# How many bits can you hear?

#### earlevel

##### Senior Member
Ever wonder how many bits you can hear—your system, your ears, at a volume setting of your choosing? You may be surprised how soon it becomes difficult...

The video uses the audio I generated for a blog article a few months ago, but it's helpful to see a spectrogram of the signal sweep, and a peak meter to assure that there really is still a signal playing when it gets to the lower bit levels. You can download the 24-bit audio here, so you're not at the mercy of youtube audio: A listerning test

This test is actually generous, each level is at least twice as loud as the minimum signal each bit depth can support (hence the 16-bit signal is -90 dB, not -96 dB, for instance). More details on the signal in this article: Perspective on dither

To questions on why this isn't a sine sweep, for instance, and why it's twice the minimum peak level for a given bit depth: First, I want people to hear it easily, and also a sine wave would have progressively worse signal-to-noise ration at lower bit depths, and rely heavily on dither at the lowest. A digital square wave sweep is also exact, at any bit level. And making it twice the bit level (plus/minus) allows it to have no DC offset at any bit depth. This is less about finding an exact number of bits someone can hear under any circumstance, and more about letting people surprise themselves about what levels start to become difficult for them under their routine listening conditions.

#### CinDyment

##### Active Member
What do you mean by digital square wave? Still frequency limited I assume?

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#### earlevel

##### Senior Member
What do you mean by digital square wave? Still frequency limited I assume?
Yes. The steps are on exact sample-periods, generated algorithmically (not recorded through a converter), so they are bandlimited. And on exact bit levels (plus and minus the bit level indicated).

I know some will have a little problem wrapping their head around that being "legal digital audio", but consider that if you record a square wave, through an ADC, in which the period is an exact multiple of the sampling period, and with phase such that the transitions land halfway between samples, you end up with the same thing. It's just easier to generate it algorithmically. If you look at this sweep by capturing the output you're listening to (that is, play it through a DAC and look at the resulting analog), you'll see it's simply a bandlimited square sweep.

The upside is that there are only two values, so we can talk about bit levels exactly. If you didn't have exact bit levels, the signal-to-noise ratio would change—in the data itself—as you move to lower bit levels.

#### CinDyment

##### Active Member
Not a matter of legal digital or not, what the samples will represent in the analog domain is not what the square wave pictures show. It does not work that way.

#### Axo1989

##### Addicted to Fun and Learning
I've previously ignored your interlocutor so good luck with that.

Meanwhile, having a listen to your sweep, I came up with similar results to the reply to your blog post.

Played loud-ish, so "max" level (but not true peak, which isn't relevant in this case because your voice descriptions are the loudest thing and we aren't listening to music) wass ~87 dBA SPL at my listening position I could make out the 15 bit sweep but not the 16.

It's a fairly quiet Saturday morning so ambient levels are ~27 dBA SPL overall. I listened to YouTube over my normal listening room stereo. At max levels on my MacBook (2019 16") the signal was quieter and I think I made it to 12 or so (didn't take notes). I haven't tried the download yet.

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#### earlevel

##### Senior Member
Not a matter of legal digital or not, what the samples will represent in the analog domain is not what the square wave pictures show. It does not work that way.
What "doesn't work that way"? The picture is of the samples used, because you asked what I meant by "digital square wave"—of course I'll show you a plot of the digital values. Then in your new message you seem to take me to task for them not being "in the analog domain". Now you want me to give you a plot from my oscilloscope? It will look like a bandlimited square wave sweep.

To restate:

It's a test of a audio of some p-p level that I define for each level.

I chose to create a signal that works out well because it requires no dithering, and it's easy to identify (hear). That is its only purpose of the chosen waveform. And the only purpose of the test itself is to let people reflect on what they can hear. some will be surprised at the point where they can no longer hear it—again, their ears, their listening system and environment, their choice of overall volume.

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#### earlevel

##### Senior Member
I've previously ignored your interlocutor so good luck with that.

Meanwhile, having a listen to your sweep, I came up with similar results to the reply to your blog post.

Played loud-ish, so "max" level (but not true peak, which isn't relevant in this case because your voice descriptions are the loudest thing and we aren't listening to music) wass ~87 dBA SPL at my listening position I could make out the 15 bit sweep but not the 16.

It's a fairly quiet Saturday morning so ambient levels are ~27 dBA SPL overall. I listened to YouTube over my normal listening room stereo. At max levels on my MacBook (2019 16") the signal was quieter and I think I made it to 12 or so (didn't take notes). I haven't tried the download yet.
Thanks for checking it. In retrospect, I think I was remiss in making the video public before quantifying how much youtube changes it. I figured it would affect the lowest levels, but I should have a better idea of how much, I didn't even do a full listen. Checking it now, I'm a little horrified that it seems to get to a low level, then not drop further...my best case (turned up pretty loud, quiet room) I could hear to 17 bits (maybe 18?), but now I get to that barely-hearable level...and each sweep after that is basically the same. Yikes! was hoping it wouldn't fail quite so soon.

