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Vinyl vs Digital and 24 bit vs 16 bit from vinyl.
SoAnIs
post Mar 5 2008, 10:20
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24-bit precision gives you about 16.77 million values. Assuming a total groove width of 50 x 10^-6m, the maximum movement of the cutter is physically bounded at about half that. Much more and the cutter will be in the space for an adjacent groove. Thus, 50 microns width divided by 16.77 million gives us about 3 x 10^-12m, i.e. ~0.03 angstroms.

The diameter of a hydrogen atom is 1.0 angstroms (1 x 10^-10m). That would make the resolution of a 24-bit digital signal equivalent to an analog cutter whose resolution is just about 1/30 the width of a hydrogen atom. Sadly, this seems to be physically impossible, as none of the particles smaller than atoms are stable enough to be used in records.

Of course, records aren't made of hydrogen, they're made of the polymer pvc. One molecule of pvc is about 100,000 angstroms. This means that, if the cutters were actually removing single pvc molecules the vinyl records would have about 11 bits of resolution. Sadly, they don't get even that precise, though I'm not sure the actual precision. To get down to a record made of hydrogen atoms (possible under very low temp/very high pressure I suppose) one would need 19 bits. Anything beyond that is useless as long as the laws of physics hold.

Therefore, all other things being equal, digital is superior to vinyl. That said, mastering on CDs is often terrible while the mastering on records is often made somewhat better. This varies from CD to CD and record to record, and CDs are technologically far superior to records.
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pdq
post Mar 5 2008, 13:11
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Not to be too nit-picky, but vinyl records aren't cut directly but are molded from a metal master, so the limit would be the diameter of a metal atom, which is much smaller than 100,000. Also, if they were cut directly in vinyl, the cutter needn't remove whole molecules but would readily break bonds as needed to remove part of a molecule.
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Posts in this topic
- SoAnIs   Vinyl vs Digital and 24 bit vs 16 bit from vinyl.   Mar 5 2008, 10:20
- - digital   Dig that crazy math man! Speaking as a huge v...   Mar 5 2008, 12:33
- - pdq   Not to be too nit-picky, but vinyl records aren...   Mar 5 2008, 13:11
|- - Nick.C   QUOTE (pdq @ Mar 5 2008, 12:11) Not to be...   Mar 5 2008, 13:22
|- - pdq   QUOTE (Nick.C @ Mar 5 2008, 08:22) QUOTE ...   Mar 5 2008, 18:19
- - JensRex   Best first post in years.   Mar 5 2008, 13:29
- - Axon   But the contact area of the stylus covers many tho...   Mar 5 2008, 18:39
|- - pdq   QUOTE (Axon @ Mar 5 2008, 13:39) But the ...   Mar 5 2008, 19:27
|- - Woodinville   QUOTE (pdq @ Mar 5 2008, 10:27) QUOTE (Ax...   Mar 5 2008, 20:03
- - SoAnIs   True, I simplified a lot. But, as I also showed, e...   Mar 6 2008, 03:13
|- - Vitecs   QUOTE (SoAnIs @ Mar 5 2008, 20:13) The re...   Mar 6 2008, 08:46
|- - tgoose   QUOTE (Vitecs @ Mar 6 2008, 07:46) QUOTE ...   Mar 6 2008, 11:12
- - SebastianG   Hello, SoAnIs! There's one point I'm ...   Mar 6 2008, 15:31
- - A Dawg   QUOTE (SoAnIs @ Mar 5 2008, 03:20) 24-bit...   Jun 3 2008, 04:58
|- - Mike Giacomelli   QUOTE (A Dawg @ Jun 2 2008, 23:58) As far...   Jun 3 2008, 06:10
- - A Dawg   I personally feel that 16 to 24 bit is a small, bu...   Jun 3 2008, 06:41
