The 1/8 impedance rule of thumb may or may not affect the K612. Having a lower output impedance could keep the bass frequencies from acting as an always-on bass boost and a bit of treble boost at the limits of most people's hearing, but it may not make a difference, or the distortion may actually seem pleasing.
Impedance sometimes varies with the frequency of what note is playing (bass, mid, treble, example 100 Hz would be a low note in the bass range)
Impedance "mismatch" happens when the headphone has impedance that changes depending on what frequency is playing, AND the amp's output impedance is too high to allow for sufficient dampening by the headphone. If you see a "spike" or hill in headphone impedance, FWIR that means those frequencies will probably be boosted (sometimes to the point where they lose detail) compared to the rest. If a headphone impedance is relatively flat, like planar magnetics, the AKG K601 and Q701 (haven't seen a graph for the K612 yet, but I assume it would be like these), then the amp's output impedance will have little effect.
Most people besides headphone designers didn't pay much attention to this, until a guy (who has been banned) began a flame war about impedance and distortion and blah blah blah it got ugly. His example headphone was the Sennheiser HD650 (orange line on the graph), which he assumed was like most other headphones. The Sennheiser HD650 is not like all headphones, so... the 1/8th rule is a generalization, following it won't hurt, but a small boost/distortion might be pleasant AND if the headphone impedance response is pretty straight, then it might not matter anyway.I'd say, get the headphone first, and see what you think of it plugged into a home theater receiver.
Maybe your parents or friends have one. Receivers often have headphone-outs with an output impedance of like 120 Ohms, if that sounds bad with the AKG (doubt it), then you could go with the Sound Blaster Z or Omni route with an external Amp with low output impedance. If it sounds good, then the Sound blaster Z or ZxR may be all you need. I'm pretty confident you'll be impressed either way... I love using my Q701 or K712, I usually use them with a tube hybrid amp that gives a little color to my music (and also gives me a volume knob on my desk), but when I'm gaming I have no problem plugging them straight into my Sound Blaster Z. My AKGs' impedance is low overall (lower than the K612, 62 Ohms) so they don't need the volume cranked to max, but they are low sensitivity so they need a fair amount of current supplied at listening volume (which solid state amping, like that in a soundcard or the transistors in my hybrid amp, is good at) to keep sound smooth instead of grainy. The 120 ohm K612 ought to need a higher volume setting, but at that setting have an easier time providing enough current for a smoother, grain free sound. I expect the K712 to be a little more detailed and refined, but I'm still interested in trying the K612 anyway Edited by Evshrug - 1/7/14 at 7:07pm