OK, I just captured that audio (with Screenflow), exported it as lossless, pulled it into RX 9, and...it looks something like dithered 16-bit. I'll have to do some more checking, but I need to stop for food. I uploaded 24-bit lossless in the video to youtube. I'll have to see if there is anything I can do to ensure maximum encoding by youtube. Here's a quickie zoom in RX 9; the rightmost is "24-bit", so counting backward it basically stays the same level from 16-bit (-90 dBFS) on.

#### solderdude

##### Grand Contributor
In order to hear the bits the bit rate should be well below 10kbs (when listening to the actual bits). One can listen to this for a while but counting the bits will not be possible by ear and needs a counter to know how many bits you heard.

The bit depth is another story and depends on dithering and the used recording.

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#### earlevel

##### Senior Member
In order to hear the bits the bit rate should be well below 10kbs (when listening to the actual bits). One can listen to this for a while but counting the bits will not be possible by ear and needs a counter to know how many bits you heard.

The bit depth is another story and depends on dithering and the used recording.
Just to be clear, I'm only interested in relative volume. Just a demonstration of how quickly the audio falls off—people don't usually have any idea, because they listen to music.

And of course, the original audio is not dithered (and doesn't need to be), so that not an issue. But it is an issue when listening to the youtube version. I'm even more concerned about the fact that the youtube audio doesn't seem to fall off after sixteen bits. If this were strictly a matter of dither, the sweeps would still get quieter and slip below the noise floor. Instead, they're all the same level from "16-bit" on. I was counting on this, at worst, being something closer to 16-bit, with TPDF at +/- lsb bit level. Trying to figure out if there is no getting around that—at this point it, it looks like a 16-bit dithered upload would be closer to telling an accurate story, but not what I want.

#### kongwee

##### Addicted to Fun and Learning
32 bit floating point.

#### Katji

##### Major Contributor
You're all so binary.

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#### earlevel

##### Senior Member
I have a simplified workaround: In this blog post, I have the embedded video, and an audio player beneath it (same audio as the other page I mentioned, which is the same as used in the video); you just need to start the audio a couple of seconds into the video (when the meter appears), and mute the video:

How many bits can you hear? video

#### Soundmixer

##### Senior Member
whatever happened to trinary?
It was replaced by quadrinary. These "naries" become obsolete pretty quickly.

#### xaviescacs

##### Major Contributor
Forum Donor
Using computer cheap headphones and with some computer self noise, the 18th is quite hard to hear for me and the 19th is impossible. I sat the volume a bit high, but way before the voice it's unbearable. That's the weakest point of this approach IMHO, the volume. What about playing the first one just before every other, so the listener keeps the reference with the "actual" volume? Just a random thought.

Forum Donor

#### solderdude

##### Grand Contributor
hobbits ?

This test is more about level differences using tones than about how many bits you need as that may differ depending on dither is applied or not.
Using music excerpts and attenuation levels (reference vs attenuated) says a bit more about the dynamic range your gear (and you) can handle.

#### kongwee

##### Addicted to Fun and Learning
1 bits DSD is the best!

#### solderdude

##### Grand Contributor
No... MQA is.
Bob told us so.
Maybe not hobbits but Bob-bits

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#### earlevel

##### Senior Member
Using computer cheap headphones and with some computer self noise, the 18th is quite hard to hear for me and the 19th is impossible. I sat the volume a bit high, but way before the voice it's unbearable. That's the weakest point of this approach IMHO, the volume. What about playing the first one just before every other, so the listener keeps the reference with the "actual" volume? Just a random thought.
I'm not sure what you mean about volume being "the weakest point". First, let me explain the point of the exercise:

In particular "how many bits can you hear?" is asking how many bits of the exercise, not of digital audio in general. I'm trying to make it easily identifiable, and even generously loud for a given bit level. By contrast, hearing tests I've experienced use soft edge sine tones and headphones emitting a calibrated level. That tends to leave you questioning whether you're hearing a tone or not when it's on the edge. With a harmonic-rich sweep, if you're not sure if you hear it, you probably don't.

The point of having the announcing voice (at the default output level) is so that a person knows how loud their system is. Not just to keep people from "cheating"—this is a personal test and I'm only asking "how many" rhetorically—I'm not looking for an answer from anyone. Also, if people are just going to keep turning up the volume as the sweeps get quieter, there is no point to the test at all. Lastly, I'm concerned that people will do this, and forget about it or have a system alert go off and blow out their system or their ears.

The point of this is only personal introspection. A lot of people say they can hear all the way down to 24-bits, other call for true 32-bit DACs apparently because they don't think 24 is nearly enough, usually without having any idea what -100 dBFS sounds like on their system, at their normal listening levels.

So, I think my self-test is what it was designed to be. But I still like to hear and talk about what other people think are also interesting tests, so I welcome your thoughts. I just wasn't sure if you were saying you'd like to hear the first sweep ("5-bit") as a reference ahead of each subsequent sweep, or something else.

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