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Soundstage and airiness are really the most prevalent qualities that people report changing. No machine in existence can test this, bass quality and textures all throughout the sonic spectrum are often reported. The changes are all very small but as another user here said on the last page, they add up and will create an audibly different experience from stock. So I laugh uncontrollably when someone claims burn in does not exist after they test frequency response and see no change. Its like....derpppp
Sorry, but that's just not true. The sonic differences between headphones and/or speakers which contribute to the qualities described as 'soundstage' and 'airiness' are a reflection of the sound waves. As such, they have physical properties and they are measurable. They are likely a product of sound waves interacting with each other in a process described as linear super position. Starting out with the assumption that something cannot be measured or tested is anti-scientific and implicitly relies upon supernatural explanations. If the process of burn in does exist, then I can measure it. I don't need any sophisticated machines to do it, although sophisticated machines could help.
What I would need would be a number (I'd guess about 150) of brand new model and brand matched headphones which would be randomly assigned to three different groups of equal size: untreated, and treated (burned in using some previously agreed upon method for a pre-set amount of time, say 300 hours), and a third group termed modified which would not be burned in but would be intentionally modified to be somewhat different from the untreated by introducing something like a low-pass filter to slightly modify the sound coming out of them in a way which is measurable using sensitive electronic monitoring equipment, but yet still very subtle. I would then need a much larger number of individuals (say 300-1500) to perform the experiment on. Ideally these too would be randomly selected from the Head-Fi population. Each of those individuals would state whether or not self identify as whether or not they can hear the effects of burn-in, and whether or not they believe they have golden ears.
The test would then be relatively simple. Each individual would bring with them a selection of 5 or 10 songs (to be determined prior to the start of the experiment, and every listener would listen to the same number of songs)prepared in whatever format they like. They could use their own amplifiers, power cables, whatever. The only issue would be that they would not be allowed to know which headphones they were wearing, and neither would the experimenter (double blinded). The listener would listen to every song using two sets of the headphones, randomly chosen from an of the possible combinations including: untreated and untreated, untreated and treated, untreated and modified, treated and modified, treated and treated, or treated and modified. The listener would not know which pairing they were listening to, but would be asked a simple question. Do these pairs of headphones sound the same to you or not? There would be no statement of preference recorded.
Then we would be able to address a couple of questions. The first of which would be, on average, can users hear the effects of 'burn in'? Can some subset of the population reliably hear the effects of 'burn in', while others cannot?
The null hypothesis of course, is that no one can hear any difference and any perceived differences are either due to placebo effect or because the listener had changed.
Personally, I'm agnostic on the issue of whether burn in occurs or not. I can imagine how use over time would change the voice coils and/or diaphragms involved, and that over time the positioning of the earphones on the users head would change in response to the changing earpads as a result of use. Grado headphones sound can change in quite marked ways by simply changing the earpads. On the other hand, I do think it is quite ridiculous to state that a phenomenon exists, but it is untestable.