I've used a K601 virtually since they emerged and only yesterday switched to the K612.
The K601 has a 'light' sound and in comparison to many headphones, they sound bass light and the treble is a problem for some. However, if you compare them to other treble rich headphones like the Sony 7506, they are less aggressive than you think and way more open sounding.
The K701 is similar but there is something about the treble that I really don't like. It seems harsher than the K601 for me but is perhaps a little more detailed and etched. I think the K601 bass is nicer than the K701.
They have one of the most neutral sounds I've heard from an unmodded headphone if I'm honest.
I also use a T40 modded by Solderdude (Therefore measured) and it has an active filter in order to extend the top end. The T40 doesn't extend too far up after simple physical mods, but the K601 is more open as it is.
I also have a Solderdude modded K550, which has the treble spikes smoothes out. That matches pretty well with the K601 but the K601 is warmer than the K550.
I use the Senn HD600 and 650 - and they both sound quite 'fat' by comparison. The ATH a900 is similar in sound, but I think the K601 has a more extended bass and is less coloured.
Beyer DT990 has way more bass with a top end that is ramped as well, so you are very aware of that going from the K601.
Just a few references since I have headphones growing out of my ears!!
The K612 just adds a smidgen more in the bottom and is extremely close to the K601. In fact, very little difference imo. If people were worried about paying for a headphone, I'd say, stick with the K601.
If you change the pads to K702, the mids of the K601/K612 drop and so does the level of the treble. The bass also gets boosted so that it sounds much more like a Senn HD600. So the cop out is, if it's too sharp in the top, change the pads and it really won't be. In fact, it's remarkably similar to a Sennheiser sound, which was a big surprise for me when I changed the pads.
Personally, I like the K702 pads on it, but I am aware that it skews the FR so I'm staying with the K612 pads which make it a wonderfully open sounding headphone, with a bass that really isn't overstated and an openness that isn't really matched by many other headphones.
It sells at what I'd call a great price for the quality that you get and yes, it would work really well at low level.
I think we need to see a FR chart for the K612 before we jump to conclusions. Tyll's graph doesn't show a rise at 2KHz which is strange, since some claim to 'hear' it. GE does show it.
My guess is that the K612 is very close to K601 (with perhaps the bump at 2KHz) which has been measured on here but it doesn't look too shabby a FR at all for a headphone that costs £130 in the UK. I'd really like to see its frequency response with the K702 pads. It's a very different sound. No way harsh at all. Very mellow.
What is quite strange is how Thomann are selling K702 pads, saying that these are also right for other AKG's like the K601, 612 and 701. They alter the sound of the headphone from standard and Thomann don't stock K612 pads. They have 601's which are grey but 612's are black. (and look nicer imo)
I'm lucky - mine was sent FOC and if I keep it, I don't pay tax on them so I'd get it for roughly £80 I guess. In any case, they're not exactly what I'd call an expensive headphone for the quality that you get from them.