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So it stands to say that if a headphone has better response at these two frequencies, it will at least appear to have good square wave response, correct?
Not necessarily. A square wave is made up of its fundamental frequency (30Hz or 300Hz in this case) and it's odd harmonics. If the headphone does not have a flat magnitude response and linear phase at the odd harmonics relative to the fundamental of the square wave, the square wave will not appear good. Here is a 300Hz square wave along with it's FR.
I notice that below 1kHz, there are two "major" notches. One at ~80Hz, and another at ~600Hz...
The HD598 80Hz notch is fairly close to the 90Hz component of a 30Hz square wave (third harmonic - first and most influential odd harmonic) and will influence the shape of the HD598 30Hz square wave response. Also note that, in the HD598 uncompensated FR at IF, the 30Hz component is down (on average) about 5dB from 90Hz. This difference will contribute to the shape of the 30Hz square wave response of the headphone. The 600Hz notch will probably have a lower impact on both the 30Hz and 300Hz square wave responses because these square waves do not have frequency components at that frequency (no even harmonics on a square wave).
Outside of the simple damping conditions, how much do other factors (such as earcups and positioning on the head) affect square wave response?
The response and limitations of the driver will more than likely contribute to the shape of the square wave as it contributes to the shape of the FR.
EDIT: Given that earcups and positioning on the head affect FR, they will affect square wave response... Based on the HD598 IF results, intuitively the 30Hz square wave would probably be more affected by positioning than the 300Hz square wave. My reasoning for this is that I believe the uncompensated FR responses are taken at different positions, and they show relatively large variation close to 30Hz (a little over 5dB) where as 90Hz, 300Hz and 900Hz show relatively small variations.
Thanks for the great reply ultrabike. I think I understand the concept better now.
So a headphone that performs poorly with odd harmonics would show bad square wave response regardless of the frequency that is tested, correct? Would a 50Hz square wave (and so on) look equally good (or bad) based on the headphone's prior performance? I'm guessing there will be variations if you tried to test square waves of higher frequency.