I empathize with Eric and apparently some others; I, too, like hearing music with a "melody" as someone here stated. I haven't yet tried to see how much/if I can appreciate jazz, but might give it a try after reading this thread. I worked once with someone who just loved jazz, tried a time or two at his place to listen, but it was not for me, then. I'm (much) older at the moment, with a lot more time (retired, consult on and off), three setups with three different sounds/equipment, so enough variables and time to give this a serious try. But, again as might have been stated here, this should not be work, it should be pleasure, and visceral at least as much as intellectual. Some of the music I love would be laughed at were I to list it here, but its important music to me, for a host of reasons, including memories, linkage to my long-dead parents, my youth. I am certain many here share that type of connection.
