Yes, x alone positioning a point in a line completes the explanation, very cool.
Thinking about stereo, I'd say we have two points representing the speakers plus a third representing the listener (simplified model, obviously)
I can kinda agree with this. I'm not sure I would call it another "dimension", simply because it's a variable that is unknown to the mix engineer. It's not a tool the mix engineer(other than by guessing) can work with. Maybe they can make educated guesses, though, so maybe I can see an argument. They also have the real 2nd dimension of "time". It's not a spatial dimension, but time is often referred to as the fourth dimension in our 3D world
. IMO, this is where the 2nd dimension of stereo comes from. Mix engineers know that the sound will spread out in 3 dimensions as a function of time. They can use this to make certain sounds come from "behind" you. The third dimension, "height" is something that's really interesting to me. From what I've learned recently, it seems that it comes from frequency response manipulation designed to trick the brain into thinking a sound is coming from above.
We confirm that three dimensions
can be represented by using that
audiocheck LEDR test (certainly via headphones, otherwise when adequate gear is correctly set up in-room, assuming a non-confounding room) for example. So I agree with the "stereo is 3D" argument.
It works here really well on speakers
. I would make the distinction between real dimensions and simulated dimensions(illusions). From the perspective of our brain, the sound really is coming from above us. From the speaker's perspective it's coming from the same "point" in the z plane. It's why I agree with both sides. From our brain's perspective(which is what matters, ultimately), 2 speakers are capable of moving images in 3 dimensions.
I'd also assume modern object-oriented multichannel can do it more comprehensively/reliably (but I don't have that set up, and availability of music in that format is limited).
Indeed! Multichannel (with surrounds and heights) is capable of real (not simulated) 3D. The problem is(as you say) the lack of adoption, and by consequence, lack of material. It's just not practical, imo. No doubt multichannel sounds better than stereo ever can, but good stereo gets you 90% of the way there, and clutters the room up 500% less. Luckily, I live alone(hopefully not forever), so I can experiment with multichannel. True multichannel is a small step above stereo, but it's rare(especially outside of classical), so 90% of the content I listen to is still stereo. One great tool I've found is upmixing to Auro3D. I prefer Auro3D over stereo on all but just a few songs(even with crap surrounds). Problem is it requires 4 height channels, and Auro2D or Dolby Atomos or DTS are all worse than stereo.
Shame you couldn't find that video! Something I really like about these forums are the fabulous tangents. The Sorli and Fiscaletti article (linked upthread, on time as 4d—or not) was very cool also.
I'm gonna keep looking. The concept that really helped me to understand higher dimensions is the concept of compressing 3 dimensions down into a single point. So:
0th dimension: a point
1st dimension: two points, connected with a line
2nd dimension(plane): three points connected by lines(think triangle)
3rd dimension: 4 points connected by lines(think triangular prism)
4th dimension: compress that triangular prism down into a single point, now draw another point, and then draw a line to connect those "points". That's 4 dimensions
5th dimension: draw a 3rd "triangular prism point" and connect it with a line.
etc.