Does anyone know how to effectively set stereo delay parameters for creating realistic room acoustics?

[Master Mi]

This question has been on my mind for some time now whenever I use stereo delay effects, for example when I want to work mixing-technically with a filter stereo delay in combination with a cathedral reverb as in this visualized example:

But first to the basics of delay effects.

You often have the choice between synchronized or BPM-related (BPM = beats per minute) delay times and non-synchronized delay times, where you can set the delay precisely in milliseconds.

It's possible to convert the values between both delay modes - just take a look at this helpful link:
https://sengpielaudio.com/calculator-bpmtempotime.htm

The synchronized delay time can be more interesting for electronic music (or maybe also for avoiding too much phase issues), while the non-synchronized delay time can be more interesting for a natural and organic soundscape due to some irregularities (for example, by using settings such as 195 ms instead of 250 ms).

To have more freedom, precision and a better understanding of the delay time I'm using when setting the values, I often use delay effects I can set in milliseconds.

So, in my case with the non-synchronized delay settings of this image, a played note of the track with this delay plugin will get its echo(s) on the left side after every 250 ms and on the right side after every 500 ms.

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The feedback value, on the other hand, indicates how strong or how loud a sound event transitions to its subsequent delay or echo or how quickly it loses intensity/volume over time.

With a feedback value of 50%, for example, the subsequent echo will be half as loud as the previous sound event and the delay will flatten out relatively quickly as a result.

A value of 100 %, on the other hand, would create an endless echo with the same loudness as the original sound event.
With a stereo delay, the whole thing is obviously a little more complex, which is why you would have to set the feedback values on both sides to 100% for such an endless echo (and the signal must also not be absolutely dry).

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The pan value is easy to understand and sets only the panning of the delay effects of course (panning of the source signal won't be affected by this setting).
Just like for reverb sends, I would also recommend hard pannings for delay effects to avoid an accumulation of sound mud in the center area of the mix.

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The dry/wet value is the ratio between the loudness of the source signal and the loudness of its echoes/delays.
So, extremely wet settings with very silent source signals and much louder echoes might sound pretty wild - or weird.

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And since I used a really sophisticated filter delay with a low-cut and high-cut filter in this case, I can also set the frequency range for the delay effects.
In my case with the settings in the picture, the delay effects below the frequency range of 500 Hz will be filtered out or radically reduced loudness-wise.

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But now my core question.
How do you use a stereo delay effect plugin like this in a mix to create a natural and realistic spatial impression for a certain purpose?

Let's say that the source signal is located in a big cathedral (cathedral reverb activated) and might be used in 7 different situations, after you (the listener) just entered a large cathedral:

1) In the first situation, the source signal should play pretty much in the center of the cathedral (no special heights involved here - sound source should be at ground level or at the height of the human ears).
2) In the second situation, the source signal is still in the horizontal center of the cathedral, but it's shifted much more to the front side and towards you standing in the entrance area.
3) Similar case, but this time the horzontally centered source signal gets shifted towards the back of the cathedral.
4) In another situation, the source signal should play on the left side in the back of the cathedral.
5) In the next situation, the source signal should play much more on the right side in the back of the cathedral.
6) In the following situation, the source signal should play just a little less far on the right side and a little less in the back of the cathedral. 
7) In the last situation, the source signal should play on the right side in front of you around the entrance area of the cathedral you just entered.

How would you set and change the delay values (especially the delay times for the left and right side, the feedback and the dry/wet parameters for the left and right side) for these situations in order to create a realistic and natural spatial impression (maybe also in connection with shifting some of the reverb parameters)?
Maybe somebody also knows how to create a further impression of height above the ground level for a sound source in a cathedral just with delay effects like these.

Might be a tough question even for professional audio engineers and die-hard physicists, but maybe someone already geeked out into topics like these.

Edited June 12 by Master Mi

[paradiddlesjosh]

Howdy, Master Mi! Besides calculating time-based effect durations, you can also use this calculation to place studio monitors in your space.

