I have always been fascinated by mathematics and, while I am not a very advanced mathematician, I have always appreciated the importance of math and how it applies in our everyday existence. Despite any shortcomings we may have in balancing our checkbooks, most of us in the pro audio field audio live in a mathematical world and utilize math on a daily — if not hourly— basis. From the simple addition/subtraction process of making change, calculating tips, time management and more complicated problems — such as figuring out our taxes and budgets — we are constantly using math in our everyday existence.
Consider this: If gasoline costs three dollars a gallon and I have 10 dollars, how many gallons of gas can I buy? If I need to go one hundred miles and my car gets 25 miles to the gallon how many gallons will it take for me to reach my destination? Will my 10 dollars get me where I want to go? If not, how much more will I require to arrive where I am going? Assuming I can figure out how to fill my car with enough fuel, if my destination is 100 miles away and I have to be there at a certain time and my average speed of travel is about 60 mph, how much time must I allot myself to arrive at the designated hour?
Across the Great Divide
There is also another math we use on a daily basis for such things as crossing the street, and this math requires very little conscious computation. On a street without a stop sign or light, we see a vehicle coming in our direction and in a moment, we deduce whether or not the crossing can be accomplished unscathed. We note the speed the car is traveling toward us, the space between us and the approaching vehicle, the distance we need to traverse and the speed at which we must travel to safely make our crossing. If just one of those calculations is incorrect, the whole venture could end in disaster, but — more often than not — we manage to cross the street. Of course, we can’t take into account a maniacal driver who sees us crossing and decides to speed up, but hopefully, drivers are making their own calculations to avoid hitting us.
If oncoming drivers see us ready to make a move, they might start applying pressure to their brakes to slow down enough so that we can safely make it across the great divide. Alternatively, they may decide their speed is fine and turn the car just enough to avoid a collision. This type of intuitive math takes place many times a day in all sorts of ways. Climbing up or down a staircase, catching something that’s thrown at us, shaking someone’s hand or opening a door all require calculations so that we don’t over do or under do our required intention. Fortunately, in most cases, the human brain is wired to make these calculations, and we therefore go about living our lives performing tasks that on paper appear to be complicated mathematical formulas.
Our audio lives also require a decent grasp of math to do our jobs. If one is involved in trucking gear from place to place, it helps to know weights, loads and heights. If flying the speakers is part of your job, you again would need to know weights and loads. For example, the weight that a roof can hold on a clear day differs from the load it can bear on a day where there is an accumulation of snow, thereby changing the way you might configure a speaker hang. Fortunately, there’s a mathematical formula to help us get an exact read on the weights so that we can safely fly our array. Math is an integral part of what we do as audio engineers. The fact that most of the calculating now comes pre-packaged does not diminish the need for us to have some mathematical dexterity.
Back to (Audio) Basics
Computers, new technologies and digital systems have eliminated the need for most of us to really understand the math behind Ohm’s law, impedance and the relationship between voltage and resistance. What we do know is that one channel of most modern amplifiers can readily handle a 4 Ohm load, which means we can drive two 8 Ohm speakers on one channel. Some amps can even handle a third 8 Ohm speaker wired in parallel, which then drops the impedance to 2 Ohms — actually, 2.66 Ohms to be exact. The decibel, or dB, is a ratio of two quantities mostly used to express power ratios. For example, the power value of 2 watts — expressed as dB — is 3. Does knowing the math behind Ohm’s law and dB help us while we are in the middle of mixing a band? Probably not, but it would definitely not hurt us to have a little more insight to understanding what we are doing, as it is part of the audio language.
Setting up delay speakers has become a commonplace aspect of our job, but before there were consoles and digital delay units that could give us the proper readout in milliseconds, feet and meters, we needed to know the formula to ensure the correct delay rates. All in all, there really is a science attached to audio, which is probably why — back in the day — all those EMI technicians at Abby Road Studios were running around in white lab coats. Of course, that was a long time ago, and there is no comparison between the current technology and that of 50 years ago, but the math is still viable even if we aren’t required to know now what we needed to know then to get a great mix.
In this age of computer wizardry, where many of the required formulas we rely upon are expressed in an application or a few keyboard strokes, it still makes sense to learn some of the science and math behind the magic. After all, knowledge is power. Of course, the more one knows, the better they can be at performing their given job. That said, while one is brushing up on their math they should keep in mind that there are still certain ethereal mathematical relationships between instruments in a mix. And similar to crossing the street ahead of a speeding car, these don’t require working out a formula on a large blackboard as much as it does to have a good sense of what’s coming and where one is going with the given information.
