A little late to the party since I only noticed it when @Law87 and @buke9 mentioned me.
I don't think the HD660S would be a headphone that I'd suggest for someone that likes rock, classical and jazz only because they don't quite have the energy in the upper mids and treble to get that "fun" sound that you are looking for but they are quite easy to drive and sound decent/good out of most computer headphone jacks, phones and DAPs that I've tried them with. I also wouldn't suggest the HD800, HD800S or HD700 to you either since you are a bit sensitive to treble and these headphones are not the easiest to pick an amp for some.
My suggestions:
If you can DIY, buy a used one or have one custom built I'd suggest a Ypsilon G1 build since its easy to drive, has the energy in the upper mids and treble for a nice fun sound with decent sound stage/imaging and the bass is quite detailed but doesn't go as low at times but for classical, jazz and rock the bass doesn't go very low often so its not much of an issue IMO.
Next suggestion is a HE560, you should be able to find them quite cheap these days but they will need a decent amp to drive them and the Jot is not one that I liked with them, a bit to sterile sounding to me when I heard the pairing.
Last suggestion would be a lower end Stax setup, about the cost of HD660S + Jot but I'd suggest you try to listen to a Stax system first since they are quite different sounding but to me for some genres like classical and rock they are quite good.
You might also want to post your question in the HD660S thread since there are quite a few that own the HD660S these days. While I like the HD660S for its fairly easy to drive nature they are still a bit over priced IMO but I'd still take the HD650 + decent/good OTL amp over them any day, but this is just me and since we all hear differently only your ears matter in the end.
