Why reversing the polarity of "tweeter"?

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I do not think it matters. Some believe in absolute phase, some don't.

According to Nelson Pass, it matters if the amp is single ended, and I agree with him. :)

Also, many old recording equipments were single ended, so it would matter when listening to old recordings.

Clean modern recordings with PP amp (little H2), it would not, but many pop/rock music are processed with H2 harmonic processor deliberately (mimicking old recordings), you may hear the difference.
 
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I've always thought it was because most people want the woofer to push on a positive pulse. I.E. if the microphone was pushed in, the woofer pushes out. On PA systems I try to get the kick drum to push the woofers out when the mallet hits the head.

Of course once the recording gets complex, it's not all that important. I'm not sure it is with the PA, either. ;)
 
I believe that well designed commercial speakers are voiced with certain polarity, so we probably don't have to concern about it as long as we follow the manufactures instruction...

For example, speaker terminals of many old JBL speakers are inverted (Black is positive).

I found this:
Reversed Polarity on JBL Speakers,When Did It Start and Why?

"The inital standard was set by Western Electric, which is understandable since they invented the loudspeaker. The original standard stated that a positive current would result in a displacement away from the magnetic field. This was simple and straightforward for single speakers. However, with the advent of multiway speakers, and the development of the compression driver, it led to a problem. Dynamic speakers, such as woofers, have their magnet assembly behind the diaphragm. Therefore, a positive current would result in a compression wave. However, starting with W.E.'s 594, compression drivers were designed with the magnet in front of the diaphragm. This means that a positive signal results in a rarefaction. In other words, a woofer and compressrion driver in a standard two-way configuration would be out of phase. However, a dynamic woofer with a dynamic tweeter would be in phase for the same standard."
 

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  • JBL - Polarity Conventions of Transducers and Systems (1988).pdf
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In a second-order filter, it is usually seen the reversing polarity of one driver assuming the 2-way system. Mostly, it would be a tweeter. Why the tweeter, not woofer? Could anybody please explain the reason?

The reason for flipping one of the drivers is to get better phase alignment in the crossover region.

I don't think it matters which one you flip. I generally do the tweeter because it's usually easier to take out and reinstall.
 
The idea is for mid and tweeter to be presented with the same phase.

So, as an example we'll assign the mid to be our reference at 0 degrees phase at low frequencies. At and beyond crossover, the mid's output will progressively lag in phase, and its output will diminish in amplitude, and its phase will tend to -180 degrees.

Meanwhile, the tweeter. At low frequencies, its output will be much diminished in amplitude, and its phase subject to +180 degrees of lead. Now, if it's polarity has been reversed, this 180 degrees becomes 0 degrees (180+180=360) - i.e., in phase with the mid. At crossover, output increases in amplitude and phase will tend to 0 degrees. Since polarity is reversed, this equates to 180 degrees. So, at high frequencies, both drivers are at 180 degrees relative to at low frequencies.

The result is that both drivers will phase-track, but there will be a 180 degree discrepancy between low and high frequencies. Which doesn't seem to matter.

A 4th-order crossover phase-tracks inherently, without need for polarity reversal.
 
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I have recently built three 4-way speakers. When optimizing crossover, i start with upper midbass first. Its crossover is based purely on getting rid of breakups. Then i add a tweeter and work on its crossover to match sensitivity and have smooth transition and of axis response. I measure tweeter in phase and out of phase, and most of the time the correct polarity has no dip and smooth phase response between the upper midbass and tweeter.
Next steps are pretty much repeat with lower midbass and upper part. Its not that complicated, you just look at it as if you are working on 2-way.

But this rambling of mine is slightly of topic. Thread starter simply asked if absolute phase is important. Most of your answers were similarly of topic, discussing simply phase behaviour in various crossovers.
Back to the original question. Is absolute phase important? Well, that should be pretty easy to answer. Just listen to your speakers for a while, then reverse speaker cables polarity on both speakers and listen again.

Other question is...is signal polarity ever observed during recording?
Example with drum is perfect. But how do you know that every song has it recorded in the same manner?

This is not something i would worry about. Room modes in lower bass are much bigger issue.
Cheers and stay safe.
 
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