So the cited paper shows the frequency spectra difference of rectangular pulses makes them audible when 10 microseconds apart. When low pass filtered at 21,120 hz the differences were still audible at 10 microseconds apart. As the low pass filter is moved lower the gap has to become greater. No big surprise and doesn't seem to support this temporal idea in MQA. The conclusion of the paper:
In conclusion, the data collected in the present experiment demonstrate, that the auditory system is extremely sensitive to small spectral differences.
I think I figured out a systematic bias in this study (let's call it Study A). The Study A used TDH-39 headphones, which could presumably deliver crisp 10 μs square waves, with rise-fall times of about 2 μs, as it states on page 463.
Fig. 2 on page 463 depicts amplitude spectra as measured. Compare this to the theoretical prediction, as Fig 3 on the same page depicts. For single pulse, the theory predicts ~1 dB attenuation at 12 KHz. As measured (curve Ho = 65), the attenuation is actually ~40 dB, so that output signal already dropped below absolute threshold of hearing.
The author realizes this, noting on page 464: "With reference to the present experiment, we should expect then that experimental manipulations limiting the availability of high-frequency information must adversely affect performance". Nevertheless, he decides to proceed. At the end, he concludes what you cited about the spectral differences.
Let's now look at another study (let's call it study B), published in 2003 by Tatsuya Hirahara from NTT, called "Physical characteristics of headphones used in psychophysical experiments":
https://www.researchgate.net/public...headphones_used_in_psychophysical_experiments.
Couldn't he get that information from manufacturers instead? Well, see for yourself what they usually give:
http://www.schaffrath.net/tdhspecs.pdf
Let's look at how our old friend TDH-39 measures, according to study B. Such headphones are made as identically as possible, for decades, so that experimental studies conducted over the years could be compared. Because of that, the measurements in 2000s are relevant for the 1970s.
Fig. 3 on Page 3: Frequency responses of the TDH-39 on dummy head, IEC coupler, and actual ear. Big differences! They only really come together at 1 KHz. At 100 Hz, IEC coupler and actual ear are equal, but dummy head is down 35 dB. At 10 KHz, they come together again. At 11 KHz, dummy head and IEC coupler are "only" 10 dB apart, yet actual ear is 25 dB down from dummy head.
Fig. 12 on Page 6: Impulse response decay characteristics. TDH-39 is ~7dB down after 500 μs, ~14 dB down after 1,000 μs, ~19 dB down after 1,500 μs, ~23 dB down after 2,000 μs, and so on. It gets down ~40 dB by 3,500 μs. Extrapolating, it might be
only ~0.14 dB down after 10 μs. This is a ringy 10KHz-class headphone, rather than a well-damped 100-KHz-class transducer.
Now, it is reasonable to say that doubts about the suitability and precision of an experimental instrument, however serious they are, do not automatically justify discarding the results of an experiment described in Study A. However, this is only reasonable if a person expressing the doubts doesn't offer an alternative interpretation of results. I do:
The one or two pulses transfer momentum (force multiplied by time), not energy, to the TDH-39 diaphragm. The diaphragm doesn't move much during these short interactions, yet changes velocity. The diaphragm starts moving, setting into a pattern of decaying oscillation at its characteristic frequency, which is in audible range. The oscillations do transfer energy to the hearing system through the sound waves, and the hearing system responds to them in the regular way.
Since the momentum transferred linearly depends on the force application time, two 10 μs pulses transfer the same momentum as one 20 μs pulse, assuming that the first out of the two pulses didn't move the diaphragm far enough so that the applied force changed (this effect may explain small separation of the "Ho = 65" curves in Fig. 2). The same transferred momentum results in the same movement of the diaphragm, resulting in the same amplitude spectra, which Fig 2. strongly hints at.
However, the author assumes that energy, not momentum, was transferred by the pulses, and re-scales the results under this assumption. This leads to seemingly meaningful differences. To illustrate: let's take the force as a unit, then the momentum transferred will be either 10+10 or 20, which are same. If however, we assume that energy was transferred by the pulses, it will be 10*10 + 10*10 = 200 in the case of two pulses, and 20*20 = 400 in the case of one.
By assuming that the energy transferred by one pulse is two times larger than it actually is, the author introduces a systematic error of 3 dB. The effect differentiation threshold, stated in Study A as 2 dB, is thus smaller than the systematic error, which makes the conclusion of this particular part of study invalid. Since the rest of the study is based on the same erroneous assumption, the validity of the whole study needs to be reexamined.
