Line level or speaker level, scientific reasons? ?

for the majority of SANE LEVEL as well as average music material you're likely to listen to, you're MOSTLY better off running full range to your speakers(for music) as well as to the sub...basically running them both in paralell off the speaker/amp level posts! So, instead of running off your amp to your sub, then out to your speakers(enlisting the help of your sub's high pass filter), you would go from your amplifier to your main speakers(satlites), then run another set of speaker wires from your amp posts(same) to your sub speaker level in's! Otherwise, you'll run a line level connection to your sub from your pre(if you have another set of pre-out's). This way you're running both the sub and speakers from a full range signal, bypassing the subs filter. The reason for this?...what you usually get is not so pure sound to your satalites from your sub's high pass filter! You are gaining dynamic potential ultimately by doing what you're doing, but you're robbing sonic purity as well going through your sub's inferior crossover to your mains!!! I would almost always(if doing a 2 channel set up) rather leave the main signal untouched, and let a sub use off that line(speaker level). The sub will have it's own filter, but the mains will run full range from the amp in paralell to the sub(even though you're adjusting the crossover of the sub to match the natural roll off of the satalites.
I find that, except for loud level techno, hard rock, rap, and most heavy dynamic music source material at high volumes, the scenario I described will overall sound the best IMO. I've had great sucess running high end mini monitors full range from my amp/preamp set up, and running the sub off the amp(or main speaker posts) speaker level in paralell. I found that my preamp set up(I use a separate PSaudio P300 for my pre, separate from what my sub's hooked into) sounds not as good sonically when I run another differenting connection off the pre-out...to, in this case, the sub line level. So, I found that inverting the phase on my sub, which was set up in the best spot in the room as is, and connecting it speaker level from my amp in parallel to my mains worked extremely good! I set the cross on the sub to match the roll off of my mains, adjusted levels and it was dynamite!
I do find that I can get much more ultimate dynamic head room connecting the way you mentioned, or doing a digital crossover connection on my digital AV Pre/pro at 80hz, and letting my sub connect line level, filling in the bottom.
Still, for pure 2 channel dubties from my high end pre, and the majority of music dubties I have, doing speaker level connections works for me....you'll rob your sonics if you do chose to do the sub filter thing back to your mains however. So be warned.

It really depends a lot on your brand of subwoofer. If a REL ST series subwoofer is used for 2 channel music; then the high pass speaker connection is by far the best way to go.

There is no scientific explanation. This is how REL designed it to work, with the main speakers playing the normal full frequency range. They only recommend the pre-out connection for home theater applications because of the AC3/DTS bass signal.

You can read all about it at this link.

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My less than 2 cents is, I've read several comments and reviews that say using the high level input from the amp makes for a more coherent sound. In other words, the sub amp borrows the characteristics of the main amp. Using a separate pre-out line to the sub is said to create bass that can be musically disjointed from the main speakers.

The input impedance on the REL’s(and other quality self-powered subs) is supposedly such that the additional high-level connections to the sub do not affect the main amp.

Using speaker level to the sub then to the mains is an extra drain on the amp and the filters may keep things from blending well.

I like using line level better. This allows me to use all 17 watts to my mains and a good quality sub/sub amp combo. I honestly use a Janus Interphase 1/A sub amp/crossover. This allows for virtually transparent crossover at 100hz, loads of power to the sub(pair of nelson reeds) and never interferes with the amp or pre except for being in between them.

Just an FYI...what Elevick describes is NOT how a REL is setup or how it works. It is parallel to the main speakers and is self powered. It takes nothing from the amp, but the signal; just like the sub getting the signal from a second pre-out.