Take a look at
this article.
Here you can see some
TLs under construction.
TLs come in a number of guises, and there is confusion over the Voight quarter wave horn, which is really a type of TL.
The mathematical model for the aperiodically damped TL was published by G.L. Ausperger in 2000.
Many, including myself dispute that Martin King's designs are TLs. I regard them a specialized coupled cavity reflexes.
A TL in essence belongs to the family of Gedeckt organ pipes. These ranks are wooden pipes closed at one end and open at the other. The physics shows that the pipe is a quarter wavelength of the fundamental.
Now an organ builder wants a definite note and resonance. The speaker designer does not.
The TL speaker has a reverse taper, usually around 3:1. This spreads the output of the pipe over about 1.5 octaves. There is a mathematical reltionship between the Fs of the driver and the pipe resonance Fb and therefore pipe length, Lp.
Ausperger's great contribution was showing the relationship of driver VAS (equivalent volume) to the pipe volume Vb.
Now an undamped or under damped pipe will have two impedance peaks like a reflex enclosure. The roll off will be fourth order 24 db per octave below F3. However if sufficient damping material is added, then the enclosure develops one peak of impedance and the roll off is second order, 12 db per octave below F3. At the point where this occurs the pipe becomes what is called critically damped, and the sytem Qt drops to around O.5, and reproduction becomes essentially non resonant. F3 is lower, much lower than for a sealed alignment with the same woofer, and also woofer output is augmented over 1.5 octaves, whereas a closed box does not augment the woofer at all. At the smae time Qt is generally lower by a significant magnitude.
In a properly aligned TL there is a deep powerful non resonant bass, so that typms sound perfectly realistic and so do bass strings and the bass strings of the piano etc.
Very few people have ever heard a good TL. They do sound significantly different from other designs. They touch the bass line softly and gently, but an explosion, canon shot or a big bass drum really hits you in the chest. I have found this creates total surprise. The speakers do not advertise or seem as if they have a big bass. However when bass a plenty is there and called for, it right there causing total surprise to those having their first initiation.
Pipe organs are reproduced with phenomenal realism.
To give you an idea of how realistic the bass is, I a have a friend with a pair of B & W 800 Ds. Now these are a fine speaker, and not ones known to be over tubby. However my friend envies the bass definition and power of this system every time he hears it. The bass clarity and lack of muddle that is the hallmark of good TLs, allow the rest of the musical spectrum to speak with clarity, as long as the total design is competent.
A TL is really a home constructors paradise. I think that it fair to say, that since TDL closed its doors, TLs have largely been the province of the DIY community.
If you are considering building a TL, I strongly encourage you.