[Fungus]

Say if I added a resistor adpator to a pair of DT880 32O ohm to make it 80ohms, would it sound identical to the 80ohm version which has the impedance in the drivers? 
 
I'm really confused?
 
If this is true, then why doesn't everybody just buy the lower impedance version headphone so they so they have the option to use it on with a portable media player on the go just add an adaptor when plugged in to a desktop amp? 
 
Or doesn't is only apply to the Etymotic ER4? 

 

[DaveK1977]

Short answer: No.
 
Long answer: You might be able to raise the electrical resistance of the headphone to something similar to the 80 ohm version, but you won't gain the benefits of the increased resistance the same way that having the resistance in the driver itself would do.  Impedance changes the sound because of an interaction between the driver and the amp that serves to dampen the motion of the driver especially the extra motion of the driver.  This extra motion is not an accurate part of the sound that it's trying to generate and creates distortion.  When you add a resistor to make the headphones' resistance higher, the driver is still making 32 ohm reactions with the input and the resistor is creating the additional resistance, but has no effect on how the driver itself interacts as a part of the circuit.
 
Tyll Hertsens described it a lot better than I can in a comparison of three headphones that are otherwise supposed to be the same, including your DT880 32 ohm.  You can see from the response curve and other similarities that the drivers are the same and the only difference is how they electrically react.
 
http://www.innerfidelity.com/content/comparison-beyerdynamic-dt-880-32-ohm-dt-880-250-ohm-and-dt-880-600-ohm-headphones
 
http://www.innerfidelity.com/images/BeyerdynamicDT88032ohm.pdf
http://www.innerfidelity.com/images/BeyerdynamicDT880250ohm.pdf

 

[Fungus]

  Short answer: No.
 
Long answer: You might be able to raise the electrical resistance of the headphone to something similar to the 80 ohm version, but you won't gain the benefits of the increased resistance the same way that having the resistance in the driver itself would do.  Impedance changes the sound because of an interaction between the driver and the amp that serves to dampen the motion of the driver especially the extra motion of the driver.  This extra motion is not an accurate part of the sound that it's trying to generate and creates distortion.  When you add a resistor to make the headphones' resistance higher, the driver is still making 32 ohm reactions with the input and the resistor is creating the additional resistance, but has no effect on how the driver itself interacts as a part of the circuit.
 
Tyll Hertsens described it a lot better than I can in a comparison of three headphones that are otherwise supposed to be the same, including your DT880 32 ohm.  You can see from the response curve and other similarities that the drivers are the same and the only difference is how they electrically react.
 
http://www.innerfidelity.com/content/comparison-beyerdynamic-dt-880-32-ohm-dt-880-250-ohm-and-dt-880-600-ohm-headphones
 
http://www.innerfidelity.com/images/BeyerdynamicDT88032ohm.pdf
http://www.innerfidelity.com/images/BeyerdynamicDT880250ohm.pdf

Thanks DaveK1977 for you detailed response. I totally understand now