Crazy transformer?

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I came across an old E-I 25v 3A transformer, small, which i beleive would be perfect for my preamp. The thing is it outputs 30VAC (give or take, measured with my multimeter) with no load at all, but when i connect it to a bridge rectifier it outputs 24VDC *and* about 12vAC on the output terminals. This happens both with a discrete bridge and a regular 30A one, so i beleive it's the trafo... but it's puzzling me. Any ideas what could be wrong here?
 
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