The thing is, the BR-80 has a listed output impedance of 22 ohms. Following the 1/8th rule you would need 176 ohm headphones to guarantee performance, which is somewhat uncommon and nowhere near the K240s 55 ohm rating.
[22 Ohms might be the minimum recommended load. Most users don't understand the implications of source impedance and if the spec says 8 Ohms, they might think you can connect an 8-Ohm speaker. ...When you look at amplifier specs they don't give you the source impedance, they give you the recommended (or minimum) load impedance, and if you are lucky they give you a damping factor so you could calculate the source impedance.
Also, that 1/8th rule is for "critical listening". Monitoring isn't that critical, and you shouldn't be using headphones for mixing/mastering anyway.
Check out reference-audio-analyzer which has predicted frequency response change for a given headphone / source impedance:http://reference-audio-analyzer.pro/en/report/hp/akg-k-240-studio.php#rw6So in this case for 20 ohms source impedance, you're looking at +1.5dB at 100Hz, and +1dB at 10kHz and above.
This link explains where the 1:8 rule comes from it's a good read:http://nwavguy.blogspot.com/2011/02/headphone-amp-impedance.htmlIt says that the smallest audible difference that a normal person can hear is 1dB, so if you're under that number you should be good.