First things first: the speed of sound through a given medium depends on the medium's density (and temperature). At room temperature (20C or 68F), the speed of sound through the air is 343 meters/second (about 1,125 feet/second), slower at lower temperatures and faster at higher temps. To calculate space in time-based effects like reverb and delay, that's 343 millimeters per millisecond (343 mm/ms) or about 1.125 feet per millisecond (1.12533 ft/ms).

Next, sound waves radiate from the source -- almost perfectly spherical in lower frequencies and more directionally as the frequencies climb. A spherical room with a radius of about 11.25 feet will have early reflections (i.e. bounce off the walls) at 10ms. Of course, no room is spherical; most are rectangular prisms or combinations of 3D shapes, so you'd need to measure the distance from a given point in a room to all the faces (walls, floor, ceiling) to determine the travel time for the sound to reach that point from the wall and vice versa. Because higher-frequency sounds have smaller wavelengths, they lose energy faster than lower-frequency sounds. For especially large rooms like your cathedral example, it'll be necessary to roll the high frequencies off in your reverbs and/or delays for realism (and lower frequencies for mix balance). I like rolling off at 360Hz (high pass/low cut) and 3600Hz (low pass/high cut) as starting points but play around with these to suit your production.

Regardless of the other dimensions, the average height for human males is about 1.77 meters (5.8 feet), while human females stand at about 1.63 meters (5.35 feet) so the time for a sound to travel from human-ish height to the floor is about 4.75-5.1 ms (1630 to 1770/343 or 5.35 to 5.8/1.125). But unless the sound source is facing the ground, most of this first reflection is likely not getting through your HPF. For the distances to other surfaces, convert the distance to either millimeters or feet and divide by either 343 (mm/ms) or 1.125 (ft/ms).

It'll be up to you to decide how big you want this cathedral to be and calculate accordingly. You can also fudge those delay timings to simulate a colder or warmer room -- e.g. at 0C or 32F (freezing point of water), the speed of sound is about 331 m/s (1086 ft/s), or 331 mm/ms (1.086 ft/ms), so the time to the floor is about 4.9-5.3 ms. Not much slower for the first reflection, but the difference is more noticeable for further surfaces.

Edited June 12 by paradiddlesjosh
Added female average height and calculations

[Master Mi]

Thanks, @paradiddlesjosh.

Man, that was an even more detailed in-depth answer than I had expected.
And somehow it triggered a sense of déjà vu in me, as if we'd had a similar conversation some time ago.

It would certainly be more interesting to see to what extent such plug-in settings in delay and reverb can be used to acoustically recreate even more complex room structures, different types of surfaces or even temperature differences.

But my main concern was how to set primarily the stereo delay in such a way that it has a realistic effect in terms of panorama and depth.

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So let's say you have the stereo filter delay settings as in my picture in the main post - the activated stereo delay with the 250 ms delay on the left and the 500 ms delay on the right (as well as the other parameters in this filter delay).

Is this basically a stereo delay setting that would be panned rather to the left or right side in the panorama (so that it would conform to the laws of physics and not come across as unnatural)?

And how would you change all the parameters in the stereo delay accordingly if you then moved the signal to the other side of the panorama in mirror image (for the same room reverb, of course)?

Or how would you change the parameters in the stereo delay if you wanted to move the sound source more into the foreground or more into the background of the room (I'm not quite sure whether you can work with the integrated low-cut and high-cut filter in the stereo delay in the same way as with the reverb, or whether the psychoacoustic effect would be different in a pure delay plug-in)?

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I mainly ask these questions because I often use similar stereo delay settings with similar parameters without really considering the panorama (panned more to the left or more to the right side) or the depth level (sound source put more in the front or more in the back of the room) of the sound source.

And I guess that's not the way to use a stereo delay in the best possible and most effective way (especially not if you want to create a realistic and natural room ambiance).