Armageddon wrote:FYI, Shooshie, while I of course checked out your links, all it did was muddy my waters even more in regards to what 32-bit float actually means in comparison to 24-bit. If I read it correctly, I assume that, like I thought, 32-bit float is less of an actual thing and more of an internal process that allows for higher headroom/resolution, which explains why you can hear 32-bit float files on your 24-bit AD/DA converter, even if you play these files back through something as simple as your QT player. Let's put it this way, I certainly don't think you lose anything by recording, mixing and mastering at 32-bit float, and if you wind up mixing down to a two-track external recorder, like a 1-bit DSD unit or even to analog tape, you're possibly capturing more frequencies than you would if you'd just dumped it at 24-bits. And if you're bouncing to disc at that resolution, like I do, you've got a master file with all that resolution intact. As far as I can tell, most dithering algorithms don't have a problem downconverting from 32-bit float, either.Shooshie wrote:And there is an external reference that remains the excellent source of information that it was then.
You'll find that HERE.
Let me try an abstraction. I may mix a few metaphors, but bear with me, and I think I can make 32bit Float a real thing for you.
First of all: 32 bit float is actually 24 bits of loudness detail. If we were to imagine that we're drawing a picture of a mountain, and we want to see the silhouette of the mountain's profile, as the sun sets behind it. We have a roll of paper that is 24 bits high, and infinitely long. So, we draw from the highest point on the mountain down to as low as we can get within a 24 bit range. (think 24 inches tall, which if you hold it up in front of you, covers nearly all the mountain) within that 24 inches, we are able to capture every detail from the mountain's peak down to maybe a 1000 feet from its base. Most people aren't going to care what's down in that lowest part, anyway. They just want to see the majestic peak of the mountain. With 24 bit paper, we can see nearly all of that mountain. But when it goes down too far, we just conveniently have to skip that part. That's 24 bit paper.
Now we get this newfangled 32bit floating point paper. When the mountain's profile sinks down into that lower 1000 feet, guess what we do? This new paper allows us to pull on it, and it tears along a vertical line and moves the new part down to the bottom of that 1000 foot mountain valley. So, now we have 24 bit paper on which we can draw the silhouette of the valley. When the mountain's profile goes back up, you just slice the paper and slide it up to fit what you are drawing. At any given time, you have a HUGE range (24 bit paper is nothing to sneeze at. It'll capture any detail you find on the surface of that mountain's ridge). But when the mountain drops out of range, the paper just automatically slices itself and moves the next section of the drawing down. The drawing continues on it as if nothing ever happened.
Now you reach a point in the mountain where a wealthy Arab built the tallest building in the world, right there on its peak! Even your 24 bit paper cannot contain that new detail shooting up from its surface. 32 bit paper slices itself and floats the next section up so that you can adequately draw every detail of that Arab's building on its 24 bit tall surface.
We continue doing this with our mountain range until we've made a mural that wraps completely around our display room when you mount all these stretches of 24 bit paper on the wall. Linearly, as it goes around the room on the wall, you end up with a series of rectangles all touching each other at their left and right edges. But their tops and bottoms are discontinuous. This section of paper is taped to the wall way up here, and the next section that abuts it is way down here on the floor. The next section is eye-level, as are most sections. So, as the mountain range's surface leaps out of the range of our 24 bit paper (which is pretty darned tall to begin with), we simply move that portion of the paper up or down until all of it is in range.
If we had to draw the entire mountain, and not just a silhouette of its edge, we'd be in trouble. You can't draw the tallest point and the lowest point together in the exact same vertical line. But if you draw one detail in the stratosphere, then the next one at the bottom of the Grand Canyon, then our 24 bit paper (with the 8-bit instructions on how high or low to move the paper, making it 32 bits total) can capture every point along that ridge, no matter how high or low it goes. It looks like a bunch of stair-stepping rectangles, all 24 bits high, but that extra 8 bits can raise or lower each length of paper (no matter how short or long a section it is) to any height on the wall. You will always be able to continue drawing the edge of the mountain, no matter where it goes.
Another real-world example: Google Earth. Zoom out and you can see the whole planet. Zoom in and you can see what's in the barbecue grill in Billy-Bob's back yard. At each zoom, you can see all the detail that is perceivable by the human eye at that distance. You know BillyBob's sausage links are on that grill in a suburb of Nashville, but you don't expect to see it when you're looking at the entire planet. But use that 8 bit exponent to zoom in, and your 24 bits of detail can describe every bead of greasy sweat on that sausage link.
Sonically, we're describing the sound from any range -- from the sound of mitosis and meiosis in dividing cells, to the sound of exploding sunspots on the surface of stars, to that of the big bang itself. The reason it's possible is that nobody expects to hear cells dividing if their space craft is hovering over a sunspot and listening to the roar of the star.
24 bits is always describing every detail within its range. 32 bit floating point is merely that same 24 bits of extreme range, but with an added 8 bit instruction on how far out to zoom, how high to mount the graph paper on the wall as the line exceeds the range of the previous piece of graph paper, or whether to listen to microscopic sounds or listen for cosmic big-bangs. (or your wife telling you for the 10th time to take the garbage out)
This is too long, so I won't explain in detail about the benefits of doing so, but since this is the main reason for using 32bit FP, I'll summarize. Rather than rounding off the details when they're out of range, 32bit FP actually records them. When a lot of rounded off numbers get multiplied by each other in effects processing, the resulting details that we CAN hear may be quite different than the ones we'd hear if the numbers were not rounded off. Multiply them over and over, and pretty soon you're talking about simply a differently shaped line graph. It's this differently shaped line, caused by multiplying too many rounded numbers, too many times, that reaches our ears in audible form, and causes us to perceive a loss of detail at 16 or 24 bits, in comparison to the full 32 bits fp. (or 64 bits fp)
DP, recording to disk at 32 bits floating point, is simply as accurate as digital sound allows us to get. Frankly, that's a lot more accurate than anything that ever came before it. If you're listening to the Big Bang, what does it matter if you can't hear cells dividing? Nothing at all. But if you're processing those sounds such that the cell-division noises are being multiplied by themselves over and over and over, thousands of times, then the difference becomes audible.
Sorry for the long description. This is a very simple concept once you understand it, but abstract to the point of meaningless when you don't. Better to understand it, even if it takes a lot of people trying a lot of ways of explaining things.
Shooshie
