Reasons


What are the attempted advantages of a TL speaker cabinet with equal sizes channels all the way to the port, as opposed to each channel being wider than the last?
Also, what is being achieved by a decreasing size horn channel compared to an increasing size channel?
Are there any simple answers to these questions? I probably won’t comprehend a high level answer.
128x128sound22card
Tapering the transmission line, towards the opposite end from the woofer, lowers the woofer’s F3(the woofer’s 3dB down point, according to Thiel/Small parameters) and(combined with proper damping) reduces ripples, in the back-wave’s response, equivalent to what could be achieved with a longer(straight) line.   Reversing the taper raises the woofer's F3.  http://audiojudgement.com/transmission-line-speaker-design/ http://www.philharmonicaudio.com/ML-TL.html https://en.wikipedia.org/wiki/Transmission_line_loudspeaker
Of the links mentioned, the Philharmonic Audio page is the only one that accurately describes how a TL works. The first article linked is full of inaccuracies and just plain wrong information, the fact it was written in 2016 is very surprising.

There have been four different pieces of software available over the past 20 years that accurately model TLs.

1. Augspurger's TL program which I do not believe is still available.
2. My MathCad worksheets which are no longer available.
3. Hornresp
4. Leonard Audio TL progrma avaialble on DIYaudio.

If you want more in depth information on how TLs work and can be designed look at the TL page on my site.

www.quarter-wave.com

Martin
@sound22card- My post was intended to(directly and concisely) address your questions. Hopefully, that was accomplished, despite my having misspelled, "Thiele/Small".