Audio Myths Workshop

[Z1202]

Replying to everyone at once.

In regards to the mixed sines, as I said, the result will be audible only if there are noticeable unsymmetric nonlinearities in the signal path/ear.

This has to do with nonlinearity of the human hearing, because only if the hearing is linear, you can make the statement, that the audible effect of the sum of signals is the "sum" of their audible effects. In ourr case it would mean that if two sines are inaudible, then so is their sum.

I don't think noise above 20kHz had high chances to be audible, since the signal is "too even".

I just had an idea for another experiment (again it won't prove anything, a much more detailed research in regards to linearity/nonlinearity of human hearing is generally required here). This could get audible due to "other types of nonlinearities" in the hearing, I can't explain it precisely though. Anyway. Take a fully antialiased sawtooth at some 2Hz-5Hz (sic). Aliasing might be okay too, but better stay on the safe side). Filter out all frequencies below 20kHz. The highpass filter used for such filtering must be very very steep. The best way is probably to directly sum up the sinusoidal partials (note that you need to use at least double, that is 64bit, floating point precision for computations). The result might be audible.

Regards,
{Z}

[tony tony chopper]

I don't think noise above 20kHz had high chances to be audible, since the signal is "too even".

what's "too even" in noise?

The result might be audible.

Isn't it weird to say "might" for something that's so easily producable to prove your point?
Here's what you described. 5hz sawtooth up to 48khz and 22khz (to 16bit without dithering while we're at it).
http://forum.image-line.com//files/5hzsaw96khz_154.wav

But shouldn't it be to the one who claims that something established might be wrong, to bring proof that it's wrong? Whatever we provide, it won't prove that it's correct, while a single audio demo of yours will destroy our claim. So the lack of ANY audio proof in similar debates should be telling something.

note that you need to use at least double, that is 64bit, floating point precision for computations

no you don't, that's another BS myth. The only place you may need 64bit in synthesis is in stuff with feedback, where the error can be accumulating quickly. And 64bit summing in sequencers is particularly a big joke.

[Z1202]

I don't think noise above 20kHz had high chances to be audible, since the signal is "too even".

what's "too even" in noise?

That's an intuitive term here. The noise is sounding as something constant, doesn't it?

The result might be audible.

Isn't it weird to say "might" for something that's so easily producable to prove your point?
Here's what you described. 5hz sawtooth up to 48khz and 22khz (to 16bit without dithering while we're at it).
http://forum.image-line.com//files/5hzsaw96khz_154.wav

Yes, but I don't have time to produce it and to get to the equipment of very high quality, which will be required for such experiment (otherwise you can always say that your speakers didn't reproduce enough details, or that they introduce artifacts, etc)

But shouldn't it be to the one who claims that something established might be wrong, to bring proof that it's wrong?
Whatever we provide, it won't prove that it's correct, while a single audio demo of yours will destroy our claim. So the lack of ANY audio proof in similar debates should be telling something.

I said the reasoning is wrong. I didn't say the statement itself is wrong (I simply don't know). Nevertheless I wanted to prevent jumping to conclusions too quickly and giving flawed explanations. At any rate I don't have time (nor enough knowledge) to conduct a full blown scale of the required experiments.

note that you need to use at least double, that is 64bit, floating point precision for computations

no you don't, that's another BS myth. The only place you may need 64bit in synthesis is in stuff with feedback, where the error can be accumulating quickly. And 64bit summing in sequencers is particularly a big joke.

You are starting using too strong terms like BS, so I'm tempted not to explain anything further. Anyway. If the sawtooth is 2Hz, creating it by summing harmonics will require summing about 10000 partials. If every addition gives you an estimated relative error of approx 10^-8 (for 32 bit FP), then with 10000 partials you have the risk of having as much as 10^-3. Further, the phase of a 2Hz signal computed at 88kHz sampling rate will not be represented too precise, leading to noticeable phase jitter in higher partials. I'll skip the math, if you don't mind.

Regards,
{Z}

edit: a mistype 2kHz->2Hz

[Z1202]

Sorry, the top estimated error is 10^-4, of course, nevertheless I suggested using 64 bit to avoid the need to estimate the error in the first place. Plus there's that phase thing.

[Z1202]

At any rate I don't have time (nor enough knowledge) to conduct a full blown scale of the required experiments.

