## 2 Results  
### Selection and Optimization of Extraction Techniques for GC Analysis  
In the initial experiments, two extraction methods were compared, i.e., static headspace (HS) extraction and solid-phase microextraction from the headspace (HS-SPME). The results (see Supplementary Materials Tables S1 and S2) indicated that both compared parameters, that is, the number of peaks and the total peak area of the compounds presented in the chromatograms, were significantly higher for the HS-SPME method compared to the HS extraction method. Therefore, the HS-SPME method was chosen for further analyses.  
When comparing the HS-SPME results for different fibers (Table S2), it was found that slightly more compounds were extracted using PDMS (polydimethylsiloxane) fiber; however, peak areas were many times higher when extracted on DVB/CAR/PDMS (divinylbenzene/carboxen/polydimethylsiloxane) fiber. The lower total peak area achieved for PDMS fiber preferably corresponds to the extraction of nonpolar compounds, which is also indicated by the higher peak area achieved for a sample diluted with saturated NaCl solution by the salting-out effect on the polar compounds. The higher total peak area obtained for DVB/CAR/PDMS fiber can be attributed to the bipolar characteristics of the fiber, yielding both absorption and adsorption affinity of the fiber for both low-molecular-weight volatile compounds and the polar compounds presented in the vinegar sample. Therefore, the HS-SPME extraction on DVB/CAR/PDMS fiber was chosen for further optimization of the sampling process.  
The results of the HS-SPME optimization are summarized in Table S3. The evaluation of the central composite design was based on the number of peaks in the chromatograms. Peaks with a signal-to-noise ratio less than three were excluded from the evaluation. Based on the response surface analysis (see Figure 1), the optimal extraction temperature was 75 \({}^{\circ}\)C. Figure 1 shows that the number of peaks in the chromatograms increases with increasing extraction time and the amount of saturated solution. An extraction time of 90 min was considered sufficient. The amount of saturated NaCl solution is limited by the volume of HS vials used, 9 mL being the maximum. Using the polynomial Equation (1), it was calculated that using 6 mL of NaCl solution would theoretically yield a similar number of peaks as using 9 mL of NaCl solution (139 versus 142 peaks). Thus, the volume of 6 mL of saturated NaCl solution was selected, which increases the vapor space in the HS vials used.  
\[\begin{array}{ll}NoP=3.257+&2.762\times X-0.017\times X^{2}-0.592\times Y+0. 007\times Y^{2}+4.414\\ &\times Z-0.266\times Z^{2}+0.0004\times(X\times Y)-0.035\times(X\times Z)\\ &+0.035\times(Y\times Z)\\ \end{array} \tag{1}\]  
_NoP_--number of peaks; \(X\)--extraction temperature; \(Y\)--extraction time; \(Z\)--volume of saturated NaCl solution.  
Optimized extraction conditions were used for semi-quantitative analysis of samples of balsamic vinegars using gas chromatography with flame-ionization (GC-FID) and mass spectrometric detection (GC-MS). Representation of typical chromatograms of volatile organic compounds (VOCs) in the balsamic vinegar is shown in Figure 2A for GC-MS and Figure 2B for GC-FID methods. The magnified segment of the chromatograms contains compounds that have been quantified, and the results of the semi-quantitative analysis are summarized in Table S4. The compounds were assigned on the basis of the comparison of MS spectra and retention indices.