Tomic601 wrote: " ... the rear firing tweeter is 100% distortion, but in some cases pleasing."
I can certainly understand how the energy going off in other directions from any polydirectional speaker can be interpreted to be "100% distortion". It’s not on the recording, right? It just adds more of the room’s sound to what was on the recording, right? And "distortion" is certainly how a measurement microphone would see it!
Let me suggest looking at this from a completely different perspective, and along the way we will discover why this "distortion" is "in some cases pleasing".
There is a vital difference between ears and microphones: The ear differentiates between the first-arrival sound and the subsequent reflections, and a measurement microphone does not.
So let’s approach speaker design from this perspective: Let’s see design for the ears instead of for microphones.
In any non-anechoic space, the ear detects two events: The first-arrival sound, and the reverberant sound (the reflections). What we actually PERCEIVE is a combination of these two events. And the less discrepancy between the two, the better the perceived sound quality.
So if we are designing for ears instead of for test instruments, we would want the reflections to sound a lot like the first-arrival sound. Since most speakers beam in the top end, this can mean adding a rear-firing tweeter to put a bit more top-end energy out into reverberant field. Fortunately the ear is not very sensitive to time coherence in the reverberant sound, so it doesn’t matter that the reflection path for the rear-firing tweeter is different from the reflection path for the main tweeter.
Thus while that rear-firing tweeter’s contribution looks like distortion to our test instruments, it results in a more natural sound because not only can the ears tell what is first-arrival sound and what is reverberant energy, but also they BOTH matter.
So, assuming competent implementation, is the rear-firing tweeter’s contribution a "distortion"? In my opinion, only if we listen through test instruments instead of through ears.
Just for the record this post is by no means a complete examination of the subject, and I have nothing against microphones as design tools.
Duke