Adventures In Audio

How the ear hears frequency

LEARN AUDIO ONLINE ► FREE TRIAL ►

Today I'm going to give you an insight into how the human ear hears frequency, and tell you a secret about the magic frequency of 632 Hz (actually 632.45553).

In my recent post about linear phase and minimum phase filters, I used a frequency sweep from 100 Hz to 1600 Hz and talked about the centre frequency 400 Hz. So in what sense is 400 Hz the centre frequency between 100 and 1600? It certainly isn't the average.

Let's start by listening to the sweep...

That was exciting wasn't it? It's the kind of thing that pleases me. I invite your comments.

So let's listen to 100 Hz. You'll need to be listening on proper speakers or headphones. Laptop speakers or eBay earbuds probably won't do much for you.

And now 1600 Hz.

So how can we find the centre frequency between 100 and 1600? Let's take an average.

100 + 1600 = 1700

Divide by 2 gives 850 Hz. Here it is...

Let me play 100, 850, 1600 in sequence so you can judge whether its bang in the middle.

Hmm, I don't really hear it. To me, 850 seems a lot closer to 1600 than it does to 100 subjectively, but it's the same 750 Hz away from both. So this tells us something about the way the human ear works. We hear frequency logarithmically rather than arithmetically. You can learn more about logarithmic scales here...

So how do we find the centre frequency logarithmically? Well I'm sure mathematical geniuses could suggest plenty of ways, but I'm going to use what's called the geometric mean. To get this I don't add 100 and 1600, I multiply them.

So 100 x 1600 = 160,000

Then I don't divide by two, I take the square root.

The square root of 160,000 = 400

So 400 Hz is the centre frequency using this method. Let's listen to 100, 400, 1600 in sequence.

I'm convinced. It sounds halfway to me. If it doesn't to you, let me know in the comments what you think. As I said, it's subjective.

You might, by the way, have noticed that the jumps are two octaves. That's just a coincidence and you can try out this test for yourself with different pairs of frequencies.

So this brings me to the magic frequency of 632 Hz, actually 632.45553. What does it mean? Well, it's the centre frequency of human hearing. Take a moment to absorb that. So how do I work this out? Simple, it's that geometric mean again.

The frequency range of human hearing is normally stated as 20 Hz to 20 kHz. So if I multiply these...

20 x 20,000 = 400,000

Take the square root - 632.45553

Now, I don't expect you to believe me without a demonstration. I can't do it the same way as before since it's unlikely your speakers or headphones go as low as 20 Hz, so you won't be able to hear it. Likewise, although when you're young you can probably hear 20 kHz, with age that limit decreases. So again, probably you can't hear it. So what I'm going to do instead is to sweep the tone upwards and downwards from the centre of 632 Hz. Rather than try to explain, let's just listen.

Now, bearing in mind that your speakers or headphones are probably a limiting factor in the low frequencies, does 632 sound central to you? Let's try it another way...

And maybe try it in stereo...

Well, it's subjective, and you could ask whether it matters. I think it matters because the more you understand about audio, and in particular how the human ear reacts to sound, the better the engineer and producer you're going to be.

I'm David Mellor, Course Director of Audio Masterclass. Thank you for reading.

Tuesday August 25, 2020

The Audio Masterclass Music Production and Sound Engineering Course

FREE TRIAL

Ready to take your recording to the next level? Take a 30-day FREE TRIAL of the Audio Masterclass Music Production and Sound Engineering Course - Our most popular course.

Like, follow, and comment on this article at Facebook, Twitter, Reddit, Instagram or the social network of your choice.

David Mellor

David Mellor

David Mellor is CEO and Course Director of Audio Masterclass. David has designed courses in audio education and training since 1986 and is the publisher and principal writer of Adventures In Audio.

Audio Masterclass gives you all the technical knowledge and skills to bring your musical dreams to life

The Audio Masterclass Music Production and Sound Engineering Course

Get the most from your studio with the Audio Masterclass Music Production and Sound Engineering Course.

Learn more...

Learn Pro Tools with our amazing range of video courses

Pro Tools video course catalog

Browse Pro Tools courses...

Learn Logic Pro with our amazing range of video courses

Logic Pro video course catalog

Browse Logic Pro courses...

Learn Cubase with our amazing range of video courses

Cubase video course catalog

Browse Cubase courses...

Audio Masterclass gives you all the technical knowledge and skills to bring your musical dreams to life

The Audio Masterclass Music Production and Sound Engineering Course

Get the most from your studio with the Audio Masterclass Music Production and Sound Engineering Course.

Learn more...

More from Adventures In Audio...

Making a perfect sine wave and animating it

Graphic equalizer demonstration using the Waves GEQ Classic

Harmonic enhancement: In the master or individual tracks? (Can you hear the difference?)

What will happen if your snare drum clips?

EQ demonstration HF bell boost

How much bass can a Bluetooth speaker produce?

One weird trick for monitoring your mix on a Bluetooth speaker

Can a preamp's pad work as a pop filter

Get the sound you want from the tools you have

What is the phase button for on a microphone preamplifier?

Choosing studio monitors - Is it your most important buying decision?

What is a channel strip? Why should you use one?

Audio effects explained - A quick guide for beginners

How to choose the best key for your song

The amazing stereo effect that no-one can hear

What is the best studio microphone?

Bad Audio Diary BAD 9: What's wrong with this picture?

Weird and wonderful sounds using the Air Music Tech Chorus plug-in

The end of latency?

An investigation of the pre-delay parameter of the Lexicon 480L reverb plug-in

Add reverb to your recordings using the natural echo chamber technique

Why you should ventilate your home recording studio

Q: What is your main concern if your interest is voice over?

Why do microphones sound different?