From extensive review of measurements online and trials and my own measurements of headphones and speakers, I believe that after frequency response (how much) and THD (how accurate), the temporal component (for how long) is one of the most important in how something sounds. I think this is where a lot of the “technicalities” that other posters are requesting like “speed”, “punch”, “boxiness”, “nasality” or “congestion” lie.

These components can be shown in impulse or square wave or step response, but these are difficult as the scaling can be near impossible to choose in a way that will visually convey the whole bandwidth. I do like CSD plots, as they provide great detail in the upper frequencies, but are limited in the low range, whereas a frequency vs cycles plot really gets to the damping or lack thereof of diaphragm energy across the full bandwidth. If low range measurement facility noise floor is low enough and with proper gating, I feel burst decay is one of the best single-graphic ways of displaying time variability of acoustic energy.

Psycho acoustically, long duration energy will have a blurring and fatiguing character but also will add an emphasis on the affected frequencies. This will affect detail or resolution in the highs, openness in the mids and will be the difference between a kick, a thump and a boom in the bass, and especially perceived bass quantity (ie tight but basslight vs slowa and boomy but big for the same peak amplitude).

Scoring this to a single number may be difficult though, as some stored energy seems to be euphonic (eg good planars eq’d to flat; wideband low distortion, some narrow resonances possibly mimicking the outer ear and/or canal) judged to be more musical and lively than eg Sennheiser HD600-series where low distortion and very good energy control in the sensitive 1-6kHz range is judged to sound correct but clinical or boring, even when eq’d to the same as the planar. Maybe a couple separate scores? You guys seem good with logical statistical assignments of points.

Also, off-topic, but another common request amongst posters seems to be “loud” and “dynamic”. I don’t advocate listening maxed out as I hear some people on the bus do, but headroom for peaks is still important. So maybe just extend your THD testing to one or two higher dB levels, as this will cover compression and xmax nonlinearities and if applicable built in amp capability. The test level increases would stop either where the powered headphones max out or a predetermined maximum allowable distortion threshold to really get to the mechanical limits but without things getting broken (hopefully).