'The painting has a natural coloured wooden frame.'
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I am not sure about the use of 'natural', here. To me, 'natural ... frame' feels like the frame could have been made of wooden branches or twigs. That is not what I tried to express.

The frame is made of nicely polished wooden strips, and the painter gave these a kind of green-brownish colour, as often seen in Nature. How to modify coloured to express this quality?
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Thanks!