Another moment ..
I tried to draw parallels in visual perception, auditory, in music and photography. For clarity.
For vision, you can build a graph of frequency-spatial perception. It reflects the strength of perception, depending on the size of the object.

In photography, one of the characteristics of the resolution is the graph of the MTF.

I would draw parallels between sound perception and visual: pitch = angular size of the object, volume = brightness (film photography = vinyl sound).
A film photograph, gave way to a digit in resolution, dynamic range, sensitivity, convenience and speed, but so far the film exceeds the figure by the quality of tonal ratio transmission. As well as vinyl .. With these carriers we get convex, spatially-volumetric results, which make us look closely and listen .. are in themselves something mysterious.
Yes, the digital photo is sharp, bright, authentic (in this incredibly accurate). But it's worth taking a closer look at the small details that go into the darkness and there we find horror and pain. Plasticine. Small hair becomes a metal wire, texture of a stone-plastic. And the film in these places is mysterious.

In translation to sound - it's quiet and high sounds (without leaving the thresholds of perception).
This is the fault of the frequency filters. Therefore, in digital sound we have plastic and plasticine in low high frequencies.
In the photo, the dark tones are less bit and in the sound the quieter sound is less bit. In these places, where the ear and eye are still sensitive, the figure saves and introduces obvious distortions.
Even the most modern camera Nikon D850 has such a sin (well, there is no frequency filter in front of the matrix, which lowers the clarity)

In this regard, I will give a video:
(Immediately I apologize - the picture is twitching terribly - my computer can not cope with such a load) (the graphics display the sound that comes out of the socket of the headphones of the sound card and is fed to its input, ie, there is a digital-analog conversion and then an analog- synthesized sound).

https://youtu.be/RdiYSXcCqm0

Firstly, the oscilloscope shows what kind of distortions occur in the frequency above 5000-8000 Hz at a sampling rate of 44100 Hz. (this is still quite audible range). It is noticeable how the wave size is measured with a sampling rate. Perhaps this should be smoothed out (and smoothed out), but here we already have a loss (this is how to apply noise in the photo - small details are removed and becomes flat and lifeless). At 192,000 Hz only small distortions occur at the boundary of the audible range.
Secondly - pay attention when I use a small pitch in the tenths of a cent. It is clearly visible how the volume of the signal changes. Maybe it's the features of mathematics in the miscalculation of the sinusoid, but apparently it sags at some frequencies, and on some resonates.
When (in video) I use a "square" sound that has a lot of overtones, then using a small increase and decrease in tone (per cents and cents), you can clearly see how the volume levels in the overtones change wave-wise. Does Pianoteq have problems with this? Have they been resolved? After all, the piano sound is constantly moving in height with all its overtones.
Third, noise is used to hide the artifacts of digitization. But what is this noise. His nature is unnatural, his ears are bleeding (as well as in the photo - digital noise simulation .. horror.). And the quieter the sound, the closer it is to noise, the more distortions it receives a useful signal. Moreover, it becomes disgusting. But vinyl noise, the film noise has some nobility and natural softness. (although at the time they fought this critically).
In the fourth, all the surrounding sound is not static, it constantly changes in height .. sometimes at the very smallest parts, and that's probably the case, and settles most of the distortions when digitizing ..
Format 44100-16 was introduced when people tried to record a high-quality digital sound on the most volume at that time media-video cassette. It was such a quality that was a technical alternative for the possibility of recording and reading in this format of media. (that would be close to the formats of PAL and Sekam). Since then it seems sufficient. But now we have incomparably faster computers and are much freer in terms of storing data volumes. Our Internet channels are incredibly fast. So why deprive our subtle body - hearing, the possibility of a spatial adequate, undistorted presence?
Proceeding from the technical side of the DSD format, it seems to me that this format is most adequate in terms of the transmission parameters of all sound criteria critical for our hearing.
And let this all be fantasy, esoteric .. not scientific .. but I feel so ..

