[I moved this post here as it addresses the one above, which was posted almost simultaneously]I will correct a few errors-
Cheaper mics tend to roll the bass off (at least, cheaper cardiod mics).
Although the two factors may often be correlated in the mics we have available, there is no direct causation. The real deal with regards to low-frequency extension has little to do with cost. It's really a secondary association based on other things. The value of higher quality mics is mostly evident in other specifications such as self-noise, overload-level, and especially smoothness of response and pattern behavior.
There are not really many mics (
any outside of our boutique taper mic builders?) made with the intention of recording a PA from somewhere in the center of a room. Mics are designed for other purposes and we choose the ones best suited for what we do.
Most small inexpensive mics are built for use very close to the source- either mounted directly on the talent or an instrument, or very close to them. Even hanging choir mics are designed for use relatively close to the source. If they didn't have a sufficiently tapered off low end response, proximity effect would make them all sound like mud for their intended purposes.
Even most really high quality directional mics are not designed to have especially extended low frequency response because that does not benefit their typical use. Classical guys generally use omnis or subcards when they are especially interested in the lowest octave. Because of their unique operating principle Sennheiser rf mics require equalization in their amplifier, so they do use that to extend the bass respose of their cardioids somewhat more than most other quality mics.. yet not that many tapers use them (they also sound subjectivity a bit darker up top to my ear than Schoeps/DPA/Neumann/Gefell, which probably has more to do with any general preference of tapers).
Sure, to some degree good frequency extension is related to the quality of the microphone, but it is far more commonly related to design intent of the microphone and it's target market (which is almost never tapers).
Smaller mics cannot physically capture the same low end response as larger diameter mics.
Not true, yet a common misconception. Microphones are signal transducers, not power transducers. There is no correlation what so ever between a mic's size and it's frequency sensitivity (there is a direct correlation between size and self-noise, and more complexly a connection to directivity). This misunderstanding probably comes from the reproduction side of things where the impedance mismatch between a driver and the air it is trying to move becomes significant - sufficient coupling for decent power transfer at low frequencies requires an increasingly larger surfaced driver (or increasingly larger excursions, and that only works if the driver is "large enough").
The 406x in the typical use sound (for real) muddy (to me) {those do seem to have the most low end presence for small mics} but the DPA bass instrument mic when mounted on a double bass sounds a little thin (to me). So I've not really heard what I like...
The DPA bass instrument mic is a miniature super/hypercard. It's lowest frequency sensitivity rolls off partly due to pattern as any super/hyper card will. But it is intended for close-mic'ing were proximity effect comes strongly into play so DPA doesn't extend the low frequency response as much as they could, with the intent of balancing the proximity effect boost. A 406x omni used in the same position will be far more sensitive to low frequency information. BTW, the DPA bass instrument mic is the same mic as their miniature guitar mic, trumpet mic, piano mic, choir mic, and podium mic. I use it as a miniature super/hypercard in combination with 406x to extended the bass response.
I find most omnis sound similarly muddy in many situations due to their response flatness, and find I often need to use EQ to get the midrange and presence-range sounding correct. Most tapers I've heard express dislike for the 406x sound complain of an overly peaked or strident top end.. which is an intentionally non-flat response designed to address the intended application and market of the microphone- use on-talent.