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The Slide Rules


This month, I correlate the technical with the artistic using two different show-and-tell examples: multi-miked drums and an ancient analog calculator. I must be crazy. Using multiple mics on drums requires polarity awareness. Sure, polarity can be toggled in the analog domain, but once in digital form, time can be manipulated from the sample level (phase) all the way to delays that are larger than life. So if you’ve never looked for kick drum leakage in each mic and attempted to retime the kit, I’ve got some pics and clips for you. Geek first, then the tweak reward. (Translation: Roughage first, dessert later!)

Our thought processes vary depending on the task at hand — from the logically linear time manipulation example above to the nonlinear (if not abstract) world of art. Our ability to distinguish level changes varies with each person — audio geeks being hyperperceptive compared to their average consumer counterparts; aka the sonically unwashed — but from a scientific perspective, the ability to perceive change is considered to be logarithmic and that’s what the decibel is all about. Similarly, the Inverse Square Law mathematically describes the way changes in distance affect gravity, light, sound and electromagnetic radiation (EMR). If you’re an electric guitar player — or know one — then you’ve dealt with EMR.

We all have a feel for the decibel because it relates directly to our perception of changes in SPL. At the circuit level, voltage and power changes create a ratio that gets converted to decibels using logarithms. We take for granted that the scientific calculator has simplified our pursuit of things mathematical, but it was not so long ago that the slide rule — a physically linear device — was an essential part of an engineer’s tool kit. What an abacus is to basic math — like addition and multiplication — a slide rule is to higher math, such as the aforementioned logarithmic and exponential equations.

Let’s talk exponents for a minute. Most of us tech types know that 10 raised to nice round “natural number” powers (1, 2, 3, etc.) yields 10, 100 and 1,000, respectively. An exponent can also be a decimal fraction (a rational number). So, given only the exponent of 10 — that exponent being known as a common logarithm — it’s possible to determine the number using a calculator, slide rule or logarithmic table.

Applying this theory to the audio world, a signal raised from one volt to two volts or lowered from two volts to one volt is, respectively, doubled or halved. Two divided by one equals two; one divided by two equals ½, or 0.5. The log of that doubling or halving yields the same number but one of opposite numeric polarity (the log of 2 is 0.3, the log of 0.5 is -0.3), so that 10 raised to the “0.3 power” is 2 and 10 raised to the “-0.3 power” is 0.5. The log of those numbers, when multiplied by 20, equals +6 dB and -6 dB, respectively.

Aside from your workstation’s obvious emulation of traditional sonic tools (mixer, EQ, dynamics, etc.), it is also an oscilloscope, dB meter and time measurement/manipulation device. Figure 2 shows three waveforms: kick, overhead and acoustic guitar mics. Relative to the kick impulse, each waveform is delayed simply by the mic’s position and its relationship with the speed of sound. The overhead mic was positioned eight to 10 feet above and behind the kit, and the acoustic guitar was 10 to 15 feet farther behind the kit surrounded by gobos.

As you may know by now, one of my soapbox issues is low-frequency management. The point of this exercise is to help the low end without additive EQ. Note the polarity of the “kick leakage” into the overhead and the acoustic guitar — all of it conspiring to kill the kick’s low-end punch. Of course, the tracks can be left in place, polarity reversal being the only option in a purely analog world. But once realigned in the digital domain, the acoustic’s polarity was flipped so that all kick leakage was in phase. Think of it as time alignment.

Tweaking a fourth track, acoustic guitar DI, was much more difficult because its waveforms were so radically different from the mic. There was no drum leakage in the DI, but once the acoustic guitar mic was in place and locked in time to the kit, the DI track was visually ball-parked. Then I alternately monitored the acoustic tracks in stereo and mono, sliding the DI track and flipping its polarity until the “center” image came into focus and, when combined, the pair had the least amount of comb filtering. This was admittedly a little tedious, but well worth the effort, especially for a simple guerrilla recording using a student guitar that was less than optimum.

To show how aligning the timing of elements affects the mix, audible online samples are provided at These clearly show the before and after difference, both for flat and peak-limited and EQ’d versions (using mix bus processing only; the individual multitracks are always flat). The track was a cover version of Buffalo Springfield’s “For What It’s Worth.”

Did anyone hear distortion on the overhead track? It wasn’t obvious during tracking — I didn’t notice until I zoomed in for time alignment — but there it was: The negative excursion is clipped. Fortunately, the threshold of clipping “worked” with the track, providing a type of overdrive that is similar to peak-limiting. Figure 3 zooms out to show the unnaturally even peaks, the result of using a very powerful mic into an external preamp (at minimum gain) feeding a Digi 002’s line input. If you ever have a problem like this, a simple in-line pad such as Audio-Technica’s ($49 retail) AT8202 will suffice — and it’s phantom power — compatible.

There you have it — the math that parallels our hearing perception. I hope the correlation of slide rule and drum timing was not too much of a stretch, but once the image was in my head, it would not shake loose. If you get a chance to time-align the kit, remember that you should be looking for phase issues in all the kit mics. In any case, drop me a line and let me know if it works for you — or not.

Eddie would like to thank the musicians in his spring AE282 class and Logan Erickson for the guerrilla Pro Tools rig. For more about this month’s topic, visit