## 4 Discussion  
Measurements of the IAR were reported in combination with FRF charts for all three musical instruments. In general, the low-mid IAR and FRF frequencies were near to each other in all cases, while correlations at the higher frequencies were lower. This result was already found for the kettedrum, and is a typical result of frequency analysis (with a narrow band of 10 Hz). Moreover, the thar and si-thar had a comparable frequency response. Both had a resonant frequency at 322 Hz, although they differed rather significantly at medium and high frequencies. Due to the large amount of cords and the more complicated form of the sound chest, the santoor generated a more balanced sound spectrum, which differentiated it from the other two string instruments.  
By analyzing the results in more detail and comparing the IAR with modal analysis, we found the following:  
In case of the thar, the most significative modal patterns that resulted were those at 322 and 462 Hz (i.e., a difference of 140 Hz). Moreover, if we consider the ratio between 322 and 140, it yields 2.3, whilst the ratio between 462 and 140 yields 3.3. This means that the ratio between the mode at 462 Hz and the mode at 322 Hz is 3:2 (i.e., a fifth), demonstrating that the dimensions of the two components of the soundboard allow a proper tuning of the frequency response of the musical instrument. This is not obvious, since the dimensions of the two components of the soundchest (i.e., the volume) are roughly in a 1:4 ratio.  
In case of si-thar, analysis of the IAR showed that the two most relevant frequencies (i.e., the two main peaks) were 322 and 602 Hz, whereas for the FRF the most relevant frequencies among the 8 modal patterns reported here were 269, 322, 549 and 645 Hz. It could also be noted that 602 represents an important frequency for IAR, as it almost corresponds to the 592 Hz frequency at which the FRF has a minimum value and is between the two main values (549 and 645). Analyzing these frequencies, we see that, starting from 269 Hz while considering the value of 602 Hz for the IAR, they are in ratios of 6:5, 2:1, 18:8 and 12:5. This sequence represents almost a perfect minor natural (Zarlinian) scale, with 269-549 and 322-645 almost in the ratio of 2:1. This could be a reason for the typical melodies composed for this particular musical instrument.  
The third musical instrument differed from the others for several reasons. For one thing, it is a percussion instrument, with a higher number of strings. Furthermore, the resonant cavity is much smaller and does not vibrate like the others, and the strings of the musical instrument are struck by little wooden hammers (mezrabs).  
The analysis of IAR and modal patterns underlines the strong differences with the previous musical instruments. There was little evidence of specific resonant frequencies, even considering the IAR and FRF. The modal patterns were not very clear, unlike the previous cases. However, we could find a certain importance of the frequencies at 269 and 538 Hz (i.e., in the ratio 2:1), even if the corresponding modal pattern did not seem to underline a specific or noticeable shape. The other frequencies did not provide any specific evidence.