OK, here's an observation that some may find interesting: I have ptq Standard, which of course is limited to 48khz. However, I noticed a while ago that I can set a higher sampling rate for my audio interface. Hmm, I wondered, is there any point in doing that... well, what the heck, let's try it anyway - so I tried 96khz (I also tried 192, but my CPU didn't cope too well with that). To my ears there was a subtle, but noticeable improvement at 96 - more refined, with more 'space' around the sound. Some people might not notice any difference at all, and it probably depends on the interface and how well it processes the samples. It's way beyond my technical knowledge, but I'm pretty sure I haven't fallen for an aual 'placebo effect' - there does actually seem to be a difference.

I can also play at 96khz while I have the standard version. But I think this implies some kind of resampling that should have a cpu cost and increase the risk of dropouts.  I also hear something different with more resonance but I am not sure I like that.

Check it out - it's about 13 minutes into this 30 minute video.  The benefit of higher frequency recording is that it allows building low-pass filters that function better, with less artifact, making the recordings sound better, even though our ears still aren't hearing better than 20KHz (for those of us who are so privileged):

https://www.youtube.com/watch?v=FG9jemV1T7I

Since I purchased a sound card that supports high sampling frequency, I decided to make an attempt to check the difference in sound with different sampling rate settings. I recorded the midi:

midi

Using the following FXP settings:

FXP

And the file was generated at 192,000 kHz and 44,100 kHz. :

192,000kHz

44,100kHz

When listening for me, there are differences in the greater nobility of sound. The high sampling frequency has more spatiality. You can clearly feel the soft, slow, spatial rocking sound. A more specific arrangement of the sounding overtones in the sound picture. The softer interactions between them. There is a sense of the ocean. Against the frequency of 44,100, where it all dissolves, there is a stereotype, but without a sense of depth. At 192,000 this sound spatial flicker and slow overall wiggle I find to a very large extent realistic tool behavior. So soft for the ears ..

When loading into the Isotope RX, small visual differences are visible in the frequency chart.

There is some difference in the sound duration of the sound (from the 12th second):

192,000kHz - 12 sec

44,100kHz - 12 sec

At a frequency of 44,100, one clearly noticeable overtone comes out to the fore. There is a feeling of itching and unnaturalness. At a frequency of 192,000 it merges into a common natural picture and does not manifest itself as a foreign matter.
In this regard, there was a bad and crazy idea (you can throw stones): can there be such a situation that when a few notes sound, the processor calculates them with a certain speed.
Of course, I do not know how this process happens in time, but it is possible that the calculation takes place somewhat cyclically. Accordingly, the cyclicity of the calculation of the mass of notes has some repetitive frequency, which can correlate, for example, with the sampling frequency and lead to some distortions in the form of interference, which in turn introduce distortions and cloud the spatial picture, and sometimes distort the timbre (making it " electrical "). It looks like artifacts arising for example when scaling images or fonts without applying anti-aliasing to a specific screen matrix resolution. There are "burrs". And in sound this is manifested as a clouding of spatial clarity. Either distortion of the instrument's timbre ..

I verified your and Gilles's graphs at 48kHz and 192kHz sampling rates. I also tested keeping the DAC and DAW software at 192kHz and switching the PT SR from 192kHz to 48kHz and it appears to have very little impact versus keeping it aligned with the DAC and DAW at 192kHz. The fundamental and overtones at 48kHz are much more defined, but at 192kHz are smoothed and flow into each other.



honjr wrote:

... but the graphs show two different volumes (decibels) and the lengths of the horizontal scales differ, making the top graph more compressed thus giving it a denser appearance.

They are positionned differently horizontally because of the higher sampling rate for the 192 kHz file, but the scaling is the same. There is no visual compression. Measure the space between corresponding ticks and you'll see. The vertical scale goes a bit higher for the top graph, but the partial values are similar (see the 98 Hz G2 value). It's just that there is more of them for the 192 kHz file.

EDIT: In fact, the question is: does pianoteq generate a better result when using 192 kHz than say 48 (what I use) EVEN THOUGH there is no frequency generated higher than 8 or 10 kHz (for the piano). Is there more quality in the computation of the model, at least at low frequencies where there is more overtones. This could maybe satisfy people wanting a better result for better computers since it would be precisely an answer to that quest...

