Harmonics of the violin mode are not exact multiples of the first mode frequency. So one cannot just take the frequency of a line at multiply it by 2 to look for the second harmanic. For example the 3 lines between 896.2Hz and 896.6Hz, do not have corresponding lines between 448.1Hz and 448.3Hz (there is no significant line between 448Hz and 448.5Hz in Kamiel's plot).

I do not know what is the relation between the 1st and 2nd harmonic of violin mode, there might be an impact of gravity across the fiber (the top part of the fiber has a higher tension than the bottom, because of the weight of the fiber) and/or of the not infinitely small size of the bending points of the fiber near the anchors.