Good speakers less efficient?

There are good speakers that are also efficient. While "good" is often quite subjective, some speakers that have been praised by some audiophiles that are also efficient include the Klipschorn, Avantgarde Duo, and Wilson Audio WATT/Puppy.

The low impedance characteristic is often the result of crossover design. The Thiel 3.6 is an example of a good speaker whose impedance dips below 3 ohms at certain frequencies due primarily to a design goal to preserve phase coherence.

Inefficiency can arise from crossover design also but is often due to driver and enclosure issues. The Acoustic Research 3a was a well-regarded speaker that employed an "acoustic suspension" design for its woofer. This sealed box design helped extract extended low frequency performance from a speaker of moderate size, something that was considered quite difficult to achieve at the time. The acoustic suspension design was inherently inefficient. (The AR 3a was also a 4 ohm speaker.)

I have not seen any statistical analysis of impedance and efficiency versus speaker quality. Would you share with us the basis for your cited "correlation"?

No stats, just observation. Nor did I say "all", but rather "many". Dali Helicon, Dyanaudio Contour, Harbeth, Totem Mani-2, some of the Tylers, et al.

Not looking for a fight, just information.

Not being a speaker designer, I have a fairly crude impression of how crossovers and drivers are used. My impression is that drivers function naturally over characteristic frequency bands, e.g., woofers only go up so far and start to drop off below a frequency inherent to their configuration and loading. Their performance over their bands is typically not flat. Designers use crossovers to boost and/or cut to smooth the speakers' frequency responses, as well as to extend performance beyond the speakers' natural bands, like coaxing a woofer to go lower. Beyond frequency response, designers also have goals for phase coherence (like Thiel), dynamic range, and low level performance, among others. This often results in unusual impedance loads and inefficient speakers. Nowadays, the availability of high powered solid state amplifiers allows the speaker designer generally to ignore such issues. The utilization of new speaker materials, like beryllium, diamond, or sandwich composites, allows the designer to achieve specific goals without as much complexity in the crossover and hopefully with less penalty in impedance and efficiency. I am hopeful other posters will have more specific responses to your question.

Accepting low efficiency allows a designer to get deeper bass in a given box size. All else being equal, most people will pick the speaker with deeper bass.

Passive equalization in crossover networks is pretty much limited to "cut" instead of "boost and cut". If the designer needs to reduce the efficiency of the tweeter and/or midrange to mate up with a low efficiency woofer, he can do some response-smoothing while he's at it.

Fairly low impedances (4 ohms nominal) will better utilize the capabilities of high quality solid state amplifiers. A 4-ohm speaker will draw twice as much power as an 8-ohm speaker from a high current solid state amp, so it will play 3 dB louder. All else being equal, most people will choose the extra free 3 dB.

Not being constrained to keep the impedance up around 8 ohms increases the range of drivers the designer can choose from, and gives him more lattitude in what he can do and how he can do it.

With all those advantages, why in the world would any designer not shoot for low efficiency and low impedance?

Diversity in philosophy abounds amongst loudspeaker designers, for the above-mentioned "all else" is seldom "equal". It's all about juggling tradeoffs. Each of the advantages cited above comes at a price. My own designs tend toward higher than average efficiencies and impedances, as I place tube amp compatibility high on my priority list - but I make trade-offs in doing so.

In my opinion, those loudspeakers that really sound good do so for two reasons: First, in combination with the rest of the system the speaker must recreate some aspect of a live performance convincingly enough to allow the listener to suspend disbelief and get lost in the music. That aspect can be timbre, impact, coherence, warmth, sense of rhythm, ambience, inner nuance, sound source localization, liveliness, whatever. Second, the speaker must avoid screwing up some aspect of the sound badly enough to destroy the illusion. Sometimes efficiency and impedance play a significant role in these characteristics for good or for ill, but most often it is other technical attributes that are the dominant factors.

Duke

It's not a "high performance attribute", nor is there a relation of performance to sensitivity. It has to do mostly with the evolving of amplifiers producing enough current to drive bigger cones and achieve lower frequencies in smaller boxes.

Tube amps, which came first, produce little current output. This meant that speakers needed drivers to be relatively light and the magnets small in order for the low current to move the cone. Lighter cones limits their size (to prevent cone deformation), which limits the low frequency response. One way to get lower frequencies out of relatively small cones is to horn load the cabinet, however; the lower the frequency the bigger the cabinet. Another limitation is the number of drivers as a crossover splits the already small current further. So by keeping the impedance and sesitivity high, a tube amp can be practical.

With transistors, amplifiers are able to generate many times the output current of tube amps. This makes it possible for larger, stiffer drivers with bigger voice coils and magnets to be installed in smaller, closed boxes producing tighter bass response. Also, lower impedances will not over-tax a SS amp they way it does a tube amp.

Since solid state amps are more prevalent, speaker designers are more free to mix and match cabinets, drivers and crossovers because, for one thing, it makes economic sense. Sometimes lower sensitivity and impedance gets them where they want to go (like the ones you mention) or sometimes it's in the other direction (e.g. von schweikert, Fried).