- 14 February, 2012
- 21 Comments
I’ve been putting together a blog post on the way to get the best sound out of MP3s, but there are so many elements to deal with, I thought I’d tackle it in pieces. For this post, I’m just going to talk about the missing frequencies in an MP3.
One of the ways we can fit more music into an MP3 is by discarding the least important information. High frequency sounds have a lot going on very quickly, and they can take up a lot of space, so there’s a lot to be gained from getting rid of them.1
Still. We don’t want data to be missing. If the range of human hearing is 20-20,000Hz, and everything above 16,000Hz is missing, that feels like a lot. It seems like that would be 20% of the music.
That’s not how frequencies work, though. Every time we go up an octave, the frequency doubles. Going up like this, numbers can get pretty big, pretty fast, and it makes the high frequencies look a lot more important than they really are. If you wanted to make a piano covering the entire range of human hearing2, you’d need to give it 120 keys instead of the normal 88. If, halfway through building it, you decided you only wanted it to go up to 10,000Hz, not 20,000Hz, you wouldn’t remove half the keys. You’d only remove 12 of them – seven white ones and five black ones.
In any case, 20,000Hz is the highest anybody can hear, not the highest everybody can hear. Above that, your pets might notice, but you won’t. Our sensitivity to high frequencies deteriorates with age, so for most adults the ceiling is more like 16,000Hz. Your kids can probably hear things you can’t, and your pets can hear things your kids can’t.
If, like me, you’ve spent a lot of time around very loud music, your hearing might top out even lower. I can’t hear much above 13,000Hz.
Try it for yourself: this is a 30-second sweep across the full range of human hearing, from 20hz to 20,000hz. Hit the play button, and listen until it goes quiet: that’s as high as you can hear.3
[If you’re reading this in a feed-reader, you might have to scroll to the bottom of the page or visit the site the see the player]
It goes up by 666Hz/Second, so the frequencies are:
1 Second: 686Hz
2 Seconds: 1,352Hz
3 Seconds: 2,018Hz – The highest note in the Queen of the Night’s Aria
4 Seconds: 2,684Hz
5 Seconds: 3,350Hz
6 Seconds: 4,016Hz – The highest note on a piano4
7 Seconds: 4,682Hz
8 Seconds: 5,348Hz
9 Seconds: 6014Hz
10 Seconds: 6,680Hz
11 Seconds: 7,346Hz
12 Seconds: 8,012Hz
13 Seconds: 8,678Hz
14 Seconds: 9,344Hz
15 Seconds: 10,010Hz
16 Seconds: 10,678Hz
17 Seconds: 11,342Hz
18 Seconds: 12,008 Hz
19 Seconds: 12,674 Hz
20 Seconds: 13,340Hz – This is where it goes quiet for me 5
21 Seconds: 14,006Hz
22 Seconds: 14,672Hz
23 Seconds: 15,338Hz
24 Seconds: 16,004Hz – Very few adults can hear anything above here
25 Seconds: 16,670Hz – A 192kbps MP3 won’t have much above here
26 Seconds: 17,336Hz
27 Seconds: 18,002Hz – A 256kbps MP3 won’t have much above here
28 Seconds: 18,668Hz
29 Seconds: 19,334Hz – A 320kbps MP3 won’t have much above here
30 Seconds: 20,000Hz – Still audible to other animals6
There’s an argument that, while these frequencies might be inaudible by themselves, they add character to other sounds in ways that are perceptible to our ears. If this were true, it would be relatively straightforward to prove it and, as far I can see, nobody ever has. It also doesn’t stand up to common sense. Sounds simply don’t become more noticeable when there’s other noises, indeed, the opposite is widely accepted.
So there you go: unless you’re a dog, you can test your hearing and pick and MP3 format that only excludes frequencies you can’t hear. There are, of course, other aspects of MP3 encoding that affect the quality of the sound. Next time, we’ll look at bit rates, fixed and variable, and the effect these have on the sound.
1The point I wanted to make here is way too nerdy for the first footnote.7
2Most notes produced by musical instruments are a combination of several related frequencies, overtones or harmonics. In the piano analogy, I’m only talking about the lowest (and loudest) of these frequencies, called the “fundamental”.
3This is a bit of fun, not a diagnostic tool. If you’re concerned about your hearing, you should see a professional. If you’re interested in playing around with acoustics, though, you should check out the tools at this site. The sound clip on this page is a linear sweep at constant amplitude (-3dBFS). If it seems to get louder and quieter over its range, that’s because your hearing is more sensitive to certain frequencies, (normally around the range of the human voice). This clip is itself encoded as an MP3, but because it contains an extremely simple sound, it doesn’t need to filter out the high frequencies. The MP3 specification is quite flexible on encoding, but all decoders are essentially the same, so I can be confident that your computer will decode the same sound that I get from this file, regardless of the software used to play it back.
4The fundamental frequency of the highest note on the piano is 4186.01Hz, but its overtones will extend upwards beyond the limit of human hearing. If you’re interested in this stuff, I’d recommend this video and, if you still want more detail, this one.
5I won’t speculate on what happened to the top end of my hearing, but Google Scholar is a good place to explore the considerable research on hearing loss in orchestral musicians.
6Dogs can hear up 60,000Hz, mice up to 90,000Hz and bats up to 120,000Hz.
7Ok. You’ve been warned. An MP3 describes a complex sound wave in terms of lots of little bits of a sine wave: “At this point, the wave goes up with a bump this tall and this long”. If you want to lose the rest of the day in articles about mathematics on Wikipedia, then it might help you to know that this is called a Fourier Series. The reason I bring all this up is because if you’re encoding music this way, the high frequencies take up a lot of space: at 20Hz, there are 20 wobbles in the line to describe each second of music. At 20,000Hz, there are 20,000 of them. By getting rid of a small number of high frequencies, you can get rid of a very large amount of data. The trick is to find the frequencies you won’t miss.