Do you still have the grot you cleaned out of it? Can you locate it exactly in the place you found it, so someone could date the soil stratum it was embedded in? The location is much like where the "Dordrecht" recorder was found, and that was only dated by the building rubble that covered it.

(Sorry, I am NEVER going back to Chiff and Fipple, after one of their moderators rewrote one of my messages into mealy-mouthed idiocy and posted it under my name).

The scale you got out of it isn't one of the standard pentatonic ones - it's a gapped pentachord with an overblown tonic. Common in Southern European folk music for at least the last 2000 years, so not a lot of help in dating it.