In part one we looked at 632Hz as the centre of the audible spectrum, and then divided the spectrum into equal parts. Let's follow the trend and further subdivide into even smaller equal parts, so we can draw up our map of the frequencies in more detail.
If we divide the spectrum from six sections into twelve, splitting each sixth in half, we get:
20 35 63 110 200 350 630 1100 2000 3500 6300 11000 20000
So we meet two new magic numbers: 35 and 110.
As before, the ear hears each of these steps as about the same size. 63-110 sounds roughly the same as 2000-3500, 6300-11000 sounds like similar sized jump to 350-630 etc.
We now have a pretty detailed picture of the hearing range, split evenly as our ears perceive it. And apart from honing in on specific, absolute frequencies like a 50Hz hum or a literal note (the F above middle C), these 12 equal divisions represent a great way to navigate the spectrum. We're at a level of detail that's fantastic for mixing and mastering, and if you learn no more than these you've got a solid map for navigating the spectrum when working with medium/broad Q values on your equaliser (which should be most of the time but the argument against narrow Q's is for another article).
But we can of course go further again, this time introducing 4 new magic numbers (27, 47, 84 & 150):
20 27 35 47 63 84 110 150 200 270 350 470 630 840 1100 1500 2000 2700 3500 4700 6300 8400 11000 15000 20000
Why is this important? The short answer is speed.
Initially it will take a short period to adjust to all these new numbers but once you're used to moving around the frequencies with these distinct steps, you begin to move and make decisions much faster.
Say you want to change a sound with EQ, you'll first be confronted with something that you don't quite like the sound of, and you have realised it's the tone you don't like, and you feel this can be remedied with EQ. That sounds like a long thought process but really these things usually happen in a split second, 'on feel'.
Now you can navigate the audible spectrum in descending levels of priority. Thinking in these levels of coarseness, starting broad and going down to fine tune can really help guide your ear around the audio as you work:
If you're experienced you might cut out the early steps, something like:
Having this framework in your mind, these decreasing levels of priority, allows you to focus on getting in and out quickly, starting coarse and only going as fine as you need to go, then moving on to the next task. Sometimes you might find that you need to go finer than the chart above, and that's okay (see 48 divisions below). These aren't hard and fast rules, just a loose framework to keep you oriented as you work with frequencies.
Okay for the sake of completeness I'm going to divide the sections in half once more. But I will point out that even as a mastering engineer I seldom go beyond this level of granularity. Very occasionally I need to zero in on an exact frequency number but that sort of situation happens surprisingly rarely. Here goes. More magic numbers this time 8 new ones: 23, 31, 41, 55, 73, 97, 130 & 170.
20 23 27 31 35 41 47 55 63 73 84 97 110 130 150 170 200 230 270 310 350 410 470 550 630 730 840 970 1100 1300 1500 1700 2000 2300 2700 3100 3500 4100 4700 5500 6300 7300 8400 9700 11000 13000 15000 17000 20000
It's no accident that famous equalisers like the Sontec 432 have steps that are pretty similar to these numbers, with a bit of offset/overlap thrown in for good measure. Each step sounds like an equal jump to the ear. Each step sounds discretely different (in a way that moving continuously doesn't) so you can quickly compare two neighbouring steps to see which one you prefer.
So there you have it. Memorise a couple of key numbers (starting with 20 and 63) and you're well on your way to a deeper understanding of how the audible frequencies relate as a whole.
If you can turn off your display all the better (for many reasons). Navigate around, let your ears be the driver and a few of the numbers above, your road map.