I’m not familiar with the rearward polar response of the 8Cs, so I'll mostly restrict this to attempting to answer the non-8C related question. Sorry if any of the following is repeating what you already know
The short oversimplified answer is that with a short distance from the speaker to the front wall you’ll get a broadband 6dB boost from the low bass up to approximately the frequency of wavelength 4 times the distance from the front wall to the acoustic centre of the woofer, and then a series of decreasingly severe higher frequency nulls (eventually resembling more a comb filter effect) up to the point at which the speaker stops projecting significant rearward energy. At 20cm, for example, with typical box speakers this will most significantly result in a nearly 6dB boost from 0 Hz to just under 430Hz, then a very deep null at around 430Hz, then further nulls (of decreasing severity) higher up in frequency, until eventually the response flattens out at the point at which the speaker projects so little sound rearward that interference between the front wave and the reflected back wave becomes negligible.
The longer answer is as follows:
Firstly, the distance from the speaker to the front wall determines the
extent to which the direct sound and the reflected sound from the front wall interact at the listening position.
The shorter the distance, the closer in level the reflected wave from the rear wall will be to the direct wave from the woofer at the listening position. So, as the speaker is moved closer to the front wall, the influence of the reflected rear wave on the frequency response at the listening position becomes more severe. At a distance of 20cm (assuming a typical say 2m+ listening distance and a purely reflective front wall) there will be a difference of only one or two dB between the direct and reflected waves, meaning maximum interaction. The first result of this will be a large broadband
boost at the listening position to frequencies up to the frequency 4 times the wavelength of the distance from the front wall to the woofer's acoustic centre.
Secondly, the distance from the front wall determines the
frequencies at which that the rear reflected wave and the direct wave interact (sum and null).
To illustrate, take your example of a 20cm distance from the front wall (I'll assume this is 20cm from the acoustic centre of the woofer). 20cm is 1/4 wavelength of about 430Hz. So at this frequency (assuming the speaker is omni, which it will more or less be at this frequency if it is a conventional box speaker), the reflected wave will bounce back and combine 180° out-of-phase with the direct wave, creating a deep null. The same will occur at various higher frequencies if the speaker is projecting significant rearward energy at those frequencies too. Meanwhile, in between these nulls the reflected wave from the front wall will be
in phase with that of the direct wave, resulting in summing (i.e. narrowband boosts of up to 6dB).
If the reflected wave is almost as high in SPL as the direct wave (which it will be if it's travelled only 20cm before bouncing back, and if the front wall is basically reflective), the cancellations at these frequencies will be almost absolute. Here is a graph which assumes a listening position of 3m, an omni source at all frequencies (obviously false at mid-high frequencies for a monopole box speaker but used here to illustrate), and a purely reflective front wall. You see massive nulls beginning at the frequency with a wavelength of 4 x 20cm, i.e. 430Hz. This first null in particular will tend to destroy the midrange.
View attachment 15182
As we move the speaker away from the front wall, the difference in SPL between the direct and reflected wave increases, meaning that (1) the
extent of the interaction becomes less extreme, and (2) the
frequency at which the waves begin to interact decreases. Meanwhile, the distances between peaks and nulls at any given frequency above the 1/4 wavelength frequency become closer together, so that the peak/null behaviour begins to resemble a comb filter at a lower frequency.
Here is the same idealised example (omni source, 3m listening position, purely reflective front wall), but now with a distance between the woofer's acoustic centre and the front wall of 1m. As you can see, the overall boost is now not as great, and the nulls now begin lower in frequency, are far less pronounced, and closer together at any given frequency. The frequency of the first null is now that of wavelength 4 x 1m = approx 86Hz.
View attachment 15183
What these idealised graphs don't show (among other things) is that, in reality, a monopole box speaker will tend to become less omnidirectional as frequency increases, i.e. the differences in SPL between the direct wave and the wave reflected off the front wall will tend to become greater as frequency increases. In most cases, a typical modern narrow-baffle closed box speaker will be truly omni only up to about 300-500Hz depending on baffle width and speaker depth, and will project very little rearward energy above around 1 or 2KHz, so there will be little interaction above these frequencies. In other words, the graphs above will begin to look less boosted and less ragged above around 300-500Hz. This transition range in which there is some interaction, although not as much as the graph assumes for an omni source, will tend to continue up to about 1-2KHz, or whatever frequency the speaker stops producing significant rearward energy.
In terms of how to deal with this, as a general rule, for decent midrange reproduction you’d want to keep the distance from the woofer(s) to the front wall at least around a metre, which should reduce the magnitude of the peaks and nulls to under 6dB in most real-world cases, and keep that first widest and deepest null down below the Schroeder frequency (more on this below). In a studio context, I also try to solve this problem two additional ways. Firstly, I use broadband front wall absorption that extends in frequency to below the 1/4 wavelength distance to the woofer (or the point at which the woofer crosses to the subs, whichever is higher). Best is usually dense, thick rockwool with an air gap between it and the front wall (obvs not practical at home). Secondly, I try to ensure that the cancellation distances between the woofer and each of the front wall, ceiling, floor and sidewalls to the listening position are all different; remember that a similar effect occurs not just with the front wall, but with all the room's first reflection points. By ensuring these distances are all different from each other, nulls due to out-of-phase first reflections are spread out in frequency (this is still difficult, but often possible, in a home context).
Use of subs is another way to improve the situation, since these can be placed along room boundaries so that there is no cancellation within their operating frequency range from reflected waves bouncing off first reflection points (the frequencies reproduced by the subs have long wavelengths so the distance from sub to wall will never approach 1/4 wavelength when placed along room boundaries).
Ofc none of this takes into account room modes, which tend to have the most significant impact on the response below the Schroeder frequency, and which require a whole additional set of room treatments and considerations to mitigate. For this, best to use corner bass traps and at least two subs (also positioned along room boundaries).
Finally, it's always a good idea where possible to get the first reflection nulls (especially from the
front* wall) below the frequency at which the mains cross to the subs. As mentioned, the subs can then be placed along the boundaries, avoiding any first reflection-related nulls. And then ofc to try to fix any remaining problems using DSP if possible...
Regarding the 8Cs, if they do indeed project very little rearward energy, it can be assumed that this will result in zero or negligible boost/cancellation from front wall reflections. So both the broadband boost and narrowband nulls shown in the above graphs will basically disappear down to the frequency at which the 8Cs cease to effectively control directivity (wherever that is - I think around 100Hz IIRC).
(NB: I believe there would still be similar broadband boosts and narrowband nulls resulting from floor and ceiling reflections, since AFAIK the 8Cs are constant directivity horizontally but not vertically. I haven't seen measurements of the 8C's vertical polar response, however, so I'm not sure about this.)
The 8C's ability to dispense with these front-wall related nulls is an excellent thing; the trade-off, however, would be a flatter power response, resulting in less low-mid frequency broadband boost. This is just speculation as I don't have a full picture of how the speakers measure, but this may lead to them being perceived as thin/bright due to the fact that we (and perhaps more importantly, the engineers who mix and master our music) are used to the room/speaker interaction providing a broadband boost to low and (to a lesser extent) mid frequencies, in-room.
*edited to correct mistake