How toread the tone number when doing a sum of different tones?

Let’s say I generate 2 tones in two tracks, 324,23 and 521,89. If I play them together I get a different sound, if I use "Tracks > Mix > Mix and Render to New Track " then this combo is mixed into a single track.
What I want to know is, what number is that resulting tone?
I need to put in a spreadsheet (Libreoffice) the formula so that I can put in 2 or more boxes the numbers and then receive the result of that sum of frequencies.

Searching I found this

But I haven’t used this sort of math in more than 5 years so I am a bit lost.
Maybe since Audacity is open source the code of what is being done could be “open” but I am not that savvy, so…help please?

The beat frequency is simply the difference frequency. But that’s modulation. It’s not a new tone. If you have two tones one Hz apart you can hear the 1Hz modulation but there is no low-frequency audio. If you low-pass at 1Hz, there will be nothing. Or if you filter-out or subtract-out one of the tones, you’ll get-back the single-remaining tone.

The tones are simply superimposed on each other, both existing at the same time. If you mix a singer an a guitar either acoustically, electronically, or digitally, they both exist simultaneously.

So basically I can’t create a single tone that reproduces what the sum of those 2 sounds like then?
Then what are those equations for?

what number is that resulting tone?

324,23 and 521,89.

If you hear anything else it’s because your ear is mixing the two tones together. Combinations don’t actually exist. If you notch out one of the two tones from the mix with Effect > Notch Filter, you’re left with the other pure tone. There are no second, third and forth harmonics, overtones, beats, mixtures, etc.

Audacity is not the best tool for scientific experiments. If for no other good reason, if it’s a toss-up between perfect scientific accuracy and sounding good, Audacity will always pop for sounding good.

If you export your duo-tone sound test to a sound file, you may find that Audacity has added dither noise to the mix and if it doesn’t do that, you may get sampling errors from bit depth conversions.

None of this concerns you if you’re recording your guitar.


Then what are those equations for?

That’s non-linear mix. That’s what your ear is doing. Half Volume to your ear is barely audible. Free-air volume can double or half many times before your ear runs out of steam. Those are the equations that go into advanced math.


Here. This is the analysis with just a straight mix between the two tones.

Screen Shot 2020-06-14 at 9.31.57.png
Its just the original two (measured along the bottom).

Now I’m going to apply a distortion filter similar to fuzz guitar. Suddenly, it’s not clean, pure, perfect, straight, linear any more and all sorts of nasty, messy tones pop up.

Screen Shot 2020-06-14 at 9.33.25.png
I didn’t add any musical tones to that. All I did was distort the mix of the original two. I made it non-linear. Audacity stopped accurately following the original two tones.


Well thank you two very much for the quick replies, I guess this thread is done.