I see, well could you explain that to me, what do higher and lower ohms means? Also can you tell me if the amp I listed is good enough for these head phones?
Lol sorry, I am a newbie.
The "ohm" is the SI unit of electrical resistance, it's named after some dead guy named Ohm. The specs you're reading are nominal impedance (impedance being the complex resistance of an AC system, basically it's resistance that varies with frequency) - so they'll say something like "62 ohms at 1khz" which means those headphones are 62 ohms at 1khz. That doesn't tell the whole story though, and you can't even start talking about "amps" at that point. All you know is that at a given frequency, these cans are 62 ohms. So then you have to go and find sensitivity, which is the ratio of input power (in mW; I hate it when manufacturers goose their numbers and state it relative to RMS volts (because it produces NICE BIG NUMBERS)), to output intensity (in dB SPL). So for the K701 it's something like 90 or 93 dB/mW. So for 1 mW of input power, they will produce 93 dB SPL (which is LOUD). So back to impedance - you have to know that your amplifier can deliver X mW into whatever impedance in order to satisfy your output requirements (these are arbitrary, but generally I suggest you listen between 50 and 70 dB), and that's where impedance becomes "a thing."
Higher end dedicated amplifiers usually mean more output power which makes them better suited for insensitve headphones, or headphones at either extreme of the impedance range (low impedance loads "see" less voltage but more current, high impedance loads "see" more voltage but less current - an easy way to keep this straight is to consider your stereo loudspeakers, that require a lot of current and generally have very low nominal Z, vs electrostatic headphones that require essentially zero current, but thousands of volts - examples of "extreme" headphones are things like the Beyer DT48A.00 (5 ohms) and some of the really old Sennheiser pro models that run around 2000 ohms (both of these happen to be fairly sensitive though, so you don't need to get too nuts with an amp)).
For the most part, 1 mW is more than enough power to take your head right off with most headphones. There's a few exotics that defy this. The K701 are not one of them. And most portables can dish out more than 1mW.
As far as high Z cans on portables - here's where a lot of the myths come from. Something like a DT880/600 (which has a 600 ohm nominal impedance, and a spike that takes them to closer to 1k) will have problems with some portables, not because there's not enough power, but because the portable can't swing enough voltage to drive them (which is a limitation of it's battery). But there are portables that are able to deal with some of those higher Z cans (and I'm aware of no "murder scenario" super high Z and super insensitive cans; the Beyers are some of the "worst" in current production, and they're all pretty sensitive).
The sound quality benefits of proper drive for headphones can come from a variety of sources, like removing clipping, having suitable dynamic headroom, or having an appropriate Zout (output impedance). The last one is probably responsible for most differences people hear between amplifiers, and can do quite a bit to confuse the issue altogether. Basically I don't advise people to worry about Zout, as long as it's lower than Znom, and the amp is otherwise stable into the load. With reactive loads (where impedance is not constant), a higher Zout will result in non-linear attenuation of the system's FR which means you change the sound (and in some cases, quite a lot!) - an example is the Etymotic E4S and E4P (which are two separate models, separated only by a resistor). If the impedance is relatively stable (like a Grado), you'll just attenuate the entire thing, and you're wasting (some) power after a point (for example if you're driving a Grado off of the headphone jack on your big'ol stereo receiver - it's driving an amp section that probably has a Zout of less than 1ohm through ~500 ohms of resistors and then into the cans, you're dissipating power across the resistors (it's fairly minimal overall, but it's potentially equal or greater to the power going into the cans themselves)).
There is no simple, linear, relationship here - it's not a Consumer Reports rating metric.
Since you've mentioned mobile use, if you're going to consider a Beyerdynamic, I would get the 32-ohm variant of whichever model you pick (they're designed for mobile use). Grado headphones are also fairly easy to drive, but you need to consider that like the DT990 and the K701 and the PRO2900, these are all open-back headphones that will leak sound out and in, and provide you with no isolation. I don't know if this will be a problem with your usage, but it's worth noting.
I don't know if you missed my question on the first page: what was your issue with the Bose QC15?
Also, as a general request to a few posters in this thread - please do not suggest or recommend hardware with which you have zero experience. It doesn't help anyone.
