Carpet, or an area rug, helps to control floor reflections which will otherwise muddy up the sound and potentially cause a sense of brightness.
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It's not so easy. Carpet covers a large area with a lot of Sabiens--this can be very good in an other wise live or bright room, it can be bad in room that's already over damped. In general, I like hardwood floors with area rugs. This provides maximum flexibility, and I like speakers on the floor (mainly for 2 channel listening--things are different for HT and multi-channel), with short reflection times bouncing off the floor, but make sure there is ample absorption near the listener. These short reverberation times add to spaciousness and imaging, but this can be totally irrelevant if the rest of the room is right.
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