DAC audible differences are finally proven with ABX?

[pma]

composite test signal of 32 tones with final THD and noise

A small correction, it is not THD and noise, but TD and noise. TD+N. THD+N is reserved for harmonic distortion and noise and the word harmonic says it is for a single tone. TD+N also covers intermodulation products that are non-harmonic. Total distortion and noise.

 

[rjp]

A small correction, it is not THD and noise, but TD and noise. TD+N. THD+N is reserved for harmonic distortion and noise and the word harmonic says it is for a single tone. TD+N also covers intermodulation products that are non-harmonic. Total distortion and noise.

That makes sense. Total distortion (TD) is the superset including both HD and IMD. I used only THD because that seems to be what Amir uses in his SINAD calculation as shown below. But this was a single tone, so I guess there can be no IMD. Is the general formula SINAD = 1/(TD+N)?

 

[pma]

Is the general formula SINAD = 1/(TD+N)?

1/(THD+N). That's why talking about SINAD for Multitone distortion is a bit incorrect. TD+N is correct. REW is very good in this.

 

[JustAnandaDourEyedDude]

Yes! Your revised post answers my questions very well. In fact, this is by far the best technical answer I have ever heard on this topic Thank you!

Your answer seems to be a solid technical explanation for how threshold-based parameter testing can indeed imply audible transparency, even without the support of ABX testing.

You're quite welcome! I'm happy my explanation helps!

This may actually be provable. Since we know from Fourier theory that all bandlimited input signals can be represented as the superposition of (complex) scaled tones, this suggests any such signal passed by this system should be indistinguishable from the input. i.e., the system is transparent.

Yes, this is the key concept that allows us to apply our results to all allowable audio signals. I called it "mathematical equivalence of an allowable audio signal into a sum of sine waves", but you are right that switching to complex numbers allows simultaneous handling of amplitude and phase. We just need to verify that the analog output of the DAC does an excellent job of representing the tones across the entire audio bandwidth. Shannon showed that we get a finite basis if sinc functions are used as the basis functions to completely reconstruct the analog signal.

I expect when you have a lot of individual tones as in very complicated music, it is the requirement of limiting the SPL that keeps the Total Distortion in check, though the IMD may grow a little. Each tone you add contributes more distortion but also more to the total energy, and the latter must be limited in playback. Thus, when you scale down the tones to limit the max SPL, the distortion gets scaled down too, and is held in check. There may be nuances such as whether the DAC is accurate enough to reproduce "beats" arising from tones close in frequency without audible distortion.

 

[pma]

But it still about audibility, in the end. It might be surprising to some readers how high THD+N or TD+N remains inaudible, not speaking about music. Many orders above the numbers discussed here. This is the reason why the goal of the possible test repeat remains unclear to me.

 

[pma]

Audibility of multitone distortion

I am really curious - anyone would tell a a difference between multitones with TD+N = -132dB and TD+N = -34dB?? Files attached (link below), ABX report if yes. Thank you! (multitone BT goes through Bluetooth device).

https://pmacura.cz/multitones.zip

 

[SSS]

Audibility of multitone distortion

I am really curious - anyone would tell a a difference between multitones with TD+N = -132dB and TD+N = -34dB?? Files attached (link below), ABX report if yes. Thank you! (multitone BT goes through Bluetooth device).

View attachment 549072 View attachment 549073

https://pmacura.cz/multitones.zip

Did test it. The difference is very small for me. The original has a bit cleaner sound. Test done with PC and small good loudspeakers. With headphones it may be easier but would need extra setup which I skipped. Need to say that I have very old ears with limited high frequency.

 

[pma]

Did test it. The difference is very small for me. The original has a bit cleaner sound.

Thank you for doing the test. Do you have an ABX protocol with resulting p < 0.05?

 

[NTTY]

Audibility of multitone distortion

I am really curious - anyone would tell a a difference between multitones with TD+N = -132dB and TD+N = -34dB?? Files attached (link below), ABX report if yes. Thank you! (multitone BT goes through Bluetooth device).

View attachment 549072 View attachment 549073 View attachment 549076

https://pmacura.cz/multitones.zip

Thanks for sharing, I’ll test asap when I return home next week!

 

[SSS]

Thank you for doing the test. Do you have an ABX protocol with resulting p < 0.05?

No. I did it by switching the two audio files. My experienced listening clearly repeatedly found the distorted file more harsh. I do not have an ABX box nor special tools for that.

 

[JSmith]

I do not have an ABX box nor special tools for that.

