Put them both on the binding posts. This will do no harm. Don't dangle unused cables...an amp disaster waiting to happen. Jallen
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I've heard some say running multiple similar cables between a single amp and speaker connection can make a big difference in sound (for the better). Don't some cable manufacturers like Nordost use a parallel multipath conductor design in their high end cables?
I don't think it can hurt to try. Try it both ways and see if there is a difference I'd be interested to know.
Having bananas at the speaker ends makes it difficult.
If you want to keep the biwire capability of the wires for later, I suggest swapping one of the speaker-end pairs (either one) of banana plugs with spades. Most binding posts will accept a spade and a banana plug with no problem.
Otherwise, if you're not planning to sell them and don't mind a little butchery, you can just clip the bananas, twist all the proper ends together and have a single "bare wire" connection.
You might even notice an improvement in sound when you get the connectors out of there. :)
I agree with Eldartford with the caveat that if you run both conductors from the amp to the given speaker you will be doubling the cross section of the , thus providing a slightly lower resistance and reducing I^2R losses. This will likely not have a noticeable effect as your speaker wire is probably no smaller than 16 guage and you likely are not passing enough current through the conductors to make a difference.
As to why some companies use multiple conductors in a cable that is meant to be connected at only one point on each end- the proffered theory is to reduce the impact of skin effect - which is the tendency for current density to be greater away from the center of a conductor. Technically true - but skin effect is frequency dependent and the flaw in the proffered theory is that at audio frequencies the impact of skin effect is negligible.