THE SLIDE RULES
The August Tech's Files for MIX Magazine
©2005 by Eddie Ciletti

This month I’ll attempt to correlate the technical with the artistic using two different show and tell examples — multi-mic'd drums and an ancient analog calculator. I must be crazy…

The use of 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 (and I don’t mean Tom DeLay). So, if you've never looked for kick drum leakage in each mic and attempted to re-time the kit, I’ve got some pics and clips for ya. Geek first, then the tweak reward. (ALT: Ruffage first, then the sweet cake!)

Our thought processes vary depending on the task at hand — from the logically-linear time manipulation example above to the non-linear (if not abstract) world of art. Our ability to distinguish level changes varies with each person — audio geeks being hyper-perceptive compared to their average consumer counterparts, a.k.a., 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 electro-magnetic radiation (EMR). Don't gimme dat look! If you're a guitar player (or know one) then you've dealt with EMR.


Uh, you guessed it!  It's a Slide Rule!!!
We all have a feel for the decibel (dB) because it relates directly to our perception of changes in Sound Pressure Level (SPL). At the circuit level, voltage and power changes created 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 multiplication and division — a slide rule is to higher math, such as the aforementioned logarithmic and exponential equations.

Inverse Square Link

You should all know what a "power" is — ten-to-the-second-power or "ten squared" is 10 x 10 = 100, ten being the base and two being its exponent. Ten raised to nice, round "natural number" powers (1, 2, 3, etc.), yield 10, 100 and 1000, respectively. An exponent can also be a decimal fraction (a rational number). So, given only the exponent of ten — that exponent being known as a "common logarithm" — it is possible to determine the number using a calculator, slide rule or logarithmic table.

In our audio world, for example, 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 1/2 or .5 (point five). The log of that doubling or halving yields the same number, but one of opposite numeric polarity (the log of 2 is .3, the log of .5 is -.3), so that ten raised to the ".3 power" is 2 and ten raised to the "-.3 power" is .5 — the log of those numbers, when multiplied by 20, equals +6dB and -6dB, also respectively.

FIGURE-1: The decibel is a much easier way to compare two voltages. When comparing two powers, in watts, substitute a "10" for the "20" in the formula.

LOG LINK

BACK TO THE ART
Like it or not, DAWs have heightened our awareness of the technical. The ability to correlate what is heard to precise amounts of amplitude, frequency and phase is sweet 2 me, but that bugs lots of engineers who prefer to fly blind and just listen. The old school put tape over the VU meters, but here in geek-ville, the SPCM* prefers a switch to re-scale the meter. (* = Society For The Prevention Of Cruelty To Meters.) 

Pre-workstation, there were analog computers that did all sorts of things, a VU meter being one of the best examples. Simply by changing its fascia, a meter (which is essentially a motor with wristwatch-style pivot points) can be used to indicate dB, volts, current, temperature, etc.

WRONG SIDE OF THE TRACKS
Aside from its obvious emulation of traditional sonic tools (mixer, EQ, dynamics, etc.) your workstation is also an oscilloscope, dB meter and time measurement / manipulation device. Figure-2 shows three waveforms — of 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 ten feet above and behind the kit, the acoustic guitar was ten to fifteen feet further behind the kit and surrounded by gobos.


FIGURE-2: The speed of sound reveals itself in these three waveforms. At top, the initial impact of a kick drum and below, its leakage is delayed by the time it reaches the kit overhead mic as well as an acoustic guitar mic.

You all should know by now that 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 polarity of the acoustic was flipped so that all kick leakage was in phase. Think of it as time alignment. 

Tweaking a fourth track, the 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. I then 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 guerilla recording using a student guitar that was less than optimum.

To show how time alignment affects "the mix," check out the .wav samples in the table below.  They clearly show the before-and-after difference, both flat as well as peak limited and EQ'd versions (using mix buss processing only; the raw tracks are always flat). The track was a cover version of For What It's Worth by Buffalo Springfield. Click Here for Student mixes.

Track
Description
1
Raw mix of four tracks - kick, oh, acoustic guitar (mic and DI) - as originally captured and detailed in Figure-2
2
Time Aligned (TA) mix with faders in identical postion to previous mix. Note the extra bottom!
3
RAW, but normalized to compete with Track-2 
4
RAW after peak limiting
5
TA after peak limiting
6
RAW after peak limiting and EQ
7
TA after peak limiting and EQ
Table-1: Two versions of  Four tracks - kit, overhead, acoustic (mic + DI) - mixed in mono with identical fader settings and processing to show how Time Alignment of individual tracks improves bottom end without EQ.

OOPS!

Did anyone notice the distortion on the overhead track? It wasn't obvious during tracking — I didn't notice until taking the tracks home and zooming in for time alignment — but there it is, the negative excursion is clipped. Fortunately, the threshold of clipping "worked," a type of overdrive that it is very 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 the Digi 002's line input. If you ever have a problem like this, Audio Technica has an in-line pad, model AT8202 ($49 list, $38 street) that is phantom power compatible.


Figure-3: This Drum Overhead track has unnaturally even peaks, the result of the inability to attenuate an exceptionally hot mic signal before the preamp.

TAIL OUT
So 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. Once the image was in my head, it would not shake loose. If you do get a chance to time align the kit — keep in mind that you should be looking for phase issues in all the kit mics anyway — let me know if it works for you (or not).

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Eddie would like to thank the musicians in his spring AE282 class and Logan Erickson for the guerilla PT rig.  All of Eddie's mixing and processing was done using Adobe Audition, V1.5.

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