36 Keys

The following riddle is attributed to Aristides A. Messinesi and was originally printed in the January 1904 edition of "A Posy of Puzzles".

My first is in mouse, but not in rat;
My second is in bonnet, but not in hat;
My third is in store, and also in rock;
My fourth is in hen, but not in cock;
My fifth is in rye, but not in rice;
My whole is a wood for furniture.

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