No need for all that, just use Foobar;

foobar2000 for Windows

foobar2000

www.foobar2000.org

You will need to add the ABX component;

foobar2000: Components Repository - ABX Comparator

foobar2000

www.foobar2000.org

Foobar2000:How to install a component - Hydrogenaudio Knowledgebase

wiki.hydrogenaudio.org

1. Open the foobar2000 preferences dialog (click "File | Preferences" or use the CTRL+P keyboard shortcut).
2. Select the Components page.
3. Either click the Install... button and locate the component archive, or simply drag it on to the list.
4. Click OK. You will be prompted to restart foobar2000 in order to load the newly-installed component.
5. Click OK again to restart.

You can take as long as you want for each response and seamlessly cut between the two WAV file, choosing A is X, B is Y etc. Foobar will track the process and produce a verifiable report.


JSmith

 

[pma]

You can take as long as you want for each response and seamlessly cut between the two WAV file, choosing A is X, B is Y etc. Foobar will track the process and produce a verifiable report.

And the report would look like this:
(such code can be verified) /copy and paste complete abx report with the signature/ /Note: the result below was obtained by chance, random clicks. One needs to get 12/16 for p<0.05/

foo_abx 2.1 report
foobar2000 v2.0
2026-08-04 10:23:25

File A: MT_orig_96k_PCM24.wav
SHA1: 4c4f8dec5424ed619a31c41ed27c557900d26a79
File B: multitone_bt.wav
SHA1: 7268d563203b2c0125bc1f39bca89b7c7af06f6e

Output:
ASIO : Focusrite USB ASIO
Crossfading: NO

10:23:25 : Test started.
10:23:35 : 01/01
10:23:40 : 01/02
10:23:44 : 01/03
10:23:48 : 01/04
10:23:52 : 02/05
10:23:57 : 02/06
10:24:00 : 02/07
10:24:04 : 03/08
10:24:08 : 04/09
10:24:11 : 04/10
10:24:16 : 04/11
10:24:18 : 05/12
10:24:20 : 06/13
10:24:22 : 07/14
10:24:24 : 07/15
10:24:26 : 08/16
10:24:26 : Test finished.

 ----------
Total: 8/16
p-value: 0.5982 (59.82%)

 -- signature --
168ff7088280c2f0acdbada544b710a86f3ac16c

 

[RandomEar]

Audibility of multitone distortion

I am really curious - anyone would tell a a difference between multitones with TD+N = -132dB and TD+N = -34dB?? Files attached (link below), ABX report if yes. Thank you! (multitone BT goes through Bluetooth device).

View attachment 549072 View attachment 549073 View attachment 549076

https://pmacura.cz/multitones.zip

Holy sh*t, it is an assault on the ears!

Anyway: Definitely not easy, but manageable. Always refreshing to see how close to the original the "bad" stuff sounds. I'd like to point out that I missed 10% of the trials and wasn't overly certain in each run despite the level of destruction we're talking about here, while the ABX result discussed in this thread is 110/112. So Josh missed just 1.8% of the trials with differences which I would estimate to be at least two orders of magnitude (= 40 dB) lower...

foo_abx 2.2.3 report
foobar2000 v2.25.10
2026-08-04 14:32:38

File A: MT_orig_96k_PCM24.wav
SHA1: 4c4f8dec5424ed619a31c41ed27c557900d26a79
File B: multitone_bt.wav
SHA1: 7268d563203b2c0125bc1f39bca89b7c7af06f6e

Output:
Default : Primary Sound Driver
Crossfading: NO

14:32:38 : Test started.
14:33:04 : Test restarted.
14:33:04 : 01/01
14:33:13 : Test restarted.
14:33:13 : 01/02
14:33:22 : Test restarted.
14:33:22 : 02/03
14:33:40 : Test restarted.
14:33:40 : 03/04
14:33:45 : Test restarted.
14:33:45 : 04/05
14:33:50 : Test restarted.
14:33:50 : 05/06
14:34:05 : Test restarted.
14:34:05 : 06/07
14:34:10 : Test restarted.
14:34:10 : 07/08
14:34:15 : Test restarted.
14:34:15 : 08/09
14:34:25 : Test restarted.
14:34:25 : 09/10
14:34:25 : Test finished.

 ----------
Total: 9/10
p-value: 0.0107 (1.07%)

 -- signature --
55d68b7a8d25298796b2cbbb059bab3a2f977eec

 

[voodooless]

Holy sh*t, it is an assault on the ears!

