Greek _kithara_ and German _Gitter_

Hallo Indo-Europeanists!

Could these be cognate (from a PIE *ghidh-ro-)?

I know that a harp is not the same as a grid, but they *are*
somewhat similar - both have a frame, one has strings and the
other has bars. The Duden Herkunftswörterbuch gives a different
etymology for _Gitter_, but that one looks contrived to me.

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