Strings and tuning

There are two groups of strings on the zither:

Chords

20 strings: 5 chords of 3 strings, with an additional bass string at each chord

• chord '5' (A chord): E - A - C# - A
• chord '4' (D chord): D - A - F# - D
• chord '3' (F chord): F - C - A - F
• chord '2' (G chord): D - B - G - G
• chord '1' (C chord): E - C - G - C

The strings made me think of the (open) strings on a cello: A-D-G-C (fiths intervals). But there is an additional F string/chord, a minor third from the D.

Melody

21 strings:
C - C# - D - E - F - F# - G - G# - A - B - C - C# - D - E - F - F# - G - G# - A - B - C

Each octave has 10 strings: the D# and A# are not there. This made me wonder if this instrument has some kind of strange tuning:

• Chromatic would have been 12 strings (the same as on a piano)
• Diatonic would have been 7 strings (only the "white notes" on a piano).

I am still searching for this 10-string scale. For now I assume that the D# and A# are left out because they are not part of the chords on the left. But then it is strange that the G# is there on the melody section (and not in the chord section)...