The tested F3 is different from the in-room response if testing was done in controlled conditions but yes, a HT system can sound amazing with higher F3. Only special effects and few other sounds occupy the lowest part of the spectrum.
The driver determines the enclosure and response- you can change the tuning frequency, but if the port tuning frequency is far from the box's tuning, the response looks a bit like a clothesline that isn't very tight- two peaks with a negative curve between those two points. Also, if the port is tuned too low (below the Fs), the air movement isn't well controlled.
TLS referred to Quality of bass- the Q was originally called 'the Quality factor' but the full name has since been shortened (still is, in some crowds). High Q is good for a Rap/Hip Hop system, with a strong peak frequency and this is like an undamped bass drum head that rings after hitting it. Well damped results in the note, followed by no ringing and the driver's Qts determines its usefulness in various cabinet configurations.A driver made for sealed cabinet won't work well in a vented cabinet and vise-versa. There is a middle range where it can work in either, but don't expect the low frequencies to be extended or sound great.
If you are starting out your career in speaker design, or are an audio enthusiast, you will have heard the term "speaker Q" thrown around.
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