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How does improved bass also improve the midrange as well?

IME/IMO:
  1. Excessive bass tends to "overwhelm" the midrange, making the tonal balance "off" when the sound is undesirably bass-heavy;
  2. Distortion from the bass reaches well into the midrange (at 80 Hz, the second harmonic is at 160 Hz, third at 240 Hz, and so forth);
  3. Excessive bass can overload an amplifier used full-range and thus distort the entire frequency spectrum;
  4. A crossover does not fall instantly to 0 on either side; there can be significant energy an octave above and below, so too much bass can affect the mains as well; and,
  5. Integration may be the culprit, with interaction among sub(s) and mains as well as the room causing frequency peaks and dips well above crossover (see (4) above).
I'm sure there are twenty other things I forgot but hopefully that's a start... I found many years ago that adding a sub to my system really cleaned up the lower midrange and above by offloading the amp (minor) and speakers (major) from having to reproduce the lowest frequencies.

FWIWFM - Don
 
^^^With high-pass filter to main speakers, or regardless (even without high-pass to mains?)
 
With regard to #1 of DonH56's response, I believe he is referring to intermodulation distortion (I think of it as FM, frequency modulation) where, for example, a 50 Hz note's piston-like movement modulates, or alters the 500 Hz note that is playing at the same time. Having separate high and low pass filters eliminates the distortion. When a sub with its own amp is used, more power is available for the mids and highs, and one is less likely to cause the amp to clip. One can play music louder and cleaner without as much fear of damaging (read: blowing up) a driver or two.
 
A driver's amplitude or distance of displacement is a contributing factor to distortion: large movements tend to be less linear. And bass frequencies usually have larger amplitudes than mids or treble. When the same driver reproduces both bass and midrange (as in many heaphones, and in some speakers), the midrange is a smaller ripple riding on the larger bass wave. The means the driver is producing mids at those more extreme displacements needed to reproduce the bass. For example, suppose you have 3% distortion. Perceptually, in the bass most people won't notice or hear it. But that same 3% distortion in midrange becomes audible.

This is a way in which measurements made from frequency sweeps can be misleading. When you measure the system with a frequency sweep, it doesn't play the bass & mids simultaneously. So the measurement might say 3% distortion in bass and 0.5% distortion in mids. But when you play actual music, bass & mids are playing simultaneously, which causes 3% distortion in the mids due to the driver excursion required for bass.

Back to the original question: this is one way in which improved bass, improves the mids too.
 
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