Tom and Nigel,
I barely have a grasp of this stuff myself, but I've been studying this subject quite a bit lately and can say with some certainty that the following statements are true. (How's that for a disclaimer?)
1) Amps don't mind seeing a greater load (running uphill), but can be damaged by seeing a load that's less than that for which they are designed (running downhill). So... you don't have to add resistance in parallel (across the + and - of each channel), for the sake of protecting an amp that's designed for the 4- or 8-Ohm load of speakers from the greater impedance (i.e. 38-Ohms) of a headphone. For the amp's sake, it's perfectly OK to run without adding parallel resistors to a load that has a higher impedance than that which the amp expects.
2) Headphones, like speakers, can tolerate only so many watts peak from any given amp. If the amp can produce more power than the headphone can handle, it's a good idea to add parallel resistors - for the sake of the headphones, not to protect the amp. I've just read that the HE-500 has an impedance of 38 Ohms, but I can't find a specification for the number of Watts it can handle. The Audeze LCD-2, can handle up to 13-Watts rms (where rms is typically about 70% of peak) into its 50-Ohm load. You need to find out how many watts your HE-500 can handle into its 38-Ohm impedance. If the amp does not exceed this rating into 38-Ohms, you don't need to add parallel resistors for the sake of protecting the headphones.
3) How do you translate a power rating into 4- or 8-Ohms into that for a higher impedance (i.e. 38-Ohms)? For most amps, the relationship between power out and impedance of the load is not linear, but we can get in the ballpark by using an inverse proportion. The TP60 is rated at 80 Watts (rms) into 4-Ohms, but the HE-500 presents a 38-Ohm load.
Power Rating of Amp * Expected Impedance / Actual Impedance = Watts into Actual Impedance (approximate)
80 Watts * 4-Ohms / 38-Ohms = 8.42 Watts (into 38-Ohms)
So, if the HE-500 can handle 8.5 Watts into 38-Ohms, there's no need to add parallel resistors for the sake of protecting the headphones, but you may want to do so for the sake of tailoring the sound, because the amp might actually sound better, or at least different, by adding parallel resistors (or for that matter, by adding series resistors). More on that in the next points...
4) Keeping all of the above in mind, even if you don't need parallel resistors to protect the headphone from excessive power, you can use parallel resistors to tailor the sound. Adding parallel resistors will make the amp sound more aggressive or sharp, less muddy or fuzzy, generally speaking. The parallel resistance should be 1/10th to 1 times the impedance of the headphones - to decrease the effective output impedance. The lower the value of the parallel resistors, the harder the amp has to work to deliver the same SPL at the headphones. So when you add parallel resistors, SPL at the headphones will increase. It may seem counter-intuitive, but you're allowing the amp to see less total impedance, not more (just as when switching in two pairs of 8-Ohm speakers instead of one pair, on an amp that offers the ability to drive two pairs simultaneously, presents a 4-Ohm load to the amp, not a 16-Ohm load.) A lower value of parallel resistance gets closer to being as if there's no parallel resistor. (Duh!) Increasing the value of the parallel resistor decreases the effective output impedance, but don't bother going any higher than the impedance of the headphones.
5) And now let's talk about series resistance... If you want your amp to sound less aggressive or sharp, more relaxed, you can add series resistors to the + side of each channel - to increase the effective output impedance. The series resistance should be 1 to 3 times the impedance of the headphones. Once a series resistor hits a value that's 3 times the headphone driver impedance, you've done all the good you're going to do in terms of reducing an aggressive sound by increasing output impedance. Increasing the series resistance to values higher than three times the headphone impedance will only make things worse, with insufficient damping factor making things muddy. But there's more...
6) Understand that with dynamic headphones, when adding series resistors, you will also be changing the frequency response, because impedance is not flat across the frequency spectrum with dynamic headphones. With planars, which have a purely resistive impedance, their impedance is flat across the frequency spectrum, and thus, you will not get a shift in frequency response by adding series resistors.
Wow... I wrote a book - a book that's completely off-topic for this thread. Sorry!