Anyway: Definitely not easy, but manageable. Always refreshing to see how close to the original the "bad" stuff sounds. I'd like to point out that I missed 10% of the trials and wasn't overly certain in each run despite the level of destruction we're talking about here, while the ABX result discussed in this thread is 110/112. So Josh missed just 1.8% of the trials with differences which I would estimate to be at least two orders of magnitude (= 40 dB) lower...

foo_abx 2.2.3 report
foobar2000 v2.25.10
2026-08-04 14:32:38

File A: MT_orig_96k_PCM24.wav
SHA1: 4c4f8dec5424ed619a31c41ed27c557900d26a79
File B: multitone_bt.wav
SHA1: 7268d563203b2c0125bc1f39bca89b7c7af06f6e

Output:
Default : Primary Sound Driver
Crossfading: NO

14:32:38 : Test started.
14:33:04 : Test restarted.
14:33:04 : 01/01
14:33:13 : Test restarted.
14:33:13 : 01/02
14:33:22 : Test restarted.
14:33:22 : 02/03
14:33:40 : Test restarted.
14:33:40 : 03/04
14:33:45 : Test restarted.
14:33:45 : 04/05
14:33:50 : Test restarted.
14:33:50 : 05/06
14:34:05 : Test restarted.
14:34:05 : 06/07
14:34:10 : Test restarted.
14:34:10 : 07/08
14:34:15 : Test restarted.
14:34:15 : 08/09
14:34:25 : Test restarted.
14:34:25 : 09/10
14:34:25 : Test finished.

 ----------
Total: 9/10
p-value: 0.0107 (1.07%)

 -- signature --
55d68b7a8d25298796b2cbbb059bab3a2f977eec

I wonder how well you would do if you band limit the signals to 10 kHz. Beyond that frequency response seems to start deviating.

 

[pma]

Holy sh*t, it is an assault on the ears!

Anyway: Definitely not easy, but manageable. Always refreshing to see how close to the original the "bad" stuff sounds. I'd like to point out that I missed 10% of the trials and wasn't overly certain in each run despite the level of destruction we're talking about here, while the ABX result discussed in this thread is 110/112. So Josh missed just 1.8% of the trials with differences which I would estimate to be at least two orders of magnitude (= 40 dB) lower...

Thanks for testing! Now imagine that it was a multitone distortion of TD+N = -34.6dB (3% approx) vs. original with TD+N = -132.2dB (0.00003%). 100dB difference, 100 000x. Now imagine trying -100dB vs. -132dB .....

 

[pma]

I wonder how well you would do if you band limit the signals to 10 kHz. Beyond that frequency response seems to start deviating.

There is a bit more of "rumble" noise in the Bluetooth sample rather than that 20kHz difference. That 20kHz difference is masked by equivalent level tones spread up to 10kHz. Anyway, it is much easier to hear 3% THD+N of a single 1kHz sine tone than the multitone distortion.

 

[NTTY]

Thanks for testing! Now imagine that it was a multitone distortion of TD+N = -34.6dB (3% approx) vs. original with TD+N = -132.2dB (0.00003%). 100dB difference, 100 000x. Now imagine trying -100dB vs. -132dB .....

I did not realize before that Josh’s IMD test was done with 32 tones, thanks to you for highlighting that. So there can’t be a TD+N and IMD calculation, unless they were two different measurements. That’s what mislead me. That said I don’t know the software he used.

Anyways, I’ve not seen often the TD+N for multitone test go much beyond 18bits in REW. And per my experience it is necessary to increase the FFT length to have a good reading.

By the way, the one you show at -132dB TD+N, was it performed from a WAV file? EDIT: yes it is.

 

[pma]

All agreed , though I did not read Josh's explanation, only very briefly.

 

[SSS]

There is a bit more of "rumble" noise in the Bluetooth sample rather than that 20kHz difference. That 20kHz difference is masked by equivalent level tones spread up to 10kHz. Anyway, it is much easier to hear 3% THD+N of a single 1kHz sine tone than the multitone distortion.

Sure. It is not easy to get a transducer with THD well below 1 %. Lot of loudspeakers distort when hearing a single tone, also the human ear itself creates distortion when higher SPL.

 

[rjp]

You're quite welcome! I'm happy my explanation helps!

Yes, this is the key concept that allows us to apply our results to all allowable audio signals. I called it "mathematical equivalence of an allowable audio signal into a sum of sine waves", but you are right that switching to complex numbers allows simultaneous handling of amplitude and phase. We just need to verify that the analog output of the DAC does an excellent job of representing the tones across the entire audio bandwidth. Shannon showed that we get a finite basis if sinc functions are used as the basis functions to completely reconstruct the analog signal.

I expect when you have a lot of individual tones as in very complicated music, it is the requirement of limiting the SPL that keeps the Total Distortion in check, though the IMD may grow a little. Each tone you add contributes more distortion but also more to the total energy, and the latter must be limited in playback. Thus, when you scale down the tones to limit the max SPL, the distortion gets scaled down too, and is held in check. There may be nuances such as whether the DAC is accurate enough to reproduce "beats" arising from tones close in frequency without audible distortion.

It really is refreshing to hear such a good technical justification. You should flesh this out a bit, add a few equations, and use it as a standard reference link for why measurements alone can provide competent evidence for (perhaps even prove) audio transparency. I have seen this issue come up many times over the years by well meaning, technically literate, individuals and they are rarely given a satisfactory answer. Sadly, such threads often end in ridicule.