Time coherence - how important and what speakers?

Karls, I believe that John Bau of Spica designed time coherent speakers with other than 1st order cross-overs.

Well, I'm going to take one last technical stab at this. What we are talking about is the time that elapses between the arrival of the electrical signal at the input of the driver and when the acoustical signal leaves the driver. This will vary depending on the size and frequency range of the driver. This is not the time the acoustical waveform travels through the air. If it doesn't leave at the right time, it sure can't get to your ears at the right time. That is why I said that the baffle slope doesn't mean a lot, relatively speaking. We must be phase correct to assure that the amplitude of the fundamentals and harmonics are not altered and time aligned. By adjusting the acoustical centers of the drivers, we can compensate somewhat for the time alignment. It has to be precise.
The crossover network may need to be very complex to accomplish a 6db/octave ACOUSTICAL roll-off because the electrical and mechanical characteristics of the drivers must be considered. Single caps will not do the job. Phase has to be considered in this equation because phase will create acoustical timing errors. Also, we are talking about acoustical phase, not electrical phase. We are looking at wavelengths here. If you know the frequency of a sound pressure wave you can calculate the "Wavelength" of each cycle. We can also add in "transfer function."
This could be a very long discussion but I hope this gets us all on the same page.

Time coherence is difficult to achieve because the acoustical center for a moving coil driver is not a fixed physical point, but actually varies somewhat with frequency. Source - The Loudspeaker Design Cookbook, sixth edition, page 113.

Phase coherence in a multi-driver system requires first order acoustical slopes for both the low-pass and high-pass driver. The acoustical slope is the sum of the inherent driver response and the crossover response. Note that time and/or phase coherence can only occur in a single plane with a multi-driver system.

Human hearing characteristics aren't linear, but are full of thresholds and masking effects. For example, after .68 milliseconds the directional cues from a repetition of the original signal (an echo) are suppressed, and this suppression (masking effect) lasts for about 40 milliseconds. Now, if we knew precisely the thresholds that apply to time and phase coherence, we could take them into account in loudspeaker design. Alas, the published research is inconsistent on the audibility thresholds of phase and timing errors.

There may be more than one way to skin a cat. John Bau's classic Spica TC-50 claimed time and phase coherence via this arrangement: slanted baffle with cossover: high-pass slope, approximately first-order, 6 dB/octave; low pass slope, fourth-order 24 dB/octave; both drivers connected with same polarity.

Unsound---they lied! It HAS to be a first order filter period. The phase shift created by a 24 db slope would be tuff to fix. Read Richard Hardesty's issue #3 of the Audioperfectionist. You might not like his recommendations but his science is correct.