Closed/sealed box design strategy

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Hi!
I would like ask the experts about closed/sealed box design technics. What is the most prefered way:
-Butterworth (Qtc: 0.707)
-Bessel (Qtc: 0.577)
-Critically damped (Qtc:0.5)
What are the advantages of the closed ended TML boxes? (Like the Nautilus?)
What is the "best" closed box laudspeaker on Earth? :)
Nowadays I can see most of time only vented designs. Why?

Greets:

Tyimo
 
There is no best design, it's all a matter of individual taste.

Lower Q sealed gives better transient response and group delay/phase at the expense of larger box and earlier roll-off.

Vented is popular because it gets lower cut-off and better efficiency, at the expense of transient response and group delay/phase. Box size is larger than closed, but not terribly so.

Different applications (sub, only main speaker, satellite etc.) require different approaches.
 
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