May 8, 2008

Dear Editor,
I just got around to reading the article in your October 2007 issue, where Bruce Botnick talks about transferring the master tape of The Doors’ first LP to ProTools. Something he said confused me: “When the Scully 4-track machine it was mixed on neared the end of a full roll of tape, it would slow down because of the tension. . . the speed was pretty much normal at the beginning, but. . . “Light My Fire” is a quarter-tone off by the end. . .”

Now, this scenario presents a mother of a calculus textbook “word problem” -- something like this!:

A 2,500’ spool of 1.5MIL-thick audio tape weighing 3 lbs. plays at 15 i.p.s at its head, but by the time it reaches its tail it has slowed by a musical quarter-tone. Assuming a uniform resistance against the tape machine’s capstan, pinch roller, heads, tension arms and internal motors and spindle-brakes; a uniform tape drag; and that the aluminum takeup reel is exactly the weight of the spool’s reel when empty, determine the following:

a. the tape’s playback speed at its tail;
b. whether the rate of speed change from head to tail is constant or curved; and
c. the speed change algorithm, if curved.

Any takers? Without knowing the answer, and without having access to the original un-corrected Scully for transfer, I don’t see how it’s possible to correct the problem in ProTools or in any other way, though I suppose a very sophisticated auto-tune program might be able to fix the ever-changing pitch sample-by-sample!?

And why 4-track for mastering?

Thanks,
Christian Matthews, Appollo Records
Pleasant Hill, California

I can't speak for Bruce Botnick, but I think I can address your questions.

If a reel slows down by 25 cents over, say, 30 minutes of tape, that's less than 1 cent per minute. So for a three minute song, the delta from start to finish would be three cents - hardly notcieable at all. You could simply speed up the entire tune by, say, 2 cents and be pretty much in the ballpark.

As to four-track mastering, I knew some engineers who preferred mixing down each channel on two tracks, thus giving the equivalent of more track width because four-track machines usually handled wider tape than equivalent two-track machines.

It would be easy if you had the original tape, because then you could build a better tape player that wouldn't slow down (i.e. have motors and an encoder that would speed up the motors if the tape was moving too slowly etc.) Now as far as your question goes, I have an answer, and then more questions.

(a) the tape by the end of the reel is moving through at 14.573 ips. (I'm assuming this is inches per second?)

(b) Considering the complexity of the physical system, I think it unlikely that the relationship is linear. See part (c) for details.

(c) in order to answer this question, I need to know under what assumptions I will be working. Should I assume that the motors are strong enough that they will move at a constant rate from start to finish? Note that this will still lead to a nonlinearity due to the changes in radius as the tape reels increase in size. This would, however, increase the pitch of the music, so it seems that this is not the only effect going on. In other words, do you want this to be calcuated as a physics problem where forces are taken into consideration or as a calculus problem where forces are considered?

Daniel