Depth perception is indeed mostly down to the reverberant signal to direct sound signal ratio. But another important cue is due to HF absorption of the air, so brighter sounding sounds are perceived as closer. Quite how the brain determines that the frequency response of signal is degraded I don't know; perhaps the brain subtracts the frequency response of reverberant to direct to get a another depth cure, or perhaps its simply bright sounds is inferred as being closer.
For sure, if the reverberant signal is attenuated or distorted with respect to the larger direct signal then depth perception suffers. Indeed, in all of my career of listening and then explaining the results of listening tests, small signal non-linearity is the only factor that I have correlated with depth perception. With noise shapers you get distortion of very small signals, in that signals below the noise shaper noise floor are lost and signals that approach the noise shaper noise floor have reduced amplitude. This is why fundamental linearity measurements are important, as they show the amplitude of small signals changing with level. Using FFT's with the result calibrated at -60.000 dB, then re run the test at -120 dB you check that the level is actually -120.000 dB (with results adjusted for noise). Using my Pulse Array DAC's you get pretty much perfect results (no consistent error). Conventional delta sigma have measurable errors, R2R DAC's have even more, as its impossible to match resistors accurately enough.
In the bad old days, when my designs had significant fundamental linearity errors, improving this problem did lead to better depth perception. Moreover, when I used to design cables in the 80's, one could always hear a correlation between conductor purity, metal surface oxides and depth perception. In this case, the oxides in metal to metal interfaces (crystal to crystal inside the wire and contact to contact) create small signal non linearities, with resistance being a tiny bit higher for small signals than larger signals. But although it was easy to hear depth being degraded, you could never measure this distortion.
Before the Dave project, my target for noise shapers was better than 200 dB distortion and noise performance. that's around 1000 times more capable than high end noise shapers. But with Dave I had ten times more gate capacity than ever before; also whilst listening to different noise shapers when developing Hugo I could hear large changes in depth perception. This indicated that my assumption that 200 dB was good enough was not correct.
At this stage I should indicate that there are actually two entirely different distortion mechanisms that are important to noise shaper designs (there are other things but this is the most important). These are:
1. Noise floor modulation. This is where the noise floor modulates with signal level - so large signals give greater noise than small signals. The brain is remarkably sensitive to this problem, and can easily hear unmeasurably small levels; it perceives it as smoothness or warmth to the sound when the problem gets smaller. With gross noise floor modulation you hear it as grain in the treble. Now all DAC's (except mine) have very large and measurable noise floor modulation, which explains why they sound harder (they normally add some 2nd harmonic to fatten up the sound to hid the innate lack of warmth). Additionally, reducing noise floor modulation improves instrument separation and focus, and you reduce the loudest instrument taking your attention problem.
2. Fundamental linearity - how accurately small signals are reproduced (small signal linearity). Now this only affects depth perception, it does not do anything else. And I have not come up with any change in depth that wasn't explained by small signal linearity.
Now a noise shaper has both problems - making a better noise shaper with say 220 dB performance than 200 dB will have lower noise floor modulation and better small signal linearity.
So when I designed a 220 dB noise shaper and listened to it, I could easily hear better depth - and maybe a bit smoother. So better than 200 dB is a good rule of thumb for noise floor modulation, but certainly not for depth. Indeed, over a 90 day period I constantly improved the noise shapers and came to the absolutely remarkable and frankly amazing conclusion that there was no limit to how good the noise shaper needs to be in order to resolve depth perception. I ended up with an very complex 17th order noise shaper that had 350 dB performance.
With 90 days of work and getting an improvement every day in depth, I could hear now a cavernous depth perception. This is very exciting, as its long been a major problem of mine that one can hear depth so accurately in real life, but high end audio sounds flat as a pancake. Listen to a real organ and choir in a cathedral - if you are 100 feet away and shut your eyes, it sounds uncannily 100 feet away. I am now starting to get something like that depth perception with loudspeakers - but I guess the weak link now is the ADC, which is my next design challenge.
Now when I first got to 350 dB performance (that's the best I can do with available FPGA and flip flop speed) I was simply amazed that the brain was so sensitive. How can it detect such small errors? Perhaps its down to something else, and the noise shaper number is merely a proxy for something else going on in the analogue domain. But recently (a month ago) I upgraded internal digital (no analogue consequences at all) noise shapers within Dave from 220 dB to 350 dB - and lo and behold depth did get much better. So that suggests that the brain really is sensitive to absolutely no error for small signals. But it still perplexes me that minute effects can be so easy to hear.
But this brings me full circle. I have always been puzzled that cable small signal non linearity was never measurable and if its true that -350 dB performance is necessary then this proves why we can't measure cable effects - they are simply too small, and the brain is just too sensitive.
Funny that work in noise shapers can solve a puzzle with metal purity with wires...