I don't think it would matter if there were higher freqs or not. The higher\faster sampling rate would just capture more of the "phantom" freqs that appear so briefly that individually they barely register, but cumulatively make a difference. If I understand correctly, the situation is similar to that of early motion picture cameras. The fewer number of times that the shutter closed per second, the less motion was captured, and the more jumpy the motion when the movie was watched. If we were to combine all of the stills from the roll of an old camera and all of the stills from the film of the same action from a later camera that rolled at 24 frames per second, and analyze the quantity of a particular hue, we would see that there is obviously going to be a greater quantity of that hue in the later camera. And a wider spectrum of nearby hues that shade into that hue, since the later camera would have caught more moments when the actor or horse was exposed to different degrees of light and shadow. Stepping out of the analogy, I would imagine that a faster sampling rate would capture more of the stages in the volume fluctuations of everything that was vibrating, as well as more "near-partials" and noise that appear between the frames of the lower sampling rate.

As far as I know, it's the last note of the same MIDI file posted by scherbakov.al rendered at two different sample rates.

Well, when I have time I'll do the same thing with my setup (just have to find a good frequency analyzer). The effect, if genuine (of which I have no doubt at this stage) COULD be the result of downsampling. Also, scherbakov.al's mp3 example COULD also be the result of downsampling differences (two differently tuned downsampling filters applied to the different SR's), or even dual downsampling discrepancies if scherbakov.al converted two files that had already been downsampled (or one of them was downsampled and the other was not)... but the graphs are rather striking! I did read hastily that some engineers like having higher sampling rates, and others hate having them. They seem to agree that downsampling, even from 192kHz to 44.1kHz, often results in inferior sound quality. I would surmise that engineers have come up with some good filters and up- and down- sampling algorithms for all sampling rates (but probably have not successfully implemented them in all consumer DACs) and that depending on the device and software (e.g. PT) higher rates can indeed sound better to some.

honjr wrote:

... but the graphs show two different volumes (decibels) and the lengths of the horizontal scales differ, making the top graph more compressed thus giving it a denser appearance.

They are positionned differently horizontally because of the higher sampling rate for the 192 kHz file, but the scaling is the same. There is no visual compression. Measure the space between corresponding ticks and you'll see. The vertical scale goes a bit higher for the top graph, but the partial values are similar (see the 98 Hz G2 value). It's just that there is more of them for the 192 kHz file.

EDIT: In fact, the question is: does pianoteq generate a better result when using 192 kHz than say 48 (what I use) EVEN THOUGH there is no frequency generated higher than 8 or 10 kHz (for the piano). Is there more quality in the computation of the model, at least at low frequencies where there is more overtones. This could maybe satisfy people wanting a better result for better computers since it would be precisely an answer to that quest...

Correct - looked confusing without measuring. Clearly something is going on here, and the differences are rather extreme, and probably only partly based on slight volume differences, and I too do not know what it is that's making them so different! If the note(s) was(were) struck identically and under virtually identical circumstances, then your data indicate that they would indeed sound differently under the two rates.

... but the graphs show two different volumes (decibels) and the lengths of the horizontal scales differ, making the top graph more compressed thus giving it a denser appearance.

They are positionned differently horizontally because of the higher sampling rate for the 192 kHz file, but the scaling is the same. There is no visual compression. Measure the space between corresponding ticks and you'll see. The vertical scale goes a bit higher for the top graph, but the partial values are similar (see the 98 Hz G2 value). It's just that there is more of them for the 192 kHz file.

EDIT: In fact, the question is: does pianoteq generate a better result when using 192 kHz than say 48 (what I use) EVEN THOUGH there is no frequency generated higher than 8 or 10 kHz (for the piano). Is there more quality in the computation of the model, at least at low frequencies where there is more overtones. This could maybe satisfy people wanting a better result for better computers since it would be precisely an answer to that quest...

192000

Convert to mp3 also you can find the difference ..