Cassette tapes: where the fun never stops

Because, dammit, somebody is going to read this and think it's cool, like I do.

The chronology of music-that-travels-with-you is a long and lengthy one. Sheet music, cylindrical things made out of wax that probably weren't very good, vinyl records, cassette tapes, CDs, mp3s. For a long time you had to actually be able to produce the music yourself; then, for a while, you had really crappy music that you couldn't store anywhere warm. Eventually, not only was the music itself portable, you could even listen to it as you ported it around. The cassette tape, and its bastard technological cousin the Walkman, began the trend towards entertainment-on-the-go that would eventually culminate in my wholly inappropriate feelings of emotional intimacy with my li'l iPod.

That is not what I want to talk about.

What I want to talk about is something I figured out which has no practical applications whatsoever, especially considering nobody uses cassette tapes anymore. But I'm still going to blog about it, because I thought it was cool and it allows me to do something I haven't done since fifth grade: pretend that I have a rudimentary understanding of mathematics.

Now then. Note: any similarity between the terminology below and the actual technical names for what I'm talking about is purely coincidental.

We all know how cassette tapes work. There's the skinny plastic box, and inside is the actual 'tape' wrapped around two spools. The music is on the tape itself -- I am not an engineer, but magnets are involved -- and the music is ‘read’ and turned into sound as it passes over the read head. The tape is drawn over the read head by the drive spindle -- the spindle that turns the tape spool when you press ‘play’. The drive spindle turns at a fixed rate, no matter what, so for each revolution of the drive spindle a length of tape equal to the circumference of the spool is pulled across the drive head.

‘So what?’ you would say if you were still reading this.

Well, each revolution of the drive spindle puts an additional turn of tape onto the spool – hence, every time the spindle turns, the diameter of the empty spool (D) is increased by 2x the thickness of the tape (T). Hence, on the ‘xth’ revolution (Rx), the length of tape pulled across the drive head may be expressed as:

π[D + (2Rx-1T)]

At the very beginning of the tape (when the drive spool is empty) the first revolution (R1) will draw a length of tape equal to πD over the read head. By the thousandth revolution, however, the cassette player will be drawing a length of tape equal to π(D + 1998T) across the read head -- and even though magnetic tape is very thin, a few thousand layers of it add up to many, many times the spool’s initial circumference.

Hence, it can be seen that the rate at which tape passes over the read head is not fixed, but is in fact accelerating from the moment you press ‘play’. Of course, you can’t ‘hear’ this when you listen to a recorded tape, because precisely the same effect takes place during the recording process: tape is drawn across the write head faster and faster as recording progresses, just as it is drawn faster and faster across the read head when played.

What does this mean? Well, it must clearly mean that the ‘density’ of information stored on a cassette tape must decrease constantly from beginning to end. Assuming that the actual quality of the recorded information does not vary, one must presume that the ‘efficiency of tape usage’ decreases dramatically as recording progresses. If you were to unspool a cassette tape and pull it across the read head by hand at a fixed rate, you'd find that the resulting music played slower and slower. The corollary of this is that a given length of magnetic tape could, if recorded and played back at a fixed rate, store many times more music than a traditional cassette tape with no loss of quality whatsoever.

So basically, when you listen to a cassette tape you're hearing three things:

1/ Music being played slower and slower…
2/ …from a tape that keeps moving faster and faster…
3/ …and a lot of tape being wasted.

This is not important at all. I very much doubt that Sony will pay me thousands, perhaps millions of dollars for this revelation. And it’s not as if anybody even uses cassette tapes anymore.

Still.

-A