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SO ... HOW do we measure soundstage???

It's an obvious fault in the component chain if the channels leak into each other already in the electrical domain, opposite to the natural crosstalk that occurs in the acoustic domain, where both ears should hear the sound of both channels similarly as the ears would hear a real sound 30 degrees in front of them.
That’s a tautological argument that ignores the fact that crosstalk is crosstalk regardless of where it happens in the audio chain. There is no such thing as “natural crosstalk” you are misapplying an adjective to make a semantic argument. Crosstalk is crosstalk. It’s objective and measurable. And it’s effect on the sound doesn’t depend on arbitrary labels of natural or unnatural

A sound that is not canceled out in the opposite ear.
You just made that up to suit your argument

No, it isn't. Even if the recording is mixed to a separate left and a right channel, and the playback consists of one left loudspeaker and one right loudspeaker, it doesn't mean that the sound of those two channels is exclusively meant to be heard just in the left or the right ear.

How do you know what is “meant?” That is an assumption.

For a stereo recording to sound natural, we must be able to hear everything in the mix with both our ears in the same way as we would hear the sounds live.

That is just patently wrong. If we are talking about *recordings* sounding natural you are dead in the water with any studio multi track recording. We are then limited to minimalist recordings of acoustic performances. And make no mistake about it. Crosstalk cancelation will give you objectively more accurate and more natural imaging, sound staging and and ambient hall retrieval by an order of magnitude.

Ask yourself this: If a real sound object was positioned 30 degrees to the left in front of you, wouldn't you hear that sound with both your ears and be able to know exactly from what direction that sound was coming?
Yes

And take that experiment further, do you think you would be better able to pinpoint that sound position more accurately if you blocked your right ear with your finger?
That’s not what crosstalk cancelation does. You are conflating actual live sound that eminates from individual sources with stereo play back of a recording of such objects. THERE IS NO CROSSTALK TO CANCEL in real life. If you record an object at a 30 degree angle the recording picks up the spatial cues and encoded them discreetly in 2 channels. If the playback adds crosstalk it is corrupting those spatial cues.

In the example below you have the left channel only of a Norah Jones song.
https://www.dropbox.com/scl/fi/m12w...-sec.wav?rlkey=8ncp6ex7ah2fmhwbx7dllchnm&dl=0

1. When you listen to this track you will hear that the sound is coming from the exact position of the left loudspeaker, that is of course expected because that IS the exact position of the sound, and that's the correct direction this sound IS coming from.

2. Try now to keep your head looking straight forward between your speakers and now block your right ear with your finger. By doing that you will most likely notice that the sound seems to be coming from a position outside the left speaker, but do you find this to be more correct than when you heard the recording with both your ears? No, you shouldn't think that because you fully well know that is not a more accurate way of hearing it. But still, that's exactly your argument when you say that the sound would be more accurate if you use crosstalk cancellation.
This is a bizarre experiment which assumes there is a universal desire to locate images on the speakers.

There is no crosstalk to cancel in a normal 2-channel audio production either

Actually there is but you are conflating recording with playback.

, that is if you like to hear the mix naturally in a similar way as our hearing normally works in real life. It's of course perfectly okay if you may subjectively prefer the recordings with crosstalk cancellation, but please don't say it's a more accurate way of hearing things.
You keep on making this same semantic argument by misapplying the word naturally.

And I will keep saying it’s more accurate because it is more accurate and that accuracy is easily demonstrated. I’m not going to back down on facts because they don’t fit your narrative

Yes, yes, and yes. But crosstalk cancellation will not solve those problems, and unfortunately, it introduces new problems.
You are simply in incorrect
 
Do you realize that we only need 17 db channel separation for full right/left stereo effect?
According to the studies Edgar has done with his team at Princeton it tops out around 25-30 db. But yes I was aware that crosstalk is insignificant when it comes to the signal path. Even many phono cartridges which are wrongly maligned from poor channel separation have channel separation that exceeds the thresholds of audibility.

