Sonic Differences Between 2-Way and 3-Way Speakers


I have owned a succession of 2-way loudspeakers. I have read comments suggesting that there are certain things 2-way speakers excel at and other things that 3-ways do better. What have I been missing?
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That type of arithmatic would beg the question of, why bother with tweeters and why don't we only go with with one midrange driver? There is an ease to the presentation that three ways can more easily provide the complete musical spectrum.
There seem to be some shocking simplifications in people's responses. A two way will cost less, given equivalent quality components. However a two way places a severe constraint on the low frequency driver .. it must shift enough air to provide bass, but it must also cover the midrange frequencies that are critical for imaging. The advantage of a 3 way system is that the lowest driver can have quite a low roll off frequency and handle the shifting of a lot of air. The mid range (which can now be a smaller cone than in a 2 way design, and can therefore be crossed at a higher frequency with the tweeter) does not have to handle power, not does it have to be crossed in the high mid range, so could theoretically produce a purer midrange. Finally the tweeter comes in at a higher frequency than in a 2 way design, because of the smaller midrange, and so now this opens up the possibility of ribbon tweeters, super-tweeters and the like that give a beautiful and extended HF.

I own a 3 way design (Heybrook Sextet) and a 2 way design (Spica Angelus) and both are great, and different. The imaging is similar on both (very good on both) but the Heybrooks have much more at the frequency extremes. The spicas really need a subwoofer for anything other than chamber music.

I don't think one could say that 2 way design is better than 3 way or vice-versa, and 3 ways don't seem to come into play below $2000 per pair, but I can definitely see advantages of a 3 way design, even if they are more expensive and complex to pull off.
The bass response of a given design is the easiest to psychoacoustically adjust for.In other words one won't miss it or pine for it's absence or whatever if the speaker is very good in all other frequencies.Thus for a profound cheepskate bargain hunter like myself I can get about 90% of the way there with a great one way or two way AND have money left over for cd's and or vinyl.My experience has been that around 2,500 dollars is all you need to spend on speakers and after that diminished returns kicks in.DIY folks can achieve even greater value in their systems performance.
Great comments everybody. While I agree (I think we all do) that a single driver is the theoretical ideal, the points that unsound and seandtaylor make are what I was looking for when I opened this thread.

Is there a fundamental "sound" of a three-way that is different from a two-way, in the way that acoustic suspension bass sounds different from bass reflex, or mosfets sound different from other transistors? (This is a purposefully naive question.)
"The bass response of a given design is the easiest to psychoacoustically adjust for.In other words one won't miss it or pine for it's absence or whatever if the speaker is very good in all other frequencies"
I'm sorry .. is this personal opinion, or scientific fact? I have to say that my system is much more enjoyable since I added the subwoofer, and live recordings of some blues bands are in a whole new league since the sub adds the scale of the venue. That is my personal opinion ... if you don't have good bass to below 40Hz you're missing out.