Greg, thanks for the maths - even if I don't understand it.
Wouldn't be correct to say, at constant ouput impedance, an headphone with lower impedance is going to be louder than an headphone with higher impedance?
No. As I showed before, it depends on what the output impedance actually is, and also what the sensitivity of the headphones is.
I contacted Yamaha, and the output impedance of the N1/N2/N3 is approximately 33 ohms.
I've calculated the relative loudness of all headphones mentioned so far in this thread except for the Phillips (can't find the sensitivity specs) taking into account the 33 ohm output impedance. I used the headphone.com measurement for the AH-D2000. The DT770 Pro, HD650, and AKG K701 are all pracitally identical. The Denon AH-D2000 is 4.4dB louder, and the HD-598 is the loudest, being 2.3dB louder again than the Denon. To get an idea for what these dB figures represent in terms of how loud it actually feels
to humans, a 3dB increase is about 23% louder, 6dB = 50%, and 10dB = 100% (twice as loud). Note that all this is very approximate - the overall loudness will also depend on the frequency response of the headphones, and I have not made any attempt to account for that.
Good headphone amps can be bought very cheaply now.
FiiO make pretty good stuff that doesn't cost a lot. For your AH-D2000, I'd look at something like the E6
(it won't be able to drive some of the other models mentioned very loudly, but it should be loud enough for the Denon I think).