While the small Ukrainian tsymbaly is the dulcimer of choice in the Hutsul villages of the Carpathians, music educators throughout the former Soviet Union prefer the Hungarian system (aka the Shunda). There were even factories producing Hungarian-system concert cimbaloms in Chernihiv and Kamyanets-Podilskiy, Ukraine and Kishinev, Moldova from the 1960s until the late 1980s.
Every cimbalom player seems to have his or her own preferred method of tuning the instrument. Some tune by octave starting from c1, some tune the bass first, etc. I recently asked my teacher Dmytro Matkovskiy, what his tuning method is. As it turns out, it’s in a textbook by the Soviet publisher “Музична Україна” (Musical Ukraine) printed in 1984. The book includes a string diagram that indicates the order in which strings should be tuned.
The middle numbers nearest to the note names indicate tuning order. Thus, a1 should be tuned first, then d1, then a, then e1, then b1, then e1, etc.
My teacher tunes the bass strings by octave along with the treble strings (after a1, d1 and a, he tunes the bass d and A strings.) I added numbers to the chart showing this option as well.
You can download my modified tuning diagram here.
Tuning practices were quite similar in the Moldavian SSR. In their 1982 cimbalom method “Metodă de Tambal” Moldovan authors Vasile Crăciun and Vladimir Sîrbu provide a string diagram and tuning instructions:
We should start by concentrating on one course. Tune a string at the top of the course (one that is located closer to the smaller end of the cimbalom), then, one by one, the other strings in the course, bringing them to the same level. We will tune the whole instrument in this manner. As a rule, tuning begins with LA1 (course 18, see diagram). The same course gives us note RE1 across bridge 3. LA1 should be tuned to concert pitch or to an instrument in the orchestra, then proceed down by an interval of a fifth and tune note RE1. The whole procedure described makes the upper part of the chord. Verifying the fifth, one by one, we continue to tune other strings in the chord.
We are then instructed to tune the upper octave completely, then the bass strings. For me, this tuning method seems more time consuming than the one I’ve observed in Ukraine because it leaves the bass strings for last, requiring subsequent retuning of the upper registers due to the lowered tension.
Still, if you want to try the Moldavian system, here’s the description and tuning diagram (with my translation).