[HiAudio]

I think there is no such sudden change on how you hear the sound. The sound may change gradually when the impedance change in the absence of an amplifier. I bet very few people have plenty of headphones with various impedance that cover wide range with minimal incremental changes.
 
My K712 has rated impedance of 62 Ohms and VHX330 has 64 Ohms. But the HD650 has 300 Ohms. So HD650 definitely needs amplifier while the other two may not. Besides, if I use the blue tooth connection of VHX330 I have no means to use amplifier.
 
My RS 220 wireless just connect to CD player and play. I do not know its impedance number and Sennheiser did not list it.

 

[PleasantSounds]

  I think there is no such sudden change on how you hear the sound. The sound may change gradually when the impedance change in the absence of an amplifier. I bet very few people have plenty of headphones with various impedance that cover wide range with minimal incremental changes.
 
My K712 has rated impedance of 62 Ohms and VHX330 has 64 Ohms. But the HD650 has 300 Ohms. So HD650 definitely needs amplifier while the other two may not. Besides, if I use the blue tooth connection of VHX330 I have no means to use amplifier.
 
My RS 220 wireless just connect to CD player and play. I do not know its impedance number and Sennheiser did not list it.

Impedance is not the only factor you need to consider when deciding if you need an amp. Probably even more important is efficiency. If I remember correctly, HE-6 have 50 Ohm impedance - try to run these without an amp... Your K712 would do much better with a good amp too.
 
High impedance headphones may need an amp because they need higher voltage to get to the same volume level as low impedance cans. On the other hand, if they are very efficient, they may be loud enough even without an amp.
 
Wireless headphones are totally different, as they have an amp (and sometimes a DAC as well) built in. For those it is enough to provide line level signal. Their input impedance is very high, so they don't create much load on the source of signal. You could connect them through an amp, but that is rather pointless.