Here's a question that may be interesting. I currently have a very "analytical" stack: Topping D90SE+Topping A90. If I wanted a more "musical"/"refined"/"smooth" sound, I could:
(1) Switch the D90S with a "smoother" or more refined DAC, say an R2R (though I'm considering a Qutest), while keeping the clean and transparent A90. This might be like hearing the "pure" sound of the DAC without any "extra" sound signature added (or at least it seems that way to my naïve intuition).
OR
(2) Keep the D90SE, but switch the A90 to a smoother amp, say a tube amp (though I'm considering the SA-1). Here it seems I'd be hearing mostly the sound signature of the amp, with the D90SE providing a neutral and detailed "base" to that signature.
My point is not to ask for specific recommendations (though they are welcome), but to bring up the general question of which of these two options is better motivated from both a musicality and technical standpoint.
Depends on what you’re actually looking for. From a purely objective point of view, you should find yourself the DSP(starting with a nice EQ) that does what you want, or find a headphone that sounds closer to what you enjoy. Or change the amp for one with tubes if you think you’re after that. And finally maybe change the DAC for something weird.
In term of magnitude of change and variety of sounds, you should consider things in that order!
Because no amp or DAC should drastically alter the frequency response, but FR is a leading variable in term of personal preference. At a different level, it’s not too hard to get some old tube design that would reach 1 or 2% distortions. But if a DAC did that, everybody would recommend to shoot it with a rifle. Even the worst DAC is expected to be more accurate than everything else.
So in term of amount and variety of change, my order of progression is logical. But that doesn’t account for what you want in particular(if you even know it). A more musical sound means nothing. It’s a completely subjective notion where just the album being played would have different people reach different conclusions. Refined? IDK what that is. I would assume that a nice album on a fairly transparent system can bring plenty ”refinement”. Of course a given headphone will almost never have the right frequency response for you, so, using some EQ seems to be the common and necessary step. The first one I take when I get a new headphone or IEM.
About”smooth” sound, again, many ways to interpret and handle that. A smoother, maybe warmer FR for the headphone(or a headphone that is already like that)? Maybe some good old tube distortions would do the job for you? If you have some amount of nostalgia about tube of even turntable sound, then go for it. You might still have to try a lot of gears to get something similar, if similar ever existed(the danger of good memories is that they're usually not accurate). But at least you’d know what to look for.
Finally, if what you’re really after is speaker sound, that’s a different problem. It would be good to know if that’s your actual target or not, because headphone playback is
significantly different.
When I said finally, I lied.
I feel the need to mention that I don’t know those Topping products. Only that Amirm made them(too?) famous. It’s great to have some measurements of gear, and I’m grateful that he decided to do it. But by being almost the only one on the web to provide such measurements, he becomes the only judge of what’s good. Which is a risk, regardless of who his friends are, or how seriously he does the measurements. Replication is a key part of science. One that even real research has slowly abandoned... The result is de facto a much lower confidence in the data. And while most scientists consider that when shopping for data, I do not think the average Joe does.
Not being part of the solution, I’ll leave it at that.