Actually I was a little too bold in the above statement In fact the research field (the linearity of the human hearing and related areas) is probably large enough for a couple of hundred of scientific articles and a few dissertations.

Regards,
{Z}

[Z1202]

Here's what you described. 5hz sawtooth up to 48khz and 22khz (to 16bit without dithering while we're at it).
http://forum.image-line.com//files/5hzsaw96khz_154.wav

I must be misreading something. Looks to me like a normal bandlimited saw. What I described was a saw with a 2-5Hz fundamental and partials onlyabove 20kHz (highpass filtered with an extremely steep cutoff). Best is to use additive synthesis with 64 bit precision.

[tony tony chopper]

Further, the phase of a 2Hz signal computed at 88kHz sampling rate will not be represented too precise, leading to noticeable phase jitter in higher partials.

I only agree about the phase, if it's done using an accumulator, yes it needs to be 64bit.

I said the reasoning is wrong. I didn't say the statement itself is wrong (I simply don't know).

There's nothing wrong with this reasoning. If you claim "there are no monsters under beds", it's something you can claim but not proof. You can't check every bed in the world, nor be sure that in the future there won't be a bed with a monster under.
So one makes the claim "there are no monsters under beds", and it's up to others to prove it wrong, by pointing even just 1 bed under which there's a monster. By the lack of any bed under which there is a monster, then "there are no monsters under beds" is true, until proven otherwise.

We could post hundreds of samples, you would still claim "but that's only one case / what if / you never know". While you would just have to post 1 proof, and annihilate all of our claims. But why do you think that we're never seeing any proof, only useless debates?

Of course the monitoring software/hardware also matters, so once someone has claimed "I can hear the difference between this & that sample", we can investigate further. That wav file I've posted, sounds different in my Winamp through the DirectSound output, probably involving bad resampling somewhere. This didn't prove that there was a difference, but that the monitoring was flawed.

[Z1202]

There's nothing wrong with this reasoning.

Consider the statement: "since 2 times 2 is 4 and since 2 times 3 is 5, it must be that 2 times 4 is 8". The conclusion "2*4=8" is correct, but not the reasoning. My only point was that the statement "since humans cannot hear sines above 20kHz (and since human hearing is linear), humans cannot hear differences in the signals above 20kHz" has wrong reasoning, because the part in the parentheses is not a proven fact.

Regards,
{Z}

[Z1202]

edit: ignore

[tony tony chopper]

What I described was a saw with a 2-5Hz fundamental and partials onlyabove 20kHz (highpass filtered with an extremely steep cutoff).

here (still to 16bit with no dithering)
http://forum.image-line.com//files/5hzs ... _2_980.wav

[aka_bip]

If humans cant hear sine waves above 20kHz
And per Fourier, any periodic function is equivalent to the sum of a series of sine waves
Then humans cant hear anything above 20kHz

Did I miss something?

[tony tony chopper]

since humans cannot hear sines above 20kHz

that's your own statement. I never read anything that said "humans cannot hear sines above 20khz. We don't know about other signals, because we never thought of testing with anything else but sines"

[Z1202]

If humans cant hear sine waves above 20kHz
And per Fourier, any periodic function is equivalent to the sum of a series of sine waves
Then humans cant hear anything above 20kHz

Did I miss something?

Yes, you missed an implicit assumption of linearity of human hearing, since otherwise you cannot infer the latter from the former (explained a few posts above).

[Z1202]

since humans cannot hear sines above 20kHz

that's your own statement. I never read anything that said "humans cannot hear sines above 20khz. We don't know about other signals, because we never thought of testing with anything else but sines"

Please clarify what you're trying to say here. I don't understand.

[Z1202]

since humans cannot hear sines above 20kHz

that's your own statement. I never read anything that said "humans cannot hear sines above 20khz. We don't know about other signals, because we never thought of testing with anything else but sines"

Oh, I see now. It doesn't matter, whether the experiments involved other signal shapes or not. The point is, unless there is a proof that the human hearing is linear (well, maybe I missed one), then its not enough to test with any number of signals. Because you could always have missed an important class of signals, which are audible, or for which the partials above 20kHz are critical. Only the assumption of linearity allows to extrapolate the results obtained with the experimental signals to all other signals (and under this assumption it is sufficient to test only with sines).