How do records hold so much music?

[IDontNotDoThings]

Okay, so hear me out here.

A 12" record has 12" diameter, right?
According to this, the average size of a groove is around 0.00654".


& according to this, the size of the label is 1.5" in radius, or 3" in diameter. (the image shows a 7" record but I'd assume the labels are the same size)

(Edit: I'm dumb & can't read, that's clearly a measurement of the printable area only & it says it's 3.875" but my point that I make later in this thread still stands so continue)

So that's 9 inches. So that'd mean it could have a maximum of 1376 grooves per side, minus the empty area around the outside.

But keep in mind that there also has to be an elevated area between each of the grooves, which would half our number to 688

So if a turntable is set at 33 1/3 RPM, that means that it goes through 33 1/3 of those grooves in one minute, but we counted the grooves horizontally all across the record, meaning the needle would get to two of those per revolution.

So it reaches 66 2/3 of the 688 grooves in one minute.

688 / 66.66666 = 10.32

So how is it that records can have up to 20-25 minutes of music when these calculations only give an answer of 10? 

[pg1067]

Well...your math seems right, so that leaves two places where you may have gone wrong:  (1) the premise that the average groove size is 0.00654"; and (2) the premise that the ridges between the grooves take up the same amount of space as the grooves themselves.

Here's an article that covers this subject:  https://www.gzvinyl.com/About-vinyl.aspx

Among other things, it notes that "[t]he basic width of the groove is approx. 0.04 – 0.08 mm (40 – 80 µm or 1.6 – 3 mil)."  If that's right, then your reference to "the average size of a groove" being 0.00654" is way off because 0.04mm converts to 0.0015748" (or 0.08mm converts to .00314961").  I also suspect that halving the number of grooves to account for the ridges between grooves is excessive.

Using the 0.08mm figure, the analysis proceeds thusly:

We lose 3.875" off the 12" diameter for the center label, which leaves us with 4.0625" of usable radius, and let's subtract another 0.75" for the outer lip and inner area between the end of the last song and the label.  That leaves us with 3.3125" for our grooves and ridges.  If we assume that the ridges take up 25% of that space (I'm simply making up this percentage), then we're down to 2.484375" for the grooves themselves.  At a width of 0.00314961", we have room for about 789 grooves and, with one groove per revolution and 33 1/3 RPM, we have about 23 2/3 minutes of recording space (which obviously can increase significantly if we reduce the groove width from 0.08mm to 0.004mm).

My guess is that your "record groove detail" image is talking about a 45 rpm single (7"), which holds only about 3-6 minutes of music, rather than a 12" LP.

[a51502112]

I always thought it was some kinda voodoo-magic.

[pg1067]

Here are the RIAA "Dimensional Standards - Disc - Phonographic Records for Home Use":  https://www.aardvarkmastering.com/riaa.htm

Indicates a minimum groove width for 33 1/3 and 45 RPM records of 0.001" for stereo and 0.0022" for mono.

These standards are from 1963, and I have no idea if anything changed over the years, but my guess is that this particular detail didn't change.

[El Barto]

There aren't 1,376 grooves per side. There's one continuous groove. What matters is its length. Somebody else will have to figure that length out because fuck calculus. When they figure out they can also work out how fast the needle moves along the groove.

[Stadler]

There aren't 1,376 grooves per side. There's one continuous groove. What matters is its length. Somebody else will have to figure that length out because fuck calculus. When they figure out they can also work out how fast the needle moves along the groove.

This, but using the math above, I think there are two potential errors, one math, two assumptions: one (math) that there is a flat spot in between that halves the number, and two (assumption), that the start groove and inside groove are negligible, and three (assumption) that the width is uniform.   If you do that, the math is now at least 1376/66.66, or about 20.  If the  grooves are narrower, the tracking is harder, but there are more grooves.    We know it's not actually 40 (I think the longest album side I own is  about 30 minutes per side (Deep Purple Live In London) but most album sides are about 20 minutes.   "Minute" differentials are accounted for by the spaces we talked about above.  It's not "double", but it's not "zero" either, it's somewhere in between. 

If you Google, you can find discussions about the longer a record side is, the less reliable the tracking is, because the grooves are narrower.  I've read this related to Iron Maiden, and, I believe, Genesis. 

[Mosh]

Yup, both bands crammed their side. Powerslave side 1 probably has the thinnest grooves of any record I own. The audio quality is also not great as a result (generally you’re supposed to put the quietest song at the end of a side and The Duelists is anything but).

[The Walrus]

The first two posts in this thread give me Forest Whitaker eye. Back in math class again 

[New World Rushman]

This post reminded me of something I read on the back cover of Elvis Costello's "Get Happy" album back in the late 70s/early 80s; an album that clocked in at 48:08.

