DSPs don’t just add latency, they can flatten the frequency response at the expense of time domain distortion, so you get great measurement but weird sound. Inflated low end with ported designs also causes issues.Found the only Hedd type 07 in my country for sale lol. It's out of my budget but I may give it a try.
I'm actually interested in this claim as what seems to be the best in budget for me is the A7V which has built-in DSP. Should I just go with a cheaper A7X?
My use is mainly playing through the monitors and less mixing.
That being said, since you’re mainly playing, not mixing, my opinion is don’t worry too much about all that, just get the largest speakers for the budget and call it a day. My personal best experience for playing to backing tracks was with a pair of Presonus Eris 8s and a subwoofer. Probably all three will cost less than a pair of those Adams. Granted, those Presonus speakers are “studio monitors” only in name, but for playing they are more than sufficient, IMO, and quite fun to play through.
