## 3 Results
### Analysis for the Whole Phonation Range  
The analysis for the whole phonation range comprises of the overall and HFE levels in the 8 kHz octave band for the realistic geometry of the three vowels, with and without aspiration noise in the glottal source model. That results in the nine contour subplots are shown in Figure 5. A rainbow colour scale is used for all of them, with red and blue respectively representing the highest and lowest energy levels. Note that the realistic cases analysed in the previous Section 3.1 correspond to the vertical lines in the subplots, which have been indicated with a diamond symbol. The colour maps in Figure 5 exhibit a pattern of diagonal contours with a general tendency to increase the overall and HFE levels from bottom left to top right. That is to say the minimum levels were obtained for the lowest \(F0\) and laxest phonation, \(R_{d}=2.7\), and gradually increased when moving to higher \(F0\) and smaller \(R_{d}\) values. This means that the obtained energy levels not only depended on \(R_{d}\), as already observed in the previous Section 3.1, but also on the \(F0\) of the excitation. In regards to the overall levels (first column in Figure 5), the lowest values were similar for all vowels ranging between 57.6 dB and 59.7 dB. In contrast, the highest levels depended on each vowel and reached 91.6 dB, 80.4 dB, and 78.8 dB for [\(\alpha\)], [i], and [u], respectively. The vocal tract of vowel [\(\alpha\)] produced the highest overall levels thanks to its first three formants, which are the most prominent ones as seen from the VTTFs in Figure 2. Moreover, these resonances took place below 2.5 kHz, where the energy decay of the tense voice source was still moderate (see the top-left subplot in Figure 4). On the other hand, the contours for the overall levels in Figure 4 present some deviations with respect to the aforementioned diagonal pattern, especially for [i] and [u]. These deviations occurred at those \(F0\)s that were sub-multiples of the frequency of each vowel first formant \(F_{1}\). For instance, vowel [\(\alpha\)] presented level increases at \(F0=168.3\) Hz and \(F0=224.3\) Hz, which correspond to \(F_{1}/4\) and \(F_{1}/3\), respectively. This effect was even more exaggerated for vowels [i] and [u], since they had a lower \(F_{1}\) frequency. Note that the levels of these two vowels significantly increased at 110 Hz and 144.5 Hz, i.e., at \(F_{1}/2\). An even more interesting analysis is the examination of HFE content at 8 kHz with and without aspiration noise. When comparing the second and third columns in Figure 5, we can appreciate how the inclusion of aspiration curves the iso-contours in the bottom left corner of the subplots. Hence, the impact of aspiration noise increased as the phonation became laxer, whereas its effect was negligible for tense phonations (\(R_{d}<0.74\)) as quoted in Section 3.1. The contour maps also revealed the effect of aspiration noise increased for decreasing \(F0\). When the aspiration noise was not considered, the HFE levels were similar for [\(\alpha\)] and [i], ranging between \(-14.6\) dB and \(54.5\) dB, while they were much lower for vowel [u] with variations ranging from \(-32\) dB to \(33\) dB. Vowel [u] produced lower HFE values despite having similar overall levels to [i]. On the other hand, when the aspiration noise was added, the minimum HFE levels for [\(\alpha\)] and [i] were \(3.3\) and \(2.1\) dB, respectively. Thus, the levels for these two vowels were above the theoretically audible threshold of 0 dB, in the analysed phonation range. Conversely, the region of [u] with higher \(R_{d}\) values and lower \(F0\)s remained below 0 dB even if aspiration noise was incorporated. The minimum HFE level for this vowel was \(-15.7\) dB. Therefore,  
Figure 5: Contour plots showing the overall and HFE levels (dB) in the 8 kHz 1/1 octave band for the realistic vocal tract geometry of vowels [\(\alpha\)], [i], and [u]. HFE levels are computed with and without introducing aspiration noise in the glottal source model.