Has anyone been able to define well or measure differences between vinyl and digital?

@fair ,

I see one major flaw in your logic. CD and two channel DSD is just that, two channels. When I am in a room, out in the wilds, or anywhere, there could be an infinite number of sound sources, that all contribute to that data you mention. When I am at home, there is only 2 sound sources. They may bounce off the walls, the floor, the windows, but there is only 2 sources. In another thread we are talking about ATMOS with 9, 11 or more speaker which still only simulates all that we can hear.

Use that 11 speaker example at CD data rates. The rate is 7.8 mbits / second. 11 speakers is not enough. 24? Now 16.8 mbits/second. Well beyond your 3.5 - 4 mbits/second.

I don't think you can correlate the data rate for the cochlea with the brain, which I suspect is a WAG, from sound information that comes from all directions, with what comes out of 2 speakers.

Auditory processing circuits in the brain drastically compress this flow of information: this explains why lossy encoding works so well. Still, if some part of the original 3.5. to 4.0 MegaBits per second flow is arbitrarily removed, artifacts may occur.

As we can see, CD falls about 5.7x short of the target of complete digital transparency. DSD64 falls about 1.4x short.

DSD128 encodes more information, by factor of 1.4x, than the nerves running between cochlea and brain can transport. DSD256 exceeds the sufficiency threshold by factor of 2.8x, and thus shall be considered far more than enough.

Is there really any proof that remasters have compressed dynamic range (the so called loudness war)? Is it just a mostly baseless term intended to invoke an emotion?

Yes there is. Many Cds have been dynamically compressed since the early 90s. You can find dynamic range numbers for a lot of albums at the Dynamic Range Database:

Album list - Dynamic Range DB (loudness-war.info)

There you can find which versions of a particular album have more or less dynamic range. You can then go to Discogs, an Lp and Cd marketplace, to buy the version you’re looking for:

Discogs - Music Database and Marketplace

Albums are supposed to be listed there by specific reissue so you can find the reissue that is supposed to sound the best or 2nd or 3d best. Check with the seller to make sure his albums are listed under the correct listing before buying. Reputedly better sounding Cds and Lps (e.g.less compressed) sell for more $ and sellers don’t always list their Cds and Lps under the correct listing. Probably just an honest mistake, but I suggest checking before buying anyway.

On a related note the dynamic ranges of Lps and Cds on the DR database cannot be compared directly. It has something to do with the way the site measures DR that makes direct comparison between the formats inaccurate. I’ve read an explanation before, but I can’t remember what it is.

Vinyl sucks.  Measure that

I think it is the physics of analog crosstalk of the cartridge :)

Ps Audio recently posted on this very topic. Perhaps the answers you seek are contained within Paul’s posts.