## 3 Results
### Analysis of Tense, Modal, and Lax Phonations for Fixed \(F0\) and \(R_{d}\) Values
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Vowel** & **Geometry** & \(R_{d}\) & **Overall** & **1/1 Octave Band** & \multicolumn{3}{c}{**1/3 Octave Band**} \\ \hline  & & & & **8 kHz** & **6.3 kHz** & **8 kHz** & **10 kHz** \\ \hline  & & 0.3 & 82.3 (+0.0) & 41.5 (+0.2) & 35.3 (+0.1) & 37.6 (+0.2) & 37.2 (+0.2) \\  & realistic & 1.0 & 70.0 (+0.0) & 14.5 (+3.8) & 8.7 (+3.0) & 10.6 (+3.7) & 9.8 (+4.4) \\  & & 2.7 & 63.5 (+0.0) & \(-4.5\) (+14.4) & \(-10.3\) (+13.1) & \(-8.5\) (+14.3) & \(-9.1\) (+15.2) \\  & & 0.3 & 83.5 (+0.0) & 47.4 (+0.1) & 43.4 (+0.1) & 42.4 (+0.2) & 41.9 (+0.2) \\  & simplified & 1.0 & 71.4 (+0.0) & 20.5 (+3.5) & 17.0 (+2.8) & 15.3 (+3.6) & 14.5 (+4.4) \\  & & 2.7 & 64.9 (+0.0) & 1.6 (+13.8) & \(-1.8\) (+12.4) & \(-3.7\) (+14.3) & \(-4.4\) (+15.3) \\ \hline  & & 0.3 & 73.6 (+0.0) & 41.0 (+0.2) & 37.0 (+0.1) & 37.9 (+0.2) & 31.8 (+0.2) \\  & realistic & 1.0 & 70.0 (+0.0) & 14.2 (+3.3) & 10.6 (+2.7) & 10.9 (+3.5) & 4.4 (+4.4) \\  & & 2.7 & 65.6 (+0.0) & \(-4.7\) (+13.4) & \(-8.2\) (+12.3) & \(-8.0\) (+13.8) & \(-14.5\) (+15.2) \\  & & 0.3 & 73.4 (+0.0) & 44.8 (+0.2) & 38.5 (+0.1) & 40.7 (+0.2) & 40.5 (+0.2) \\  & simplified & 1.0 & 70.0 (+0.0) & 17.8 (+3.7) & 12.2 (+2.7) & 13.7 (+3.6) & 13.1 (+4.4) \\  & & 2.7 & 65.6 (+0.0) & \(-1.0\) (+14.0) & \(-6.6\) (+12.2) & \(-5.0\) (+13.8) & \(-5.7\) (+15.2) \\ \hline  & & 0.3 & 74.0 (+0.0) & 22.8 (+0.2) & 19.6 (+0.1) & 16.3 (+0.2) & 18.0 (+0.3) \\  & realistic & 1.0 & 70.0 (+0.0) & \(-4.0\) (+3.6) & \(-6.9\) (+3.0) & \(-10.6\) (+3.3) & \(-9.4\) (+4.5) \\  & & 2.7 & 64.2 (+0.0) & \(-23.2\) (+14.1) & \(-26.4\) (+13.5) & \(-29.3\) (+13.3) & \(-28.3\) (+15.3) \\ \([\)u\(]\) & & 0.3 & 75.0 (+0.0) & 29.9 (+0.2) & 21.5 (+0.1) & 25.4 (+0.2) & 27.0 (+0.2) \\  & simplified & 1.0 & 71.1 (+0.0) & 2.7 (+4.0) & \(-5.2\) (+3.2) & \(-1.7\) (+3.7) & \(-0.4\) (+4.4) \\  & & 2.7 & 64.2 (+0.0) & \(-16.0\) (+14.4) & \(-23.6\) (+12.6) & \(-20.5\) (+14.2) & \(-19.2\) (+15.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overall and high frequency energy (HFE) levels (in dB) obtained in the realistic and simplified vocal tract configurations of vowels [\(\alpha\)], [i], and [u]. Values correspond to vowels with a tense (\(R_{d}=0.3\)), a modal (\(R_{d}=1\)), and a lax (\(R_{d}=2.7\)) phonation without considering aspiration noise. The values in parentheses denote the increment in dB obtained due to adding aspiration noise. The glottal source not only modified the overall energy level but also introduced a spectral decay that can be appreciated by comparing the LTAS in Figure 4 with the \(H(f)\) of Figure 2. This decay, also known as the spectral tilt, is strongly dependent on the phonation type. In Figure 4, it can be observed that the laxer the phonation (i.e., for growing \(R_{d}\)) the stronger the spectral tilt, especially at higher frequencies. For instance, moving from the modal phonation to the lax one produces an overall energy decay between 4.4 dB and 6.9 dB, considering all values in Table 1. However, this reduction is much larger in the high frequency range. It can reach \(\sim\)19 dB if no aspiration noise is considered. When aspiration noise is present, the decrease was not so prominent and only ranged from 8.0 dB to 9.4 dB. On the other hand, going from a modal to a tense phonation resulted in the opposite behaviour The spectral tilt was reduced, which increased the overall levels between 3.5 dB and 12.2 dB. Again, the HFE levels were more sensitive and increased from 23.1 dB to 27.4 dB. It is worthwhile observing that in this case the aspiration noise did not play a determinant role, since as the LTAS of Figure 4 shows, the tense phonation remained unaltered. Let us then analyse the influence of aspiration noise in more detail. As seen from Table 1, the aspiration noise had no effect at all on the overall levels of any of the analysed configurations. It only affected the HFE content, resulting in significant energy increments for laxer phonations but in negligible differences for the tense ones.