# Acoustic and Aerodynamic Coupling during
## 4 Conclusions  
The aim of this study was to examine the influence of the VT on the phonatory process and to analyze if the influence of a geometry simplification can also by neglected considering the flow field in the VT. Based on the MRI-data of six professional tenors, 3D-printed replicas of the VT with realistic and simplified geometry were generated for each subject. The latter are simplified in terms of a straightened centerline and a conversion into a circular cross section based on the subjects' area functions. Additionally, we computed an averaged VT replica based on the simplified geometries to reduce effects due to individual characteristics and analyzed all VT replicas in an experimental setup including auto-oscillating vocal folds. The results of the aerodynamical investigations show that the inclusion of the VT leads to a reduced phonation threshold pressure in combination with a decreased flow rate. This confirmed the already reported facilitation of the vocal fold oscillation by the VT [32; 40]. The results of the acoustical investigation show that both the realistic and the simplified VT replicas reproduce the typical formant structure of the human VT. However, the broadband sound level is changed for the simplified VT. We assume that this is due to a change of the flow field in the VT and the resulting broadband sound due to the simplification of the geometry. This is contrary to the results of previous studies with purely acoustically excited VT models that did not include oscillating vocal folds and reported a negligible effect due to the simplification [18; 52]. The SPL spectrum of the mean VT reproduces the basic characteristics of the individual simplified VT replicas. The deviation of the formant frequencies of the mean VT replica from the average subjects' formant frequencies exhibits a mean deviation of 8%. Appearing deviations from the individuals spectra in terms of the broadband sound level are attributed to the differences between the subjects in the VT constriction in the region of the uvula. Hence, averaging individual tenor VT geometries preserves the basic formant distribution and reduces individual acoustic characteristics. However,  
Figure 10: The formant chart as proposed by [PERSON] and [PERSON] [56], shows the formant frequencies for the mean VT, which is based on the MRI-data of six professional tenors. In addition, formant frequencies of the individual tenors are shown, as detected by [PERSON] et al. [34] in the audio recordings. according to previous literature, this only holds for VT shapes singing in the falsetto register, as used here [17]. The comparison of the occurring formant frequencies with the subjects' formant frequencies shows that the agreement is better for the realistic VT replicas than for the simplified VT replicas. Occurring deviations of the formant frequencies, which exhibit an average of 12%, are attributed to the rigid walls of the replica. However, as a vowel is not characterized by discrete frequencies, but by frequency bands, the spectral properties are preserved for both the realistic and the simplified VT replicas. The comparison of the formant frequencies of the mean VT with subjects' formant frequencies shows that the formant characteristics were maintained despite the averaging. This confirms that by averaging the simplified individual VT geometries, a VT model is created that preserves the essential vowel characteristics of the VT without exhibiting strong individual characteristics. The influence of the VT on the oscillation of the vocal folds in terms of volume flow rate and subglottal pressure reduction shows that the VT not only filters the basic sound generated by the vocal fold oscillation, but also influences the generation of the basic sound itself. This shows that the already reported coupling [2; 28] between the VT and the vocal folds can also be reproduced in an experimental setup. Hence, the aim for future work is to investigate potential nonlinear coupling effects between VT and vocal folds.