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	PROBLEMS OF SINGER’S FORMANT MATHEMATICAL MODELING Radolf, Vojtěch Theme of the paper belongs into the field of acoustics in biomechanics. In co-operation with foniatric departments in Czech Republic the spatial and then simplified geometric models of acoustic human vocal cavities were created. Using various mathematical models the dynamic characteristics of the models were finding out. One of the objectives of the project is to investigate singer's formant cluster. The mathematical models are designed to find such configuration of acoustic cavities, respecting real physiological limits, which leads to excitation of predefined acoustic resonances. It is so called formant tuning. Using these models the appropriate geometry for the singer's formant cluster formation were searching for. Detailed record
	Optimization of resonance properties of the human vocal tract by variation of cross-section and length of acoustic elements Radolf, Vojtěch Theme of the paper is focused on optimization possibilities of geometrical form of human vocal tract. An optimization process is designed to find such configuration of acoustic cavities, respecting real physiological limits, which leads to excitation of predefined acoustic resonance. Especially frequency domain between the third and the fifth formant is important for voice timbre, namely for singing voice ('the singer's formant'). Two various 1D optimization methods, computing time and accuracy of solution are compared. The first method is a general procedure of numerical searching for the minimum of objection function, the second is an energetic iterative procedure using non-dimensional sensitivity functions. Both length and cross-section area of conic elements are varied. Detailed record
	Možnosti ladění a optimalizace akustických rezonančních vlastností vokálního traktu člověka Radolf, Vojtěch ; Vampola, T. The paper deals with optimization process finding such geometrical form of acoustical cavities of the human supraglottal spaces which leads to excitation of predefined acousic resonance, especially between a domain of the third and the fifth formant. The problem is solved by the transfer matrix method using conic acoustic elements for the vocal tract modelling and numerical method of searching a minimum of a goal function of several variables. The results should help to obtain a physical background for voice rehabilitation, for teaching of opera singers at musical facuoties and for better understanding of biomechanics of voice production. Detailed record

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