ngkou,
First, regarding those studies where hundreds of people discern a difference in quality... Listening to well-reproduced music cannot be fully appreciated until you've spent a lot time doing so. It's a skill that can be acquired, with practice, by anyone with healthy hearing, and the acquisition of this skill is often accompanied by adaptive hedonism - that natural tendency to become accustomed to a repeated experience that was previously pleasurable, but then becomes mundane. This drives you to find ever more pleasurable versions of that experience, ad infinitum.
I know a guy who swears the least expensive wine he can enjoy costs him $25 a bottle when he buys it by the case, so he's not really happy with the price he's paying, nor the fact that he can only get that discount when he buys it in quantity, but having experienced a lot of fine wines, he has grown to detest the wines that he can more readily afford. He argues there are some $100 wines (and higher) that he drinks on special occasions, swooning that they are "to die for," but he can't afford to drink them regularly. I say, "No thanks!" I'd rather stay "inexperienced" than go through what he's suffering. Keep me away from the good stuff!
I suspect that less than 1% of the even the world's wealthiest 1%, much less the entire population of this planet, has acquired any significant experience listening to extremely well-reproduced audio, and thus, the people who are randomly (?) selected to participate in those audio studies are no better suited to evaluate the difference between an MP3 file and a FLAC file than I am well-suited to evaluate the difference between a $5 bottle of Chardonnay and a $100 bottle (even if the gear used in the study was beyond reproach).
Most people have never heard the likes of what you'll be hearing if you supply the HD800 with a proper signal AND jade your hearing by listening to it for a few years - to the point of finding it boring or, at least, no longer euphoric or exciting.
I wasn't born with "golden ears." I only have experienced ears, and truth be known, even though I can no longer enjoy listening to MP3 files on my system, I'm probably like my friend - consuming audio at a level of quality equivalent to a $100 bottle of wine, while there are people out there consuming the equivalent of $500 bottles of wine, who would find my Head-Fi system lacking.
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Regarding Tidal HiFi (44.1 kHz/16-bit) vs. higher resolution PCM and DSD formats... I for one, can both hear and appreciate a difference between 96 kHz/24-bit recordings and 44.1kHz/16-bit versions of the same tracks. I attribute this to both my gear (my relatively "low-fi" DACs) and my experience, but I am incapable of hearing or appreciating higher resolutions. I've tried them all, but simply cannot justify the storage or expense of acquiring formats more dense than 96/24. Regarding conversion: It's much harder for a DAC to do a good job of converting 44.1/16 to analog than it is to convert the higher resolutions. In fact, DACs that support DSD files have the least amount of work to do, so to speak, leaving very little that can go wrong in designing them - as in, there's no excuse for designing a DSD DAC that sounds bad, where 44/16 DACs are all over the map in terms of quality, with plenty of room for trying different approaches to get it right. Thus, the more expensive the DAC, the closer 44/16 sounds to the quality of 96/24 in a lesser DAC. This is especially so with R2R NOS DACs. NOS means "Non-OverSampling," but ironically, there are quite a few NOS DAC enthusiasts out there who upsample their 44.1/16 files to 96/24, in advance of playing them through their 96/24-capable NOS DACs - finding that the files sound better when the DAC doesn't have as much "work" to do.
So... Lossy formats like MP3 files, are intrinsically bad. Lossless 44.1/16 PCM formats leave room for improvement and are best handled by expensive DACs - the more you spend the better they sound. 88/24 and 96/24 PCM files level the playing field a bit - still sounding better the more you spend, but nearly as bad as with 44/16, allowing a higher quality experience with a greater number of (less expensive) DACs. 176- or 192-kHz and higher resolution PCM files are a waste of money and storage, at least for my ears. DSD files are even larger and more expensive, but they can sound pretty good with even the cheapest DSC-capable DACs.
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As to measurements... We can get excited about what somebody has measured or we can get excited about what we hear. There are so many variables involved that what's measured in somebody's lab can rarely be reproduced in someone else's environment, and besides, that which can be measured is always a fraction of everything our amazing ears can detect. It is only with arrogance that any scientist could believe his test equipment thoroughly measures every variable that we experience. Measurements do tell us something, but in the end, my advice is to just listen - whether we're talking about file formats, amps, DACs, sources, power supplies, or cables... just listen! Your tastes are different, your ears are different, your gear is different, your power supplies are different - why would you want to trust anyone else's "objective" measurements any more than you are willing to trust someone else's subjective impressions? Just the gear and listen to it. Then keep it or get rid of it, trusting your own impressions. Welcome to the world of audio, where you have to buy it (new or used) before you can figure out whether you want to keep it or not. Measurements are a weak attempt, at best, to quantify what we experience.
The best you can do without trying an audio component for yourself is to look for a strong consensus of approval. Don't take any one person's opinion as gospel - including mine - even if they are using the very same gear you are using, except for one component that you are considering. You still need to buy gear and try it yourself, to know for sure whether it's of any value to you. A positive consensus only suggests that your risk of disappointment is low compared to competing products.
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Regarding balanced headphone output... It's a fad more than anything substantial, except for the additional power that can be had, when driving inefficient headphones, by using the balanced output of an amp that also offers both, with the 6.3mm jack outputting a lot less power than the balanced jack.
Here's my explanation (rant) on this subject: http://www.head-fi.org/t/260346/ignorance-cure-needed-balanced-vs-unbalanced#post_11558111
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I've never heard the Lehman, but I've read that it's warm (if I recall correctly), and yes, that it's very good with the HD800.
Buy it and try it. Then buy the HA-200 and compare them. Then sell one of them. Then wish you hadn't when you get a different component that might have worked better with what you sold. Then stop selling gear altogether, so that you can mix and match a lot of components at will, without having to buy the same component a 2nd or 3rd time, as many people have done, and then slowly but surely build yourself a headphone museum of yesterday's most fashionable gear, that nobody wants any longer, but which is, in truth, still very competitive.
Welcome to Head-Fi.