From Wiki:

The original release of the album was on 12-inch vinyl and cassette. It was unusual for a single vinyl record to contain as many as twenty songs because it was thought that what was known in the industry as "groove cramming" would result in a loss of sound quality. Get Happy's producer, Nick Lowe, mentions this issue on the album's back cover:

" 'You'll have noticed that there are ten (?) tracks on each side of this, Elvis' new LP, making it a real "long player".
Elvis and I talked long and hard about the wisdom of taking this unusual step and are proud that we can now reassure hi-fi enthusiasts and/or people who never bought a record before 1967 that with the inclusion of this extra music time they will find no loss of sound quality due to "groove cramming" as the record nears the end of each face (i.e. the hole in the middle).

Now get happy.

Your friend,

Producer, Nick Lowe' "

[TAC]

I'm trying to figure out how grooves work on a CD.

[IDontNotDoThings]

Alright, so with the corrected groove length this should work out. I found this article on how to calculate a spiral length that says that this is the formula

L = Pi * R * (D+d) / 2

where L is the total length, R is the number of revolutions in the spiral, D is the outer diameter & d is the inner diameter.

So first we'd need to find how many rotations the record has. So according to pg1067's article, the outermost recording groove is placed at an 11.5" diameter for 12" records, while I'm assuming the innermost groove depends on the recording length, so let's just put it at 3.875".

So that'd mean that the total diameter would be 7.625", which is a radius of 3.8125". If we assume the lowest possible groove length as 0.04mm, we'd still have to divide by 0.08mm to get the spaces in between them. So that's 3.8125 / 0.00314961 = 1210 maximum rotations (rounding down).

So then the total length is L = Pi * 1210 * (11.5 + 3.875) / 2

L = Pi * 1210 * 15.375 / 2
L = 29222.7 inches (1dp)

So now we have to find out how fast the needle is moving along the groove.
If a record is 33 1/3 RPM, that means that the whole record is rotating at 33 1/3 RPM, meaning that it's the total circumference of the record that that speed relates to (though I might be wrong on this).

So the length of the circumference = Pi * d = Pi * 12 = 37.7 inches (1dp)

So the needle speed is 33 1/3 * 37.7 inches per minute
That's 1256 2/3 inches per minute
which is 20.94 inches per second (2dp)

29222.7 inches / 20.94 inches per second
= 1395.5 seconds
= 23 minutes 15.5 seconds

That makes more sense 

[rumborak]

As an aside, the fact that the innermost and the outermost groove are off by a factor of 3 in terms of radius means that they're also off by a factor of 3 in terms of maximum frequency they can reproduce. They designed the LP with enough headroom in mind, but it's an easily measurable drop-off the further you get into the record.

[rumborak]

I'm trying to figure out how grooves work on a CD.

Well they're pits actually, and they don't form a continuous groove like a record. Instead it's just concentric circles, like a hard drive.

[Stadler]

As an aside, the fact that the innermost and the outermost groove are off by a factor of 3 in terms of radius means that they're also off by a factor of 3 in terms of maximum frequency they can reproduce. They designed the LP with enough headroom in mind, but it's an easily measurable drop-off the further you get into the record.

As an aside, when I finally got Hotter Than Hell and  Dynasty on CD, I was BLOWN AWAY that Strange Ways and Save Your Love didn't have  tinny static mixed into them.  Having heard them on record for so many years, and sounding like shit, it was a revelation.

[TAC]

As an aside, when I finally got Hotter Than Hell and  Dynasty on CD, I was BLOWN AWAY that Strange Ways and Save Your Love didn't have  tinny static mixed into them.  Having heard them on record for so many years, and sounding like shit, it was a revelation.

Off topic but both are TAC Top 15 Kiss Songs, with Strange Ways in the Top 5.

[Mosh]

Strange Ways still sounds like shit on CD. It boggles my mind how poorly produced that album is.

[TAC]

Strange Ways still sounds like shit on CD. It boggles my mind how poorly produced that album is.

It's still easily my favorite Kiss album.

[Stadler]

Strange Ways still sounds like shit on CD. It boggles my mind how poorly produced that album is.

It's still easily my favorite Kiss album.

One of mine, too. I think it was number two on my list when I did my discography.   Not a duff song on the album (maybe Comin' Home).  The sound is a part of the charm. 

[TAC]

Strange Ways still sounds like shit on CD. It boggles my mind how poorly produced that album is.

It's still easily my favorite Kiss album.

One of mine, too. I think it was number two on my list when I did my discography.   Not a duff song on the album (maybe Comin' Home).  The sound is a part of the charm.

Love Comin' Home.

[Mosh]

I wholeheartedly agree with all of that. It’s my favorite of the original three by far and probably second after RARO for the 70s albums.

[Stadler]

Strange Ways still sounds like shit on CD. It boggles my mind how poorly produced that album is.

It's still easily my favorite Kiss album.

One of mine, too. I think it was number two on my list when I did my discography.   Not a duff song on the album (maybe Comin' Home).  The sound is a part of the charm.

Love Comin' Home.

I said "maybe".  I skip nothing on that album.  Actually, I don't skip anything until "Hooligan" (won't go to school again!)