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I agree with one of your assertions--that we can hear sounds in three dimensions with two ears. But I disagree with the rest of your analysis because the BACCH-SP demonstrates conclusively that hearing in three dimensions from two-channel sources--especially from recordings made using only two microphones--is possible.
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But I'm skeptical about multichannel for two a priori reasons. First, we only have two ears. Multichannel recordings tend to be made using very large microphone arrays, with microphones positioned in different parts of a hall. The results might be impressive and even evocative of the experience of listening to a concert, but I suspect that the effect is unlikely to be anything like what I hear from Row 2 at the Philharmonie.
Second, I think multichannel reproduction faces the same basic problem as conventional stereo playback: placing speakers in a room and in positions that sound good, but have no precise relation to what the recording engineer did, adds a host of acoustic artifacts that were not present on the original recording.
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Height reproduction from stereo or Mch systems without additional height channels is a very on again, off again thing that is highly playback system and room dependent. For example, speaker dispersion and ceiling reflections in the room play a big role regardless of the playback technology employed. I have heard excellent systems that could provide something of a vague suggestion of height, and others equally fine that do not. I would be most interested in any theoretical explanations Dr. Chouieri can provide of how his system can accurately recreate height information from a one-dimensional, two channel speaker array. Width and depth, yes. But, with height, I am highly skeptical. And, if height is heard, I would expect other factors to be at work, as described. It is at best an even more elusive phantom image than depth, in my view.
Ah, yes, the "I have only got two ears" fallacy. With headphones, yes, the two separate channels are one for one matched with each ear. But, with speakers, the omni directional response characteristic of each ear means that both ears are hearing all speakers all the time. And, each ear can hear sounds coming from different directions simultaneously, whether from stereo, Mch or Auro 3D. There is no one sound source to one ear correspondence at live concerts or when listening to speakers. That is the upshot of binaural hearing in humans.
In fact, at live concerts there is much, much more reflected sound reaching our ears omnidirectionally than there is direct sound. But, the direct sound predominates because it is spread over a much narrower angular window than the reflected sound - it is angularly more concentrated and perceived as louder than the more diffuse, higher levels of reflected energy - and it reaches our ears sooner than the reflected energy. The Haas Effect explains this perceived predominance. So, it is difficult, impossible even, to identify the presence of the reflected energy until you remove it, one reason music in a good hall is highly preferable to an outdoor concert. That is true not only spatially, but tonally, as well. The hall and its reflections play a major role in musical tonality.
A parallel: it is easy to see why man perceived that the sun revolved around the earth. That is how it appears to our senses. But, only scientific measurements beyond our unaided senses revealed that it was the other way around. Similarly, your ears and your unaided perception do not necessarily tell you the whole story of what is going on, as with direct and reflected sound.
Yet, the stereo recordings used by BACCH do not contain much of this reflected energy from the hall, as you would hear at your seat. Nor, do they contain any angular information beyond the direct and reflected energy from just the frontal soundstage. If it also captures reflected energy from other parts of the hall, it redirects it at you frontally - from the wrong angles. Stereo contains only partial information. Mch gathers and contains much more of the information one hears in the hall.
It is also quite an eye opener to switch from Mch to stereo in my room, as I am sure that BACCH on sounds quite different than off. However, I have fooled many a visitor to my room. They thought Mch was just very good stereo, until I switched to plain stereo. I have done this countless times with visitors, and no one yet has preferred the stereo or considered it truer to live sound. If you could get to Philly, I could easily demonstrate this.
Not all Mch recordings are, in fact, done with large arrays. Some are minimalist 5-mike setups, some do use multi-mike arrays. Many of the latter are quite successful, however. I say this as one who disliked the early DGG multi miked stereo intensely. The real issue was that old multi-miking with numerous directional spot mikes each captured just a small segment of the performers together with the small slice of space immediately around them. The resulting spatial cues in the stereo mix were therefore a confused hodgepodge of spatial segments, some overlapping. Mch mixing and mastering for classical music today is much more successful in recognizing this and achieving a more consistent overall sense of space and the performers within it, which is its objective. This multi-mike spatial issue is, by the way, a problem with the Dolby Atmos system in its attempts to move sound "objects" around the 3D soundstage. They carry their own locally recorded spatial cues around with them against the larger sense of space. But, that is movies, not music.
There is little confusion over speaker angular setup for Mch. The de facto standard is the 5-channel ITU angular arrangement used by well over 90% of classical recordings over the past dozen or so years. It is also true, by the way, that the center channel plays a very significant role. Its superiority to phantom center imaging, as in stereo, becomes quite apparent when playing remasterings of old Mercury or RCA 3 channel recordings vs. their 2 channel versions on the same SACD, as originally mastered for LP. There was a brief period in the '50's when stereo was conceived as 3-channel via mag tape, just before the invention of the 2-channel LP, disc cutters and stereo cartridges. The LP then could accommodate only 2 channels, a compromise we have lived with since then, unquestioned by most audiophiles.