Remember that game you probably played when you were a kid called telephone? Maybe you called it something else, but the basic premise was to sit in a circle (or square, or oblong shape, -whatever your geometric preference) and one person would begin by whispering a phrase into the ear of the person next to him. The message would be relayed in a similar manner until everyone in the group had received it and passed it on and it got back to the person who sent it. What generally occurred -and what made the game any fun at all- was that the message would have been misheard and/or paraphrased and/or misinterpreted and re summarized, so that by the time it got back to the sender, it was drastically changed from its original form. This type of message metamorphosis occurs outside of parlor games as well - we all know how stories, once told and retold and retold, tend to become fantastic caricatures of their former selves.
With the widespread conversion of music to digital form, this same phenomenon is happening to our favorite songs; that is, in going from vinyl, to CD, to itunes, some might argue that certain works have lost their integrity, or at least been changed enough from their original form for people to take notice. The process of digital compression is one factor in this change. Digital compression allows a song to go from being a very big sound file in its natural state to a very small file in your iPod — so you can carry your entire record library in your pocket. The challenge is to maintain the quality of a CD (or record), but to stuff it into a much smaller space, and here's where your calculus comes in. You start out with a very smooth sound wave to be stored in digital form. You want to reproduce a smooth curve with square blocks, which are the digital numbers (your 0s and1s). The only way you can make square blocks look like a smooth curve is by using lots and lots and lots of very, very, very small blocks so it ends up looking as if it's smooth. Using all of these blocks means lots of storage, so practically speaking, you end up using fewer, bigger blocks- which means you end up not representing that curve very smoothly at all.
Confusing, I know. Go back and read that again if you must. You'll get it. I promise.
The difference between the smooth curve and the rough edges you end up with in the digital recording, you can think of as "noise" because it's perceived as noise. It's heard as an error, something that wasn't there in the original recording. The trick is to take the noise — which is the loss of fidelity — and just make it so you can't hear it anymore. It's kind of like having a conversation in a quiet room, versus a conversation on a loud and noisy street. You're going to miss a few words as you chat by the busy intersection.
Okay, so there are technical barriers to overcome. That can be understood, but digital compression isn't the only culprit behind the change. One must also consider what has come to be called the "loudness wars." Basically, modern engineers tweak original recordings, editing so that it "jumps out" at you. This is nothing new. It actually goes all the way back to vinyl disk cutting, when one producer after another just wanted to have his 45 sound louder than the next guy's. This is still a motivation for some producers. If their record jumps out of your iPod compared with the song that preceded it, then they've accomplished their goal, and so in the process of this editing, quiet sounds become louder and louder sounds softer, and you can see where a song's integrity might be changed.
For example, the release of Metallica's album, Death Magnetic, last year caused quite a stir because it came out simultaneously to fans as a version on Guitar Hero. The Guitar Hero version apparently doesn't have all the digital domain compression that the CD has. So players of the game were able to hear what it could have been before this compression. The result was that 10,000 or more fans signed an online petition to get the band to remix the record.
I don't think that these "remastered" versions of music are necessarily bad, but they shouldn't be synonymous with the original works. There's danger in losing the originals if we accept reworked digital forms of music as simply replacements. It'd be like "improving upon" the Mona Lisa. Yes it would be restored, maybe there are even things that could have been done better the first time around that are fixed... but is it still the Mona Lisa? Is a reproduction the same as an original work? Is a forgery -even an excellent one- worth the same to you as the original? Even if DaVinci were the one to make the changes, I think there are still some who would take issue- and, as seen with the Metallica album, there are at least 10,000.