Analytical or Laid Back

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I find generally an "analytical" tweeter is just one that not only has rising response but has to have very good dispersion. Even a tweeter with bright on-axis sound can sound neutral enough if you listen to it 45 degrees off-axis. The problem is when the tweeter has great dispersion AND rising response.

The ideal tweeter should have great dispersion and slightly rolled off response as frequencies rise, this way you get detail without the fatigue.

Most of the time "laid back" tweeters just have poor overall dispersion since the fast majority of people don't toe in the speakers and generally are off-axis, and might even be quite bright if listened to on-axis.
 
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With the same coil diameter, metal or ceramic dome should have better looking polar graph than its textile counterpart. Maybe this explains some of the sound differences? I am skeptical about the impact of harmonic distortions in the tweeters, for example 2nd harmonic from 6 khz will be inaudible to my ears, practically. Dome curvature strongly affect Sd parameter, maybe that's why many people prefer the sound of textile domes? Higher Sd should give us less distortion close to speaker's Fs.
 
Why do you think that the even order harmonics are the things responsible for what you like?? There are many reasons why tube amps are pleasant to listen to.
Words can be a limiting factor. Its not always you can explain a sensory experience you like, but I will try. The simplest answer would be that harmonics or overtones is a natural phenomena, it is present in more or less all acoustical events. Be that when you are walking in the woods and branches and leafs move against each other in the tree or a twig snaps as you step on it, or someone tapped on that wonderful 12 string guitar. What you hear is always more than just the fundamental.

I had to use the internet to find academic descriptions that add to the whole. Ken Rockwell had some:

https://kenrockwell.com/audio/why-tubes-sound-better.htm
Progressive Distortion

Not only is tube amplifier distortion harmonious, it increases as things get louder - exactly as they do in a musical performance. As instruments play louder, or as you hit a percussion instrument or piano key more strongly, they generate more harmonic content. As notes decay, the percentage of harmonic content drops again.

The Mind's Eye

All musical perception is purely intangible. We can't put a finger on a musical image and point someone else to what we're seeing as we can on a painting, piece of sculpture, a musical score, a book or a photograph.
Because musical images are created entirely in our imaginations, what we think we are going to hear is often what we hear. This is why otherwise reasonable people think they hear huge differences in foolish (but high-profit) items like cables or power cords. Even though there is no real difference, they hear very real differences that just aren't there. The differences are very real in that listener's vivid imagination, but no where else. This is why we use double blind tests where neither the subject nor the presenters know what's being heard when we try to do scientific research, like the AES research above.
Music is all about using our imaginations. This is a very good thing and why music is such a powerful art form. This is why a good HiFi can recreate the original listening experience. Unlike a TV or movie, close your eyes, and you can be seeing and feeling the same things that you do in the concert hall. I close mine and see the performers, see them moving around, breathing, moving valves and keys, turning pages, and then I see the music itself. You have to concentrate, and if you listen carefully and keep your eyes closed, you'll see the music, too.
If you think a nice, warm glowing tube amplifier is going to sound smooth, liquid and warm, it will! Our imaginations are very susceptible to suggestion; that's the whole point of music.
This did not exactly explain why even order harmonics is pleasing but it refers back what I was talking about. Another thread also talks about how harmonics (odd and even) are present in instruments and even the human voice - again, its pleasing because it is a natural phenomena.

theory - Why do harmonics sound good? - Music: Practice & Theory Stack Exchange

Not only does it sound natural, to me, it adds clarity and air. Air you say, yes, air. Even order harmonics contain spatial information, the room or space effect in a piano or guitar, or for that matter the triangle instrument. And I think I understand more of why drivers and loudspeakers should have a low presence of harmonics. If two tone are played at ones, the amplitude is double. So instead of it being a subtle addition like natural even harmonics, the end result is twice or close to that, making the 2nd harmonic overwhelming ... is that it, did I get it right ? :D - looking at crossover, it too is dealing with amplitude, that is why the slope need to be adjusted so that the plateau, aka sum of driver 1 and 2 at the crossover is horizontal or flat.

If the question is: "Which one is close to reality, the highly distorted tube amp or the clinically low distortion solid state?" then there is no easy answer. Everyone may have their own criteria but for sure none is close to reality.
You are right, it is an individual preference.
 
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