Seiji Adachi

A minimal model explaining intonation anomaly, or pitch sharpening, which can sometimes be found in baroque flutes, recorders, shakuhachis etc. played with cross-fingering, is presented. In this model, two bores above and below an open tone hole are coupled through the hole. This coupled system has two resonance frequencies ! AE , which are respectively higher and lower than those of the upper and lower bores ! U and ! L excited independently. The ! AE differ even if ! U ¼ ! L. The normal effect of cross-fingering, i.e., pitch flattening, corresponds to excitation of the ! À-mode, which occurs when ! L ' ! U and the admittance peak of the ! À-mode is higher than or as high as that of the ! þ-mode. Excitation of the ! þ-mode yields intonation anomaly. This occurs when ! L / ! U and the peak of the ! þ-mode becomes sufficiently high. With an extended model having three degrees of freedom, pitch bending of the recorder played with cross-fingering in the second register has been reasonably explained.

Cross-fingering is a technique of playing woodwind instruments in which one or more tone holes are closed below the first open hole. It usually yields a pitch lower than that played with normal fingering. There is, however, an exception resulting in pitch sharpening. This paper proposes understanding these pitch bending phenomena in a unified manner with a model of two coupled mechanical oscillators, each of which represents a bore above or below the open hole. This coupled system has two resonance frequencies ω ±, which are respectively higher and lower than those of the upper and lower bores ω U and ω L. The ω ± differ even if ω U = ω L. The normal effect of cross-fingering, i.e., pitch flattening, corresponds to excitation of the ω −-mode, which occurs when ω L ≥ ω U and the admittance peak of the ω −-mode is higher than or as high as that of the ω +-mode. Excitation of the ω +-mode yields pitch sharpening. This occurs when ω L ≤ ω U and the peak of the ω +-mode becomes sufficiently high. With an extended model having three degrees of freedom, pitch bending of the recorder played with cross-fingering in the second register can also be successfully explained.

The hypopharyngeal cavities are the narrow, complex parts of the lower vocal tract that include the supraglottal laryngeal cavity and bilateral cavities of the piriform fossa. These small regions exhibit rather strong acoustic influence on vowel spectra in the higher frequencies and contribute to determining voice quality and speaker characteristics. The laryngeal cavity functions nearly as a Helmholtz resonator to generate an extra formant in the vicinity of 3 kHz, and the piriform fossa forms a pair of side‐branches of the vocal tract to cause spectral zeros in the vicinity of 4‐5 kHz. Vocal‐tract models without employing these acoustic effects can hardly simulate natural‐sounding voices of a particular speaker. Therefore, realistic acoustic models of vowel production must include the three functional components: glottal source sounds, hypopharyngeal‐cavity coupling, and resonance of the vocal‐tract proper. This presentation demonstrates the results from acoustic experiments on solid vocal‐tract models and computer simulations of the cavities' effects based on our MRI‐based visualization of the vocal tract. A possible control for singingvoice qualities will be discussed based on the three‐component model.