## 4 Conclusions  
In this work, we analysed the relevance of higher order modes in the 3D finite element synthesis of vowels [\(\alpha\)], [i], and [u], considering different glottal source excitations. It was shown that higher order modes induced a reduction of between 3.6 dB and 7.2 dB in the HFE levels of the 8 kHz octave band which, according to previous works in literature, may be perceptually relevant. However, the influence of higher order modes strongly depended on the phonation type and fundamental frequency \(F0\). Influence was greater for phonations with high HFE levels, such as the tense ones (small \(R_{d}\)), and/or for high \(F0\)s. On the other hand, HFE levels dropped rapidly for lax phonations and/or low \(F0\)s. The presence of aspiration noise could partially alleviate such decreases for [\(\alpha\)] and [i] vowels. Conversely, the levels obtained for [u] suggested that differences between realistic and simplified geometries may not be perceptually relevant for this vowel when the phonation was lax, even if aspiration noise is included. Future work will focus on the perceptual validation of the results presented herein. To this end, we will generate pseudowords containing vowels and consonants to have a broader assessable phonetic context, instead of only considering sustained vowels. However, the synthesis of such utterances is still being developed in FEM-based approaches for voice simulation.  
Finally, we would like to point out that the outcomes for the realistic vocal tracts in this work correspond to those of a specific individual. Analysis for other speakers may result in some differences, yet we believe that the reported general tendencies will still be valid for them. In the future, though, it would be interesting to extend the investigation to further MRI-based geometries and using other glottal source models as well.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Vowel** & **1/1 Octave Band** & \multicolumn{3}{c}{**1/3 Octave Band**} \\ \hline  & **8 kHz** & **6.3 kHz** & **8 kHz** & **10 kHz** \\ \hline \([\alpha]\) & 6.0 (\(-\)0.2) & 8.2 (\(-\)0.2) & 4.8 (+0.0) & 4.7 (+0.0) \\ \([\text{i}]\) & 3.6 (+0.3) & 1.5 (+0.0) & 2.8 (+0.1) & 8.8 (+0.0) \\ \([\text{u}]\) & 6.8 (+0.4) & 1.8 (+0.0) & 9.2 (+0.3) & 9.0 (+0.0) \\ \hline \hline \end{tabular}
\end{table}
Table 2: HFE level mean increments (in dB) obtained for the simplified geometries with respect to the realistic ones. The values have been computed for the 8 kHz octave band and its corresponding 1/3 octave bands. The values in parentheses denote the additional increment in dB due to aspiration noise.  
**Author Contributions:** Conceptualisation, writing--reviewing, and editing, M.F., M.A., J.C.S., F.A., and O.G.; methodology, software, formal analysis, investigation, and writing--original draft preparation, M.F. and M.A.; validation, data curation, and visualisation, M.F.; supervision, J.C.S., F.A., and O.G.  
**Funding:** This research was funded by the Agencia Estatal de Investigacion (AEI) and FEDER, EU, through project GENIOVOX TEC2016-81107-P. The fourth and fifth authors also acknowledge the support from the Obra Social \"La Caixa\" under respective grants ref. 2018-URL-IR2 nQ-029 and 2018-URL-IR2 nQ-031.  
**Acknowledgments:** The authors are grateful to [PERSON] for the design of the vocal tract geometry simplifications and [PERSON] for the English proofreading.  
**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.