Hello Dr. Muller,

Thank you for your comments on our paper. It would be best for Berend Stoel to respond to your questions A and B regarding the quantitative analysis but unfortunately he's away from his office for another week or so. As for your C we did state "Due to the increased repair work on one of the classical instruments, it was necessary to choose the ROI's carefully so as to reflect the true wood density, not that of the repair." unfortunately we were obviously not clear enough that the ROI's for all other instruments were the same but for the central violin lower row it was necessary to slightly move these ROI's to remove any repair from the quantitative analysis. I'm sorry for the confusion. Dr. Stoel will hopefully be back and able to address your other questions quite soon.

Sincerely,
terry borman

Dear Dr Muller,
Thank you for your critical remarks and careful visual analysis of the resulting images.
As for remark A, I am not sure if I understand your remark fully: the density variations within the older violins were actually smaller, not larger. In close-up, this can be seen especially in the top plates of Figure 2 in the two rightmost older violins, although indeed the resolution of these figures may not be sufficient to visually appreciate this fully. Furthermore, one needs to realize that visual perception of intensity differences are very much influenced by the surrounding image structures (for example the well-known Mach-bands would illustrate this). As a result visual interpretation may not correspond completely to the actually measured values. Additionally, we found that the median density measurement of wood was influenced by the thickness of the plate. Therefore, we corrected these measurements, as described in the paper. The images in Figure 2 are the original images in which this influence is still visible. Possibly the most important item to remember when viewing these images is that our analysis was quantitative, not visual, so these images are secondary; our findings were a statistical interpretation of the individual ROI's chosen for each instrument.
The resolution of the individual images is exactly the same, because we used an identical image acquisition protocol, and the CT image were analyzed in a batch job, without human interaction.
On remark B; Our work was focused primarily on the top plates since they are most likely responsible for a higher percentage of the total sound radiation of a violin; that withstanding, the back plates show two "clusters", overlapping to the same degree as the top plates, although on a much smaller scale. The one modern back that is of lowest density was possibly treated. Again, as we stated in our results we don't know anything other than what we found and conjecture as to what may have caused these differences was not within the purview of our work.
Best regards,
Berend Stoel