|- - 2Bdecided   QUOTE (A Dawg @ Jun 3 2008, 06:41) I pers...   Jun 3 2008, 10:16
- - Axon   I would argue that a closer analogy than a wood do...   Jun 3 2008, 08:34
|- - tot   QUOTE (Axon @ Jun 3 2008, 09:34) That sai...   Jun 3 2008, 12:15
|- - Juha   QUOTE (tot @ Jun 3 2008, 14:15) QUOTE (Ax...   Jun 3 2008, 19:05
- - Roseval   Some calculations for you and a proof that the LP ...   Jun 3 2008, 12:20
- - Slipstreem   From the article... QUOTE The effect is to divide ...   Jun 3 2008, 12:57
- - 2tec   QUOTE (SoAnIs @ Mar 5 2008, 03:20) Theref...   Jun 3 2008, 16:10
- - 2Bdecided   But a digital recording can sound like anything yo...   Jun 3 2008, 18:04
|- - 2tec   QUOTE (2Bdecided @ Jun 3 2008, 11:04) The...   Jun 7 2008, 22:31
||- - 2Bdecided   QUOTE (2tec @ Jun 7 2008, 22:31) QUOTE (2...   Jun 9 2008, 12:03
||- - 2tec   QUOTE (2Bdecided @ Jun 9 2008, 05:03) QUO...   Jun 11 2008, 00:12
|- - sld   QUOTE (2Bdecided @ Jun 4 2008, 01:04) ......   Jul 28 2008, 08:20
|- - botface   QUOTE (2Bdecided @ Jun 3 2008, 18:04) A v...   Jul 28 2008, 14:51
|- - Slipstreem   QUOTE (botface @ Jul 28 2008, 14:51) Sorr...   Jul 28 2008, 15:41
||- - botface   QUOTE (Slipstreem @ Jul 28 2008, 15:41) Q...   Jul 28 2008, 17:03
||- - 2Bdecided   QUOTE (botface @ Jul 28 2008, 17:03) I...   Jul 29 2008, 10:13
||- - botface   Fair comment. It seems we don't disagree after...   Jul 29 2008, 10:53
||- - 2tec   QUOTE (2Bdecided @ Jul 29 2008, 03:13) I ...   Oct 17 2008, 19:44
||- - 2Bdecided   QUOTE (2tec @ Oct 17 2008, 19:44) Indeed,...   Oct 20 2008, 14:45
|- - Woodinville   QUOTE (botface @ Jul 28 2008, 06:51) Sorr...   Jul 28 2008, 18:00
- - Axon   Oh, nice! Another flat transfer partisan. Welc...   Jun 3 2008, 20:20
|- - Woodinville   QUOTE (Axon @ Jun 3 2008, 12:20) Oh, nice...   Jun 3 2008, 20:26
|- - Juha   QUOTE (Woodinville @ Jun 3 2008, 22:26) Q...   Jun 3 2008, 21:07
- - Axon   The gain structure and DR are completely f*cked up...   Jun 3 2008, 20:40
|- - Juha   QUOTE (Axon @ Jun 3 2008, 22:40) The gain...   Jun 3 2008, 21:17
|- - Woodinville   QUOTE (Axon @ Jun 3 2008, 12:40) The gain...   Jun 3 2008, 21:43
- - AndyH-ha   The Emu specs say the preamp noise is approaching ...   Jun 3 2008, 21:11
|- - Axon   QUOTE (Juha @ Jun 3 2008, 15:35) QUOTE (A...   Jun 3 2008, 22:35
|- - Juha   QUOTE (Axon @ Jun 4 2008, 00:35) BTW Juha...   Jun 4 2008, 05:10
|- - Axon   QUOTE (Juha @ Jun 3 2008, 23:10) QUOTE (A...   Jun 9 2008, 16:55
- - AndyH-ha   Are you using a moving coil cartridge? Normal gain...   Jun 3 2008, 21:18
|- - Juha   QUOTE (AndyH-ha @ Jun 3 2008, 23:18)...   Jun 3 2008, 21:35
- - AndyH-ha   No, Axon is the one turning the gain to maximum.   Jun 3 2008, 21:37
- - Axon   It's entirely a matter of the gain used. I can...   Jun 3 2008, 22:20
- - SHADES   QUOTE (SoAnIs @ Mar 5 2008, 09:20) 24-bit...   Jul 28 2008, 06:30
|- - Axon   QUOTE (SHADES @ Jul 28 2008, 00:30) Reall...   Jul 28 2008, 08:03
- - richms   My brief venture into vinyl was short lived becaus...   Jul 28 2008, 16:37
|- - pdq   QUOTE (richms @ Jul 28 2008, 11:37) My br...   Jul 28 2008, 17:16
- - pdq   What about the experiments in which an analog audi...   Oct 17 2008, 19:56
|- - 2tec   QUOTE (pdq @ Oct 17 2008, 12:56) What abo...   Oct 18 2008, 02:20
|- - Arnold B. Krueger   QUOTE (pdq @ Oct 17 2008, 14:56) What abo...   Oct 30 2008, 20:57
|- - Axon   QUOTE (Arnold B. Krueger @ Oct 30 2008, 14...   Oct 30 2008, 22:40
|- - Arnold B. Krueger   QUOTE (Axon @ Oct 30 2008, 17:40) Right n...   Oct 31 2008, 13:53
