The problem here from what I understand so far about filters is that your description about what a filter does to a signal ( "more twists/turns/distance") is not accurate.
A capacitor is a frequency reactive component . Meaning it reacts differently at different frequencies in an AC circuit.
A High/Low pass filter is kind of a voltage divider circuit on a load.
In a 1st order LOW PASS filter the capacitor is in parallel to the load and the phase will LAG by 45 deg. "T
his is due to the time taken to charge the plates of the capacitor as the input voltage changes, resulting in the output voltage (the voltage across the capacitor) “lagging” behind that of the input signal. The higher the input frequency applied to the filter the more the capacitor lags and the circuit becomes more and more “out of phase”." ( the explanation quoted is from this link http://www.electronics-tutorials.ws/filter/filter_2.html).
In a 1st order HIGH PASS filter the capacitor is in series to the load and the phase will LEAD by 45 deg, the voltage across the capacitor cannot instantly change
if there's a fast change on the input voltage it will instantaneously appear on the output side of the capacitor so high frequency pass through
That's how a capacitor work in AC circuits. Now phase shift is a difficult concept to explain, if you want to dig in in taake a look http://www.tedpavlic.com/teaching/osu/ece209/lab3_opamp_FO/lab3_opamp_FO_phase_shift.pdf but I would accept it as it is explained here
http://www.electronics-tutorials.ws/filter/filter_3.html and go on with it
If i understand correctly every order shift the phase by 45 deg, 1st order is 45deg, 2nd order 90deg, 3rd order 135deg, 4th order 180deg.
The leading or lagging part is associated with the filter type, Low pass make it lags, High pass make it leads... If I recall in this thread somewhere Piotr advised someone to actually inverse the polarity of one of it's driver so it would be in mainly in phase instead of cancelling a part of the Frequency Response. before that the guy showed he had a big dip in his measure of the headphone's Frequency response... so that's also a way of dealing with it...
So what you are describing sounds a lot like MAGIC! Lol....
This is starting to get a little sticky. Earlier, I was okay with the concepts about delay being measured in "time" and how that affects the coherence of sound. Now, we're starting to introduce phase shifts measured in degrees and how that can affect the harmonics . I'm okay with understanding both "delay" and "phase shifts" as separate and independent influences but now we have to merge the two into a single definition. I initially thought that this might not be as hard as I think it is, but then I went back to your opening post about this and read this bombshell:
"What about the rest of the higher frequencies 1501hz-20khz? they have less time delay than the 1500 hz but now they will have to travel along the tubelength appropriate for the 1500hz delay...?"
So are you saying a 1st order HP crossover at 1500Hz will cause a 88.3µs delay in only that specific frequency and that frequencies higher than this experience less and less delay so by the time we get up to 10kHz, the delay is only something like 13µs? Ohhh wait a second.......this is kind of cool and actually could explains a lot about the crossover testing I did a while ago. I'll have to go back and review my testing based on this information.
If we look at some data, this might help:
| | 1st Order | 2nd Order | 3rd Order |
| (Hz) | 45-deg | 90-deg | 135-deg |
| 1000 | 125µs | 250µs | 375µs |
| 1500 | 83µs | 167µs | 250µs |
| 2000 | 63µs | 125µs | 188µs |
| 3000 | 42µs | 83µs | 125µs |
| 4000 | 31µs | 63µs | 94µs |
| 5000 | 25µs | 50µs | 75µs |
| 6000 | 21µs | 42µs | 63µs |
| 7000 | 18µs | 36µs | 54µs |
| 8000 | 16µs | 31µs | 47µs |
| 9000 | 14µs | 28µs | 42µs |
| 10000 | 13µs | 25µs | 38µs |
| | Delay in microseconds | | |
When I look at this and I think that 10µs, while it might be the theoretical limit of the average human ear, it's not practical to correct delays above this level. Delays above 100µs might be something to actually pay attention to when doing this in the real-world; just guessing at this obviously . Similar to many of us not paying too much attention to frequency response above 8khz on our builds since most of us don't have testing equipment that can reliably and accurately show us the FR for those frequencies. And FR above 12kHz is getting into the realm that separates the hobbyists from the professionals.
I have definitely see situations in one of my prototypes where I had to reverse the polarity of a DTEC to correct a huge cancellation in my frequency response of a 6 driver setup I was experimenting with.
--Cheers
