I don't know if the Tri-Vibe designer(s) still read this thread, but I am intrigued to know how the 15:1 cap ratio for the 2 all-pass sections was determined.
I can appreciate that it is desirable to have the phase shift varying linearly with frequency over as broad a range of frequencies as possible.
However when I look at the maths, I come to the conclusion that you would need to make the all-pass stages identical in order to achieve that.
To see what I mean go to
http://www.wolframalpha.comand paste in the following command
plot (180/pi) arg(((1-ix*1)/(1+ix*1))*(1-ix*15)/(1+ix*15)) from x = 0 to 0.125
That's a phase-shift plot for 2 all-pass stages with caps in the ratio 1:15 as in the Tri-Vibe.
The horizontal axis represents frequency (normalised), and you can see that between x = 0 and 0.025 there is almost linear variation in phase from 0 to 45 degrees.
To get similar variation in phase between x = 0 and 0.025 using equal valued caps, you need to make each all-pass stage contribute 8 "units of phase shift"
rather than have one stage contribute 1 unit and the other contribute 15. The graph for that case is given by this.
plot (180/pi) arg(((1-ix*8 )/(1+ix*8 ))*(1-ix*8 )/(1+ix*8 )) from x = 0 to 0.125
You still get a phase shift of 45 degrees at around x = 0.025 but the graph is straighter over a much larger range of frequencies.
In fact when you use caps in that ratio 15:1, practically all the phase shift comes from the all-pass stage with the larger cap, so you've almost got 1 all-pass stage rather than 2.
So to my understanding, replacing the 1.5nF and 22nF caps by a pair of 12nF caps should give linear variation in phase over a wider range of frequencies..
Am I missing something here, or is this too simplistic an understanding ?