (CPPS) and vocal folds' Open Quotient (OQ), as computed with the Howard method (HOQ), demonstrated the higher correlation coefficients, when analyzed individually. DECOM method-computed OQ (DOQ) was also examined. Interestingly, the correlation coefficient of pitch difference between estimates from CM and EGG signals appeared to be (based on the Pearson correlation coefficient) statistically insignificant (a result that warrants investigation in larger populations). The study of multi-variate models revealed even higher correlation coefficients. Models studied were the Acoustic Breathiness Index (ABI) and the proposed multiple regression model CDH (CPPS, DOQ, and HOQ), which was attempted in order to combine analysis results from microphone and EGG signals. The model combination of ABI and the proposed CDH appeared to yield the highest correlation with perceptual breathiness ratings. Study results suggest potential for the use of a completed system version in vocal pedagogy and research, as the case study indicated system practicality, a number of pertinent correlations, and introduced topics with further research possibilities.