Hello all,
I have a quick question to a problem of mine. I have been trying to combine two hertz frequencies into one complete tone. For instance, if I had a 100 hertz tone and another 100 hertz tone, how can I combine them together so that they combine. I tried to mix and render and just play the tone but no good results. If I combine a 100 hertz tone and another hertz tone shouldn’t I get a 200 hertz tone?
Or is there a problem with my logic? Does mixing tones work that way?
Nope. You just get 100 Hz with more moxie. You’ll get an interesting combination if they’re not both exactly 100Hz. If you managed to get two tones with the blue waves exactly out of step, you could get a lower tone or nothing.
Do you know how to tune a guitar? You know how you hold one magic fret and that string is supposed to sound like one of the other strings – but only if everything is in tune? Remember what happens if the strings are out of tune?
You’re playing two strings on the same instrument and at the same pitch, but you don’t magically get a note an octave higher.
Don’t confuse straight mixing with modulation. If you put a tone on an AM radio station, you’ll get two additional tones, one higher and one lower plus the AM station frequency. There are filters and effects that can work that way, too. The ring modulator comes to mind. That’s how this commercial was made.
http://www.youtube.com/watch?v=YR_Bjf-a5rs
Koz
What is moxie again? Thanks for the reply also 
One mor question koz,
So in reality there is no real way to combine tones together. They are just played simulataneously and sometimes we can discriminate everything that is being played and sometimes we don’t. I’ll be honest with you the reason I am asking is because I am interested in white noise. I think it’s interesting when you combine all frequencies together you call it white. Similarly, in vision you combine all wavelengths of light and you get white light.
So do you don’t there are primary frequencies of sound that make white noise?
I presume your questions means, “if you mix primary coloured lights you can get white light, so can you mix “primary coloured sounds” to get “white noise”?”
It doesn’t quite work like that.
The term “white noise” is an analogy, but the analogy breaks down when you get onto “primary colours” and suchlike.
“White noise” does contain all frequencies within the audio range at equal amplitudes, but that is not the only condition that is required. Another condition that is required for white noise is that the frequencies must be none-correlated. That is, different frequency waveforms should not be “in step” with each other.
In some ways it can be better to think of white noise as “random” noise. In terms of digital audio, this means that each sample value is a random number within a specified range. The equivalent of a “pure primary colour” in sound would be a sine wave of a specified frequency, but for any non-random waveform, the sample values are non-random. It is not possible to create random numbers from adding together non-random numbers.
This really depends on how you look at it.
If you zoom in close on the waveform of a recording, you will see a complex waveform, for example:
Mixing is done by summing. When you add two identical waves the height at 45-degress gets added together, and the height at 90 degrees, 0-degrees, etc., and all points in-between. (With digital, you simply add the samples together.) So, you get the same waveform only bigger (louder). If the phase is shifted, you’ll get a smaller sum but the same wave-shape. If you shift it enough to where you are adding negatives to positives you can end-up with a smaller (quieter) waveform, or if you shift 180-degrees and everything sums to zero, you have no waveform.
I’ll be honest with you the reason I am asking is because I am interested in white noise. I think it’s interesting when you combine all frequencies together you call it white. Similarly, in vision you combine all wavelengths of light and you get white light.
Audacity can generate white nose - Generate → Noise.
With enough frequencies (maybe 1000 or more?) and enough randomness, you could probably simulate white noise. But normal music contains hundreds of frequencies* at any moment in time, they are not random, and they don’t sound like noise… Well… most musical genre’s don’t sound like noise! 
Color perception is different from sound perception. If you play two (or more) tones at once (or two or more instruments at once), you can hear them both. When you mix two (or more) colors together, our brain cannot see more than one color (at any one location), so somehow our brain creates a 3rd color.
If you look closely at an old color TV (or computer monitor) with a picture tube, you will see that there is only one colored dot (red, blue, or green) at one location, but at a distance we can’t focus on the individual dots so we perceive different colors as the dots/colors blur together.
Normally, digital white noise is just a completely random sequence of numbers which turns into white noise (a completely random waveform) when fed into a digital-to-analog converter. The [u]Digital Audio Tutorial[/u] shows you how digital audio works. If you generate the samples randomly, you have white noise.
Pink noise sounds more natural than white noise (maybe perceived more like white light). Pink noise is has equal energy in each octave… i.e. The octave from 100 - 200Hz contains the same energy as the octave from 10,000 - 20,000Hz. Pink noise is created by generating white noise and then filtering it.
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“Moxie” = energy or loudness.
White isn’t the only one, either. White has equal energy per frequency. Pink has equal energy per octave which is a bit more like your ear actually works. There is a Brown one, too and I don’t remember what that one is.
We are warned that putting white noise into a powerful speaker system could fry the speakers. Tweeters loaf a lot of the time during music, so they aren’t built to handle huge amounts of power. White noise has a significant amount of power in high frequencies – and it never goes away.
“What’s that smell and why did the sound get muffled?”
Koz
There are a lot of real instruments that can produce frequencies out of “nothing” or better from a few simultaneously played frequencies.
You’ll here after a while the differences and the sums of the two sounds. Church bells are extreme in this respect because some tones can take more than a second to appear.
Simple addition does not creating new frequencies (especially not over head phones, where the two sounds can’t modulate one another with the help of resonating solids).
Multiplication does the trick:
Create a stereo tone at an arbitrary frequency (amplitude 1) and enter this code in the Nyquist prompt:
(mult (s-abs (aref s 0)) (aref s 1))
We use the envelope of the left channel to modulate the amplitude of the right channel.
Let’s say we have 100 Hz, the result will be 100 - 100 and 100 + 100 Hz. The new tone will therefore also include to some amount the octave (and all octaves above and below).
I’ve used the absolute value of the left channel to ensure that the result isn’t only positive (that’s in fact the 100-100 = 0 Hz frequency).
press ctrl-r to repeatedly modulate the frequency with itself.
Where will we end up?
That’s easy to predict if we take a look at the main values of a sine period:
0 0.707 1 0.707 0 -0.707 -1 -0.707
now the first iterations of our multiplication:
I. 0 0.5 1 0.5 0 -0.5 -1 -0.5
II. 0 0.25 1 0.25 0 -0.25 -1 -0.25
inf. 0 0 1 0 0 0 -1 0
We eventually have a (tirac) pulse train.
The interesting thing is that a impulse has all frequencies equally distributed over the whole spectrum (if it is a 1 with only zeros behind it). Since we’ve started with 100 Hz, the frequencies inbetween will in fact not be present.
However, if the the deeper the start frequency, the more flattened the spectrum will appear in the end. The only difference to white noise is than the phase of the various frequency bands, the latter is randomly distributed.
We have here applied a simple amplitude modulation. frequency (FM-radio) or phase (synthesizers) would also introduce phase shifts and we could produce white noise in this manner.