To reiterate, it's a simple question: what specs does one use to make an informed decision about which sub to integrate into a given system? Hopefully you agree that choosing a sub by cone diameter does not make sense.
It is not a simple question, especially since your use case is well outside the mainstream. To reiterate, no one attempts to listen as loud as you claim to want to with your size constraints, space constraints, and budget constraints. What you are attempting is not normal, therefore you will encounter little actual practical experience with that application.
The answer for most people in domestic situations is "good enough is good enough." This assumes passive speakers. Allow me to elaborate on the process using myself as an example.
My application is a combined home theater and listening room. Passive speakers are Revel F206, which are sized appropriately for the space and have an in-room F3 of 32Hz. My goals are to:
- Extend in-room bass extension down to below 20Hz
- Increase low bass SPL at least to THX reference level
- Smooth bass response in the room (help with room modes)
- Reduce distortion in the stereo pair.
Other criteria include at least two subs to fill in room nulls, and they must be small-ish.
I read objective reviews and settle on a pair of
SVS SB-2000 12" sealed subs. They extend below 20Hz (meaningful bass will extend below 10Hz with boundary reinforcement) and are each capable of ~115dB at 30Hz according to CEA 2010 measurements, which is more than enough.
I take a day to carefully set them up via measurements: position, phase, crossover frequencies and slopes, levels, verify my results, and in the end, "good enough is good enough." The selection approach is hardly scientific, and the setup process is informed experimentation, AKA trial and error.
The result for critical listening is I can now push my stereo pair as loud as I want to without audible distortion--far louder than I can stand, and midbass clarity is improved because cone excursion of the 6.5" woofers is greatly reduced, as they are no longer trying to produce frequencies below ~70Hz.
^ The problem with the above result is that my speakers were not distortion-limited in the first place. Adding the sub made them cleaner, but I do not listen any louder, because I do not like to, which limits that benefit. My preference for loudness is high 70s to low 80s nominal, and that does not change because I technically can listen louder without distortion. I do not benefit from goal number 4 in real life. Bookshelf speakers benefit far more from this than towers.
Your situation is more complex using active speakers:
- Active speakers are power-limited
- Active speakers have protection circuits
- No one does what you are trying to do with small actives.
Taking these one at a time...
1. No matter what you do with subs, actives always run up against power limitations. You will gain some SPL by high pass filtering the stereo pair, as the amps are less stressed by not having to attempt to drive low frequencies, but there are still limits. And, you cannot throw more power at them like you can with passives.
2. Similarly to the above, actives often have several protection circuits to protect the circuits and drivers. You cannot get around this.
3. The closest area of expertise I can think of to your application is a sound designer who sets up studio control rooms, mixing studios, mastering studios. But, they do not try to reach anywhere near your expected SPLs. They are designing for the high 70, low 80 nominal dB used by those engineers. They do not have criteria for damaging people's hearing. Further, those who mix and master classical music often use passive speakers with high power amps and/or huge active monitors. There is little to no precedent for your use case.
A few words on using subs to reduce distortion...
As has been stated in this thread, you can reduce woofer distortion in the stereo pair by high passing them and filling in the missing frequencies with subs. We are not terribly interested in low bass distortion, because we are not terribly sensitive to it. In a two-way speaker, this reduces midrange distortion, because the high pass filter reduces cone excursion of the driver responsible for bass and midrange up to the crossover frequency, and this is where the real benefit is. Distortion reduction is not limited to the sub / woofer crossover frequency; the benefit extends much higher than that. Things get even better with a three-way for obvious reasons.
TLDR:
1. The process is to find objective data and choose a sub that has the FR extension you desire, will play at the desired SPL, and has the distortion and compression characteristics you desire. Then carefully integrate it into your system, then measure the results.
2. Adding a sub DOES allow you to play music at higher SPL, but the benefit is limited in active speakers. If you want louder, you really need bigger amps and drivers.
, with examples:
