How the ear hears frequency
The ear doesn't hear frequency in a linear arithmetic way, but logarithmically. So the halfway point between 100 Hz and 1600 Hz isn't 850 Hz as you might expect. This video shows how and why, and finds out the halfway point of the full frequency range of human hearing.
Today i'm going to give you an insight into how the human ear hears frequency and tell you a secret about the magical frequency of 632 hertz actually 632.45553 learn audio online with audio masterclass audiomasterclass.com in my last video about linear phase and minimum phase filters i used a frequency sweep from 100 hertz to 1600 hertz and talked about the center frequency 400 hertz i'll put a link to that video in the description so in what sense is 400 hertz the center frequency between 100 and 1600 it certainly isn't the average let's start by listening to the sweep all of the audio examples here are between around 8 to 10 seconds long that was exciting wasn't it it's the kind of thing that pleases me i invite your comments so let's listen to 100hz 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 for hertz
so how can we find the center frequency between 100 and 1600 let's take an average 100 plus 1600 equals 1700. divide by 2 gives 850 hertz here it is
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 hertz away from both so this tells us something about the way the human ear works we hear frequency logarithmically rather than arithmetically i'll put a link in the description if you want to look at the maths so how do we find the center 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 times 1600 equals 160 000 take the square root 400 400 hertz so 400 hertz is the center frequency using this method let's listen to 100 400 then 1600 hertz 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 magical frequency of 632 hertz actually 632.45553 what does it mean well it's the center 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 hertz to 20 kilohertz so if i multiply these 20 times 20 000 equals 400 000 take the square root
632 hertz is the center frequency of human hearing 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 hertz so you won't be able to hear it likewise although when you're young you can probably hear 20 kilohertz 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 center of 632 hertz rather than try to explain further 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 well it's subjective and you could ask whether it matters i think it matters because the more you understand about audio and particularly how the human ear reacts to sound the better the engineer or producer you're going to be i'm david miller course director of audio masterclass thank you for listening