Dan, it depends on the distance of the run, and 30ga(which many HDMI cables are)is fine up to about 15 feet. 28ga is usually okay for 20-25 feet, but longer than that and it'd be safer to use 24ga, as in the source that I linked(note that a 3' DVI is about $16). Yes, it also applies to DVI; the connectors are different, but DVI and HDMI are electronically identical(except that the HDMI format can carry audio)and no conversion or other processing occurs between the two.

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Enjoy the music, not the equipment.