|- - Slipstreem   QUOTE (Arnold B. Krueger @ Oct 31 2008, 13...   Oct 31 2008, 15:37
||- - Arnold B. Krueger   QUOTE (Slipstreem @ Oct 31 2008, 10:37) Q...   Nov 2 2008, 12:27
||- - Slipstreem   QUOTE (Arnold B. Krueger @ Nov 2 2008, 11...   Nov 2 2008, 17:43
|- - Axon   QUOTE (Arnold B. Krueger @ Oct 31 2008, 07...   Oct 31 2008, 17:38
|- - Arnold B. Krueger   QUOTE (Axon @ Oct 31 2008, 12:38) QUOTE (...   Nov 2 2008, 12:38
|- - Axon   QUOTE (Arnold B. Krueger @ Nov 2 2008, 06...   Nov 2 2008, 18:56
|- - Arnold B. Krueger   QUOTE (Axon @ Nov 2 2008, 13:56) Also, if...   Nov 2 2008, 23:09
|- - Axon   QUOTE (Arnold B. Krueger @ Nov 2 2008, 17...   Nov 2 2008, 23:50
- - Slipstreem   I do see your point, but I've stopped using my...   Oct 18 2008, 03:18
|- - Arnold B. Krueger   QUOTE (Slipstreem @ Oct 17 2008, 21:18) A...   Oct 29 2008, 22:11
|- - [JAZ]   QUOTE (Arnold B. Krueger @ Oct 29 2008, 23...   Oct 29 2008, 22:37
|- - Arnold B. Krueger   QUOTE ' date='Oct 29 2008, 17:37' post...   Oct 30 2008, 20:41
|- - Slipstreem   QUOTE (Arnold B. Krueger @ Oct 30 2008, 20...   Oct 30 2008, 21:07
- - Axon   ARNY SPEAKS! Took ya long enough to get here   Oct 29 2008, 22:20
- - Slipstreem   I never said that the cassette format was sonicall...   Oct 29 2008, 23:37
- - Slipstreem   @Axon: I hope you're providing the recommended...   Oct 31 2008, 01:00
|- - Axon   QUOTE (Slipstreem @ Oct 30 2008, 19:00) @...   Oct 31 2008, 01:11
- - Slipstreem   Ah. Fair enough. Cheers, Slipstreem.   Oct 31 2008, 01:24
- - Axon   ... That said, I do intend on scoring a 78 cart so...   Oct 31 2008, 01:52
|- - botface   QUOTE (Axon @ Oct 31 2008, 01:52) ... Tha...   Nov 1 2008, 10:40
- - Slipstreem   Would it not work better with the capacitors solde...   Oct 31 2008, 02:14
- - Axon   Soldering the leads on a cart is an easy way to fr...   Oct 31 2008, 02:26
- - Slipstreem   Best of luck with it when it happens. I'm hopi...   Oct 31 2008, 02:32
- - Axon   Sure, thanks - although I'll warn you, this is...   Nov 1 2008, 19:49
- - krabapple   Goodness, Axon on RAHE, Arny on HA, a mixed-race D...   Nov 7 2008, 18:41
|- - Woodinville   QUOTE (krabapple @ Nov 7 2008, 09:41) Goo...   Nov 11 2008, 19:49
|- - krabapple   QUOTE (Woodinville @ Nov 11 2008, 14:49) ...   Nov 11 2008, 21:32
|- - Arnold B. Krueger   QUOTE (krabapple @ Nov 11 2008, 15:32) To...   Nov 13 2008, 14:05
- - ff123   I feel old. Good to see you Arny.   Nov 8 2008, 03:54
|- - Arnold B. Krueger   QUOTE (ff123 @ Nov 7 2008, 21:54) I feel ...   Nov 10 2008, 03:06
- - Axon   Wow, talk about bum luck on RAHE. Or just bums. I...   Nov 11 2008, 19:58
- - Arnold B. Krueger   QUOTE (Axon @ Nov 11 2008, 13:58) I tend ...   Nov 13 2008, 14:17
- - Axon   QUOTE (Arnold B. Krueger @ Nov 13 2008, 07...   Nov 13 2008, 20:42
|- - krabapple   QUOTE (Axon @ Nov 13 2008, 14:42) QUOTE (...   Nov 14 2008, 04:06
|- - Arnold B. Krueger   [quote name='krabapple' date='Nov 13 2...   Nov 15 2008, 22:54
|- - Woodinville   QUOTE (Arnold B. Krueger @ Nov 15 2008, 13...   Nov 16 2008, 06:10
|- - Arnold B. Krueger   QUOTE (Woodinville @ Nov 16 2008, 00:10) ...   Nov 17 2008, 15:24
|- - Woodinville   QUOTE (Arnold B. Krueger @ Nov 17 2008, 06...   Nov 18 2008, 06:24
|- - Arnold B. Krueger   QUOTE (Woodinville @ Nov 18 2008, 00:24) ...   Nov 18 2008, 22:30
|- - Woodinville   QUOTE (Arnold B. Krueger @ Nov 18 2008, 13...   Nov 19 2008, 00:00
- - Woodinville   QUOTE (Arnold B. Krueger @ Nov 13 2008, 05...   Nov 15 2008, 02:03
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