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My reciever has crossover options. Would I do best to buy tweeters for on pair of channels, mid cones for another pair of channels, and cones for bass for another pair of channels?
To make this sound right you will have to keep the tweeters, squawkers and woofers together in two groups of three. You will then be right back where you started with standard stereo but your six channel receiver will be doing the job of crossover networks. That's a waste of four channels. The whole point of a surround sound system is to mimic the reverberation you get in a large hall. The sound that comes out of the rear speakers is radically different from what comes out at the front.
The sixth speaker - the sub-woofer - is only there to save money on the other five. As DVDdoug points out, an ideal setup would have five full range speakers. The sub-woofer trick exploits the fact that our ears cannot easily locate the source of the lowest frequencies. By filtering these out of the other channels you can get away with five smaller, lighter and cheaper speakers but such savings can be pushed too far. As CiTay says:
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If the satellite speakers are too small, the manufacturers have no choice but to either let the subwoofer play so high that you can easily locate it or leave a big gap between bass and highs.