But there's excaly no reason to stick to e/g a "Butterworth" type filter.
I agree that the standard calculation is not a matter of the Butterworth characteristics which is rather unimportant in a reflex design. It is the calculation of the resulting resonance frequency in the enclosure w/o port or radiator. Making the enclosure smaller and smaller than suggested (1/4th of the liters in this case) you push up the resonance and reach a situation in which no reasonably low reflex tuning is possible.
Why is the tuning not lowered down to 40Hz? Are the passive radiators too heavy already?
It should be possible to make them heavier but this might result in even less deep bass level, and many radiators become audibly ´wobbly´ when overweighted. The active driver itself and the air inside the enclosure are the limits here. If you tune the PM lower without adjusting volume and driver, you end up with the radiator producing very little SPL effectively in its resonance frequency band plus kicking the driver to enormous excursion in the region between the radiator´s maximum output and the tuning of the driver. It is usually a bad compromise.
If you want to put the reflex tuning even lower than 47Hz effectively, you need a different driver or much much more of enclosure volume. But: which driver allows a reasonable reflex of <45Hz tuning in 3.7l delivering flat response and keeping excursion acceptable over all the bands? I do not know a single one.
I still don't get the notion of someting 'natural' with a technical device.
´Natural´ was meaning solely the bass from the given driver+enclosure w/o heavy EQ or boost.
Second, that signal manipulation makes me shiver. It may work, but that is not what fidelity in reproduction should be. Reason is, that it is not flexible. It may be "good enough" for some type of musical entertainment, full respect from my side. It may fall apart with some other music.
Speakers of such volume always pose a compromise. There is no ´fidelity´ in terms of perfect bass impulses and max SPL w/o noticeable compression or other side effects. Every reasonably sized home speaker will have its weak frequency bands bringing either high-pass filtering, compression, impulse response or distortion to an audible level at medium-high SPL.
I have collected a personal listening test playlist of roughly 1,000 tracks solely for bass testing over the years. Give me a compact home speaker and one or two hours to find out which track will make it compress, limit, boom, distort, puke, grasp air or cut off lower bands. The last (and most compact ever) speaker to pass this test was equipped with a CB 12" dedicated subwoofer in roughly 32l net, pumping 500Watt RMS into the bass driver alone.
Everything below is a compromise and not suitable for each and every imaginable track containing bass. There are better concepts and less ideal ones. In recent years the knowledge on DSP and how to manage limited resources has made astonishing leaps. I would say that well-engineered active DSP speakers offering 1.5 or 2l per bass driver will surpass passive ones of the same size in terms of how the bass sounds and how many tracks will be reproduced on a satisfying level. I recommend to listen to Klipsch Detroit to get an idea.