Now, did you know the measured channel separation for traditional stereo systems at the listener position is generally 5-10 db? That’s a lot of added crosstalk

Do you know that the reason that is the case is due to our head sound shadow from one ear to the other that is about the greatest difference in level you'll get with a natural sound? And that this being the case our hearing doesn't make use of any additional channel separation.

True. But to actually get that much XTC even from a system as effective as the BACCH you need highly directional speakers in an extremely dead room. Along with custom filters and head tracking

Edgar hasn’t been spinning his wheels. He and his Princeton team have done a great deal of real science on this.

Further if you do a left-center-right mix, it will sound highly unnatural over headphones, but perfectly fine with speakers. This is because listening to speakers one channel leaks into the other. The fix for phones is crossfeed, or reduce the channel separation between each channel so it sounds okay over headphones.
“Perfectly fine” is subjective.
 
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I would like to read the measurements of the speakers with this processing to eliminate crosstalk
 
and how would a DSP intervene to deceive the opposite ear?
Something like this as a start.

XTC.png
 
and how would a DSP intervene to deceive the opposite ear?

Here is my guess:

A suitably-equalized, delayed and out-of-phase cancellation signal is sent from the same-side speaker which cancels the crosstalk from the opposite-side speaker when it arrives at the same-side ear. This cancellation signal is not as loud as the crosstalk because 100% cancellation isn't necessary.

I suspect the BACCH-SP system also cancels this cancellation signal when it wraps around the head and arrives at the other ear, again with a signal not as loud as the signal it's cancelling.

The system also corrects for any perceived changes in frequency response this process might otherwise induce, which was one of areas where the electronic crosstalk cancellation systems of yesteryear fell short.
 
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The BACCH system is probably one-listener experience, as it would be with a similar system for headphones. Headphones cancels crosstalk naturally, hence there is a "opposite" system for adding crosstalk as well.

A three-channel encoder would be more convenient, IMO. But still, I want to choose model: they being here or I being there. The first model must include reflections from my own venue EXCEPT the front wall that should be acoustically invisible. The other model must include multiple speakers to "remove all walls" and replace them with reflections from all angles from the event (if there is such a recording!).
 
Polk made speakers that did this years ago. Carver had a preamp that did crosstalk cancellation years ago. The Carver preamp worked quite well on some recordings. Was very much a one person listening position.
 
Polk made speakers that did this years ago. Carver had a preamp that did crosstalk cancellation years ago. The Carver preamp worked quite well on some recordings. Was very much a one person listening position.
Do you mean that Polk had three-channel or just crosstalk cancellation? Have been talking with the constructor of Bremen speakers and system, it is a bit secret but based on a center speaker and speakers placed on the sidewalls. I would guess these replace the L/R primary wall reflections and makes the side walls "invisible". But perhaps also act L/R speakers to widen the front scene with the center to create phantoms between L-C and C-R (i.e. three-channel). Those who have heard it says it is really very close to a real event, and you could even walk around in front of the system and get the same impression. I would really want to hear that system some time.
 
Polk made speakers that did this years ago.

Yes, and they came out with an updated version of their "Stereo Dimensional Array" with their Legend L800 speaker a few years ago.

Carver had a preamp that did crosstalk cancellation years ago. The Carver preamp worked quite well on some recordings. Was very much a one person listening position.

I owned a knock-off of the Carver electronic crosstalk cancellator back in the early 80's. Also owned the Apt-Holman preamp described in post #66. Used a Dyna-Quad hookup at one point (it was a learning experience), and even made my own bulky passive interaural crosstalk cancellator using large foam wedges. All of these approaches had advantages and disadvantages. I went back to conventional two-channel stereo each time, and that's what I'm using today, albeit with somewhat unconventional speakers in a somewhat unconventional configuration.
 
