Regarding higher driver-count coherent sources . . . it is indeed a very complex problem. The way Thiel approached phase coherence was for each driver to execute its design-ultimate slope such that when summed with the other interacting drivers, the net resultant curves mathematically summed correctly. This approach is first-principle-purist-physics driven rather than the euphonic design approach of messing with it till you like it. A surprisingly obscure tenet of the purist approach is that the net first-order slope for an individual driver slope is actually quite complex rather than simply 6dB / octave.
Let's jump right to a germane example: The woofer crossing to the midrange. Each driver roll-out assumes a 6dB slope - but that slope must be the net resultant slope, so in fact, the driver's actual behavior in that cabinet, electromagnetic environment etc. must be corrected by shaping networks such that it behaves properly, and the two drivers add properly. I have not yet addressed the meat of andy's question of more than 3-way or multiple bass drivers. I'm getting there, but before we go there, we should digest further complexities beyond this simple woofer-midrange interaction.
In a valid minimum phase array (as Thiel attempted), the woofer is not only interacting with the midrange, but the tweeter is in fact still contributing down (through the midrange's lower roll-out and) to the woofer's upper roll-out. So there is in effect a tweeter x woofer crossover at a lower signal level, since they both must be attenuated at this secondary cross-point. At that crosspoint each relevant driver must assume a 12dB /octave slope in order to add correctly in the whole system. Here we have opened Pandora's box. Every small change to any driver slope must be complementarily compensated in not one, but multiple other coexisting driver slopes. Such considerations include passive radiators and cabinet bracing and other factors which influence the roll-out behavior of any and all drivers, electrical or mechanical.
So, now let's expand to andy's questions regarding more than 3 drivers. I have already mentioned that the passive radiator counts, so the CS2 and 3 series are 4-ways in crossover considerations, although the passive radiators and mechanical coax (2.4, etc.) don't actually accumulate the expense of electrical crossover components - but the crossover must nonetheless consider their contributions.
Let's jump to the bass alignment of the CS5. The bass picks up from the lower midrange at 400. There are 3 bass drivers representing 2 alignments which all cross over to the lower 5" midrange, the upper 2" midrange and the 1" tweeter. Only the sub-bass driver pair with a 40Hz crosspoint is exempt from only the upper midrange and tweeter. The rest of the drivers interact and each interaction introduces an additional 6dB pole to its required roll-out. The required mental gymnastics is considerable. Generally, even with world-class brands and development labs, the approach is to ignore any interaction greater than -10dB or possibly as much as -20dB. We proved to ourselves that -40dB could be "sensed" as anomalous = Not Right. So we endeavored to keep it all straight in the design phase; then in production engineering, we had to determine how much mattered how much and how much we could afford to spend on any of dozens of decision points. That process generally took months to work through and hinged on value judgements of what our customers would be likely to spend on approaching "perfection". In hind sight, we missed the mark there. A product such as the CS5 could have been executed at various levels into $6 figures. In fact I conceived it as being a $15K product whereas Jim and Kathy drew a firm bold like at $10K, and we fit the final product into that frame. NB that Thiel's Cost of Goods Sold was far higher than anyone else in the business. We we wanted to be nirvana for everyman. But that price aversion kept us out of the developing ultimate-performance marketplace.
Let's focus on multiple low-frequency drivers. The CS5 is unique and effective. Let's examine the 3 bass drivers. Assume a pair of sub-woofers operating from 10 to 40Hz and a single upper woofer operating from 40 to 400 Hz. Since our baffle is sloped (to best fit) for the purpose of time alignment, we assign a group time signature to the upper (mid-high frequency) 3-driver array (lab work). The proper placement of the upper woofer turned out to be right in the "wrong" place near the floor where the lower woofers needed to be. The Aha! moment came on an overnight flight to England when Jim and I
were wrestling with how to achieve proper physical time alignment of the
bass with the upper drivers. We put the upper woofer THERE BETWEEN the subwoofers with its own tunnel-tube to a sub-enclosure in the back of the cabinet so that the two sub-woofers could see the larger remaining enclosure. The subwoofers flanked the upper woofer (above and below), creating a larger integrated waveform supported by the floor. At the 40Hz crosspoint, those waveforms are large enough that their physical center could be coincident with the mid woofer for simplification of time alignment of the whole-woofer-array with the multiple upper array drivers above it. The square wave / impulse response verified the success of the idea. It works.
Now, back to crossovers. We have fixed the time alignment of the bass array as a single entity in space, but the two slopes are different due to their differing crosspoints. In fact the upper-mid and tweeter are out of the subwoofer equation, but all except the tweeter are in the upper woofer equation. We accomplished much of the roll out work via mass loading the sub woofers for a mechanical upper roll-out and lower fundamental resonance. It took months of iterations including driver and enclosure tweaks to fine tune each of the crossovers with their compound and corrected slopes to achieve both phase coherence, time alignment and smooth frequency response. This work was supported by pretty serious test equipment which Jim conceived, developed and built in-house.
History shows the CS5 design to be technically tour de force, but commercially short-lived. The Achilles Heal is that amplification was not available and/or identified that would drive the cruel load of about 1 ohm at 40 Hz and deliver clean power to the upper frequencies. I believe that product might have succeeded if a bi-amplification scenario were implemented. Indeed if I hot-rod a pair my first move would be to separate the bass from the rest. The mid-high frequency load is pretty sweet. The low frequency demands could be addressed with the right amp and any deficiencies would be sequestered in the bass where our ear is far more forgiving. A further tweak would be to remove the mass loading from the sub-woofers and equalize the bass amp for electronic rather than physical shaping, earning significantly higher bass impedance for, I believe, potentially world-class bass.
At this point in my life, this the stuff of pipe dreams. But if granted the time, such dreams may turn to real stuff. I am healthy at 70 and gradually making room in my life for addressing this business from long ago.
