Good questions, and not so easy to answer.
1. Take a regular 48k/24b recording; that has samples every 20.8 uS. We know that the ear/brain is at least as sensitive to 4 uS (my subjective evidence suggests it's actually a great deal more sensitive). Also, we know that if we use a sinc function we will perfectly reconstruct the original bandwidth limited signal; we also know that if we do not use a sinc function the transients will not be reconstructed accurately - they will be a little too early or too late. We also know from psychoacoustics that transients are essential from a perception POV, as they are used by the brain to compute pitch, timbre, rhythm and instrument separation. The M scaler takes the 48k signal and then converts it too 768k with a guaranteed 16 bit accuracy - as the M scaler is the same as an ideal sinc function to better than 16 bits - so it will recover the bandwidth limited analogue signal to better than 16 bits. We now have a 768k recording, with an output of every 1.3 uS now, which of course is much easier for the brain to deal with.
2. But some questions remain. Every time we double the sample rate, the size of the area of the transient error gets 4 times smaller; and with a 16 times increase in sample rate we have a 256 times reduction in the area of the error - but even with a 768 k output we can still get a small transient error. Now this is still audible, and that's where the second WTA filter in my DACs takes over - and this takes the 768k signal and converts it too 12,288 kHz, or a sample every 88 nS, and this filter is still audible, even though we are now dealing with very small timing errors. So yes timing errors above 768k are subjectively important - and it's an aspect I am still researching into. We will eventually hit two barriers - there is no point in getting more accurate transients if the DAC can't accurately resolve it when the DAC converts it too analogue - and there is no point in reconstructing transients to a higher accuracy than the ear/brain can detect. It's these aspects I am looking into.
But there is something special about hitting 768k. The 768k recordings I have sound very different to 384k recordings, and have the qualities that the M scaler gives; this suggests that there is something special about hitting the 1.3us accuracy of 768k. And certainly, the WTA 2 filter currently does not sound like the M scaler - it only seems to affect the ability to perceive the starting and stopping of notes, not pitch, timbre and instrument separation, which happens when you get to 768k.
3. From a processing POV going from 384 to 768 involves exactly the same number of multiplications and processing as 48k to 768k; it's just the filter updates its input samples at a much faster rate, but the M scaler does exactly the same work. Also, the benefit of 16 bit reconstruction when using 16 bit files is obvious - but with 24 bits what do we need? Again, this is another aspect that I am researching into.
I hope that clarifies it for you. In short there are indeed more questions that need to be answered...
Thanks very interesting indeed to read.
My VERY limited knowledge of digital theory does not allow me to follow and understand everything in absolute detail. But I DO know what can hear via my HMS/Qutest and it has fundamentally changed my take on rbcd 16/44.1.
This morning I have just listened to an early digital BIS recording from Gothenburg with the GSO playing Sibelius's 7th symphony with great pleasure!
The recording was made with only THREE Neuman mics in the good acoustics of the Gothenburg hall with SONY's PCMF1 in 1984!
And what I have just heard sounded almost like hearing a mic-feed from that hall.
Playback via PCM F1 did not sound that good in those days.
Strings could sound a bit steely via that ADC.
I am amazed on a daily basis at how many more recordings I can now really enjoy not only for their musical and performance qualities, but also how very realistic 16/44.1 can sound via HMS.
I mentioned those early digital recordings in some posts here after my return from Asia earlier, and via the stock BNC they did NOT sound as good as I had hoped. But now via upgrade BNC cables they do.
And the difference is not subtle to me.
The coherence and realism,how this orchestra actually sounded playing live in their good hall with these early three mics only 16/44.1 recordings via HMS actually sound more realistic to me than BIS's multimic'd Sibelius symphonies recent remakes from Minnesota.
I was invited to those sessions too, but I would have had to pay for my own flight so I declined the offer.
But I have been to quite a few recordings sessions and many concerts in Gothenburg.
It truly sounds as if I am listening to the analogue signal before digitizing with many of those early cd's now.
But yes really well recorded hi res can sound even more realistic, which brings me to the question of which ADC can record at 768khz?
Didn't you mention 256M taps needed to recover 24 bits to the same level as 1M taps can with 16/44.1 two years ago?
The only PRO ADC's which I am familar with are still limited to 24/358 or DSD 256 which I have heard in use at recording sessions.
Have you already made test recordings with a prototype Davina or from which ADC did you get native 768 recordings?
Cheers CC