For conventional "expansion" the QSound has been mentioned. There is also the Roland RSS, used on e.g. Lisa Nilssons album "Himlen runt hörnet". It contains a lot sound that is outside the normal stereo width.

 
listening with headphones naturally removes the crosstalk and removes the possibility of listening to the live event, the sensation of presence and ambience is eliminated. The reflections of our room, appropriately controlled and treated, allow us to reproduce the environment where the recording was made.
 
listening with headphones naturally removes the crosstalk and removes the possibility of listening to the live event, the sensation of presence and ambience is eliminated. The reflections of our room, appropriately controlled and treated, allow us to reproduce the environment where the recording was made.

This has been my experience.

To be more precise, ime it is relatively late-arriving, spectrally-correct (or nearly so) reflections that are effective in delivering the reverberation tails on the recording from many different directions, thus conveying the ambience or "sense of space" on the recording.
 
listening with headphones naturally removes the crosstalk and removes the possibility of listening to the live event, the sensation of presence and ambience is eliminated. The reflections of our room, appropriately controlled and treated, allow us to reproduce the environment where the recording was made.
How possibly? The reflections of the room where recording was made are in the recording, your room adds its own reflections and thus distorts the original recording. You may like it, but it does not brings you closer to "environment where the recording was made".
 
The reflections of our room, appropriately controlled and treated, allow us to reproduce the environment where the recording was made.
I do not understand. How exactly do the reflections in my living room reproduce the environment of say an opera house, or a big concert hall? If that only would be the case.
And why do headphones eliminate the sensation of presence other than by the lack of spatial cues from missing HRTF (and low amount of ambience because this is how most recordings are done)?
 
The reflections of the room where recording was made are in the recording, your room adds its own reflections and thus distorts the original recording.

How exactly do the reflections in my living room reproduce the environment of say an opera house, or a big concert hall?

In the playback room there is, in effect, a competition between two "packages" of venue cues: The venue cues on the recording, and the "small room signature" cues of the playback room. The ear/brain system tends to accept the most plausible package of cues rather than combining and conflating two conflicting packages of cues. The desired outcome is for the venue package of cues on the recording to be perceptually dominant.

The playback room's signature is most effectively conveyed by the early reflections, while the venue cues on the recording (in particular the reverberation tails) are most effectively conveyed by the late reflections, assuming they are spectrally correct, or nearly so.

By managing the in-room reflections to minimize the early ones, while preserving the spectral balance of the later ones, it is possible for the recording venue's package of cues (whether they be real or engineered or both) to become perceptually dominant. This is sometimes referred to as a "you are there" presentation.
 
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How possibly? The reflections of the room where recording was made are in the recording, your room adds its own reflections and thus distorts the original recording. You may like it, but it does not brings you closer to "environment where the recording was made".
Given the example of the Marcus King band earlier, what is the "environment where the recording was made"? They did the recording in a van, but the final mix was done somewhere else. It's not mimicking the van, or a church or a large concert hall.

The mixer did a good job for it to sound good over speakers in home environment. So again, if you want the band coming over to your place - the reflections from your room should be included (except front wall). If you want to be transferred to the event - which event is that? The mixers idea of an event?
 
By managing the in-room reflections to minimize the early ones, while preserving the spectral balance of the later ones, it is possible for the recording venue's package of cues (whether they be real or engineered or both) to become perceptually dominant.
In my view that is mostly wishful thinking.
A concert hall has reverberation time around 2000ms. A listening room <500ms.
What later reflections should be "conveying"? And how do you get later reflections without earlier ones? At best one might control first reflections. The number of second reflections is 30 in a cuboid room, from each speaker.
 
When you are lucky enough to listen to set ups in dedicated environments where the right balance between direct and reverberated sound has been achieved, in addition to the classic acoustic scene you are able to focus on the instrumentalists, they are solid and also the distances between them perceiving the sense of space.
 
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