## 3 Results
### Analysis of Tense, Modal, and Lax Phonations for Fixed \(F0\) and \(R_{d}\) Values  
Figure 4 shows the LTAS of vowels [a], [i], and [u] for tense, modal, and lax phonations (\(R_{d}=\{0.3,1,2.7\}\)) with \(F0=120\) Hz. The figure thus contains nine subplots covering all possible combinations. In turn, each subplot presents four curves. Those correspond to the results with the realistic and simplified vocal tract geometries for activated and deactivated aspiration noise. The overall and HFE levels of the LTAS curves are shown in Table 1 for the 8 kHz octave frequency band and also for its corresponding 1/3 octave bands, 6.3 kHz, 8 kHz, and 10 kHz. Values in parentheses indicate the level rise produced by including aspiration noise in the glottal source model. Figure 4: Long-term average spectra (LTAS) of the FEM synthesised vowels [a], [i], and [u] using the realistic and simplified vocal tract geometries with and without aspiration noise. Vowels were generated with a tense (\(R_{d}=0.3\)), a modal (\(R_{d}=1\)), and a lax (\(R_{d}=2.7\)) phonation with \(F0=120\) Hz. Vertical lines depict the boundaries of the 1/3 octave bands 6.3 kHz, 8 kHz, and 10 kHz. Let us first focus on the comparison between the realistic and simplified vocal tract geometries. Looking at Figure 4, we can observe that the vocal tract geometry did not have a significant effect on frequencies below \(\sim\)5 kHz, as already mentioned before, in contrast to the high frequency range. As explained, this is because planar modes mainly propagate at lower frequencies, whereas the higher order ones mostly appear in the high frequency range. This was clearly the case for the realistic geometry. Note, for instance, that a large valley is produced close to 6 kHz in the realistic configuration of [\(\alpha\)] (generated by a transverse mode, see [5]), whereas a resonance appears instead in the simplified configuration. The lack of higher order modes in the latter due to radial symmetry will allow us to determine their influence by comparing the results from the two configurations. In general, higher order modes diminished the HFE levels, regardless of the phonation type and examined vowel. Note that in the 8 kHz octave band of Table 1 the level of the realistic geometry became between 5.6 dB and 6.1 dB lower than that of the simplified geometry for vowel [\(\alpha\)], between 3.6 and 4.3 dB for vowel [i], and between 6.7 and 7.5 dB for [u]. More details can be obtained from the 1/3 octave bands levels at 6.3 kHz, 8 kHz, and 10 kHz. The first one at 6.3 kHz only presents small spectral differences for [u] and [i], which ranged from 1.8 dB to 2.8 dB for [u] and were of the order of 1.5 dB for [i]. Actually, this 1/3 octave band did not contain higher order modes for these vowels (see Figure 4). Conversely, the dip around 6 kHz in the realistic [\(\alpha\)] vowel caused level decreases of between 7.8 dB and 8.5 dB. For this vowel, the onset of higher order modes took place at a lower frequency since vowel [\(\alpha\)] has a bigger oral cavity than [u] and [i]. In the second 1/3 octave band, centred at 8 kHz, the largest differences were found for [u]. In this case, the realistic configuration presented a valley close to 9 kHz, whereas resonances appeared for the simplified geometry. This results in variations ranged from 8.8 dB to 9.6 dB. Finally, [i] and [u] exhibited the largest deviations for the third 1/3 octave band at 10 kHz, which varied from 8.8 dB to 9.0 dB for the realistic configuration. According to [10], minimum difference limen scores of about 1 dB were obtained for normal-hearing listeners in the 1/1 octave band of 8 kHz. Therefore, one could hypothesise taking into account the aforementioned differences, that higher order modes could be perceptually relevant. However, this relevance may also depend on the HFE levels, which in turn greatly depend on the glottal source.