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I won't pretend like I understand a lot about electronics and how they relate to audio, however you can't relate impedance directly to output volume, since you also have to account for sensitivity. A pair of headphones can have low impedance and yet low sensitivity, so it will need a powerful amp (I think this is the case of the K701). However how much the sound changes when you change the amp, without looking at the volume, does relate to the impedance, although I don't know how.
Also when saying something like "these sound bad whe plugged into low power amp A, but are amazing when plugged into high power amp B" doesn't exactly mean the more powerful the amp, the better those headphones play, it might just be the case that amp B is simply better (linear FR, very low distortion) than A. For example the amp on the Sansa Clip is amazing, and yet outputs very little power.
No no... I think you misunderstood my post a bit. Yes, the impedance was brought up a few times in relation to volume and output. Of course, like yourself, I won't pretend that I know how all this works exactly since I'm no engineer. However, I do know that it does correlate, and yes of course, the sensitivity does as much as well. But the general point I was making is that I tend not to rely on these numbers, the graphs, and other stats. Yes, they're a great tool to understand the potential of headphones... But... at the end of the day, the sound you hear from them and what they reproduce, how well and how loud, a lot of times tells a different story. There is also a reason why I specifically mentioned the MDRV500DJ and the XB500. You see, the DJ's actually have a 24ohm impedance and 105db sensitivity while the XB500's rated at 40ohm and 104 sensitivity. So on first glance, wouldn't these stats paint a picture that the DJ's should be louder at given lower output source? I mean 24ohms and 105... isn't that close to the ibuds stats? Yet the Djs (tested even with proper amp, home surround, DJ mixers and a few others) still required a lot more power to get them to the optimal sound. While the XB500's, Shure SRH440 and even the 840's at 44ohms and 102db sensitivity were all pushed so much straight out of portable players, and all the same when amped when compared with those VJ500's. Even yet, a better example, the philips Oneill Stretch, headphones that are specifically designed for portable use, and a heavy one at that, like snowboarding and physical activities, rated at 102db and 16ohm... 16... !
Yes, I had to push my iphone up 85% to get good sound out them.. And these things isolate very well on-top of this..
So what's my point, clearly that there is something else going behind the scenes of headphones that results in this, which clearly goes beyond what is shown on the box... I wish I knew what it was... but I'm not sure that I ever will..
It's just that for me, I'd take my own hearing and the actual company's own words as to what is required for optimal listening experience as opposed to reading stats. After all, I can't imagine how one can't be shocked to hear that Shure SRH940, Shure's highest reference grade monitors are easier to be pushed out of an ipod than Philips Stretch.. Just hearing this makes no sense, yet, there it is...