The significance of 632Hz (I)

Image of sine wave at 632Hz.


We know that 20Hz is the lower hearing limit in the subbass region for humans and up to 20,000Hz in the ultra high treble, so what is 632Hz?

Logarithmic frequency scaling

If the lower/upper limits of hearing are 20Hz/20,000Hz then 632Hz is right in the middle of this range logarithmically (well actually 632.456Hz, for the mathematically inclined, see below). Why logarithmically? It matches how our ears work much more closely than linear scaling.

20                632               20000

632Hz corresponds to the middle of 'midrange' as we hear it.

While 632Hz, might seem like a strange frequency to fixate on, most equalisers don't have 632 marked out in any special way but once you incorporate 632 into your thinking it makes navigating the frequencies much easier.

It's still a little abstract but here's something that makes a bit more intuitive sense.

200Hz, 2,000Hz and thirds.

So 632Hz splits the spectrum in 1/2, what about other divisions? What about 1/3?

Moving 1/3 the way along the frequency spectrum we get 200Hz. 2/3's along we get 2,000Hz. This divides the audible spectrum into sections that we hear as three evenly spaced divisions.

20          200         2000        20000

Broadly speaking, this gives us bass, mids and treble. And if you want to move a third of the frequency spectrum in either direction just add or remove a zero from the end of the number.

Important numbers: 20 & 63

So we've split our spectrum first into halves, then into thirds. What if we go from thirds to sixths? Double the number of divisions, we get:

20    63    200   632   2000  6324  20000

Notice the pattern?

Lets make the pattern clearer by rounding the numbers and offsetting:

20          200         2000        20000
      63          630         6300

What we have now are only two numbers, 20 and 63. These describe how the frequency spectrum splits up into 6 evenly spaced divisions.

Just remember 20 and 63 and you can add zeroes as you move up.

So as 630Hz sounds halfway between 20-20,000, likewise the jump between 20-63 is the same perceived jump as from 63-200, or 2000-6300. We're now moving in sixths and these 6 divisions are perceived as evenly spaced steps to the ear.

If you don't know much about frequency areas beyond bass, mids and treble, thinking about the audible frequency range as these 6 areas is a great way to work in a bit more detail. These six areas can be applied as a loose framework to keep in mind as you navigate the frequencies.

Also, if you know a lot about frequency areas, and have an attachment to things like 150Hz boom, 700Hz honk or 4300 presence etc., it's useful to take a step back and think about the audible frequency range as a whole, how it divides evenly and what those divisions sound like. This allows all areas of the spectrum get equal attention in your mind.

Re-acclimatising your ear can help take in the whole picture:

  • 20: Sub
  • 63: Bass
  • 200: Low mids
  • 630: Mids
  • 2000: Upper mids
  • 6300: Treble
  • 20000: Air

There you go. You could mix a great sounding record using EQ with a relatively broad Q and just those frequency areas.

In the next part we will move forward and break down the frequency spectrum in more detail, but the 'big picture' way of thinking presented here is much more important.

Footnote: The mathematics

For the mathematically adventurous, when we speak of the logarithmic scale as applied to audio frequencies we're really talking about a 3 decade logarithmic scale. A decade is the jump from 20 to 200, or 200 to 2000, or 2000 to 20000 (count them, 3 decades).

The mathematical formula for converting between a 20-20000 3 decade logarithmic scale and a 0-1 linear proportion is as follows.

` y = 20 + ((20000-20) * ((1000^x - 1) / (1000 - 1))) `

`y` is the frequency in Hz and `x` is the fractional proportion 0-1. 1000 is 10 to the power of the number of decades, in this case `10^3 = 1000`.

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