In last month’s column, we looked at DC resistance measurements across pot lugs and determined that when measuring an audio taper pot’s carbon trace from its midpoint to the two outer lugs, different amounts of resistance will be present depending on which side we’re measuring. I stated that “10 percent is the de facto standard for audio taper pots at the midpoint because it correlates to the log plot (graph) that describes human hearing.” Let me expand on that a little.
According to Wikipedia, the term “de facto standard” denotes an accepted product, process, system or technical standard that has achieved status informally by public acceptance or market forces, such as early entrance to the market. An example of a de facto standard that might have emerged due to marketing would be the adoption of VHS over Beta as the preferred format for videocassettes, when Beta was arguably superior technically. However, many de facto standards emerge simply because they make good sense or work well, making their widespread adoption inevitable. It would seem that this is the case regarding audio pots having a 10 percent value at their midpoint, since this exactly mimics the curve that describes human hearing.
Currently, the largest supplier of pots to the U.S. guitar industry is CTS. CTS is an electronics giant with many product lines. One of these divisions makes the 15/16” pots used in many guitars and amps. Guess who is that division’s largest customer? Motorola? Panasonic? Samsung?
Nope, it’s Fender. You can imagine that in this modern world of miniaturization, where huge amounts of electronic circuitry need to fit into products the size of cell phones and iPods, a pot that’s 15/16” in diameter is absolutely enormous. In fact, while these pots were widely used in consumer electronics devices such as car radios and televisions decades ago, they are decidedly dinosaur-like in today’s world and have been largely abandoned by the consumer electronics behemoths.
Still, the fact that they were so widely used by these behemoths and their predecessors during the middle of the 20th century suggests that the standards for audio taper pots had evolved long before the likes of Leo Fender started using them. And it seems likely that the standards for pot tapers evolved not from the consumers using these devices, but from the electrical engineers and R&D departments of these large corporations. The de facto standard in this case is solidly backed up by science.
Despite the fact that there’s a lot of history behind this standard, there seems to be a lot of confusion about it in the guitar community. I’ve read many interesting claims about pot tapers from various sources that seem to fly in the face of this conventional wisdom, and I suspect that in many cases the claims are made by people who don’t understand the logic upon which the conventional wisdom is based. So we’ll look a little more closely at the curve that describes human hearing.
Let’s consider a simple graph called a Bode plot, named after its inventor, Hendrik Wade Bode. You’ve probably seen one of these before; they’re often used to show frequency response curves. The numbers on this particular plot don’t correlate to anything – I just picked them arbitrarily in order to illustrate the concept of logarithms. In a frequency response curve, you would typically see gain (decibels) as the vertical scale and frequency (hertz) as the horizontal scale. We’ll hope you never experience 10,000 decibels.
The interesting thing about the chart is that the numbers in both scales go up ten-fold with each major division line (the bold lines). But as you can see, the major division lines are spaced in a linear fashion – the distance between 100 and 1000 is the same as the distance between 1000 and 10,000, and, for that matter, between 500 and 5000. This plot’s purpose is to scale logarithmic data in such a way that it’s easier for humans to get their arms around.
Exponential changes can be difficult for humans to fully grasp, even when we understand the concept. An example is the relationship of a million to a billion. While this is more than one exponential step, we typically think about number sequences as thousands, millions, billions, trillions, etc. So we think of one billion dollars as being the next big step up from one million dollars, especially these days when there are, in fact, many billionaires living on the planet. But the difference is larger than you might imagine. Spend the money at a rate of $1 per second and you’ll blow through the million in a little more than 11 days. At the same rate, it will take you more than 30 years to spend the billion.
I’ve got more charts, but no more room! We’ll look at them next month. Until then.
Founder, Acme Guitar Works