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The question basically amounts to whether I can construct the illusion of superposition with adjacent sine waves of varying frequency.

Context

I'm trying to play music on a Tesla Coil (like OneTesla and the works). If I want to play an A for instance, I'll modulate my input signal so that the Tesla coil sparks 110 times per second. Each time, it will turn air into plasma, a volume change whose pressure wave propagates through the air as sound.

However, as of now I can only play one note at a time. For example, I can play a C, followed by a F, followed by a G, but I can't play a CFG chord. In terms of sine waves (i.e. why I'm posting to the Physics StackExchange), I'm trying to model $\Sigma_{i=1}^{n} sin(\alpha_i x)$ from, say $0<x<\pi$ time units, with the approximation $sin(\alpha_i x)$ for $\frac{(i-1)\pi}{n}<x<\frac{i\pi}{n}$ for i from 1 to n, and x from 0 to $\pi$.

At least with light, I think that humans have a visual memory - e.g. if I show you red, and then blue, and then red, and alternate really, really, fast, you see purple (I think...). Is the same possible for sound? If so, how fast do I need to alternate notes?

I'm sure the same question has been asked somewhere else, but I couldn't find any answers that apply. Also, if this is in the wrong forum, feel free to move it.

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It doesn't sound exactly like a chord, but this type of technique was widely used in the 8-bit and 16-bit computer game eras, when the number of sound channels available was limited. It has a very distinctive retro video game sound, but the ear is able to identify the chord that it's supposed to be.

Here is a YouTube video explaining how to achieve the effect using synthesis software - your situation is different, but you can probably adapt some of the advice. You can experiment with the speed of modulation, but the guy in the video sets it to around 30 Hz, which sounds good.

Actually, I think you should be able to achieve the effect of a chord through a different method. To play a note at a frequency of $f_1$ at the same time as a note with frequency $f_2$, you just need to time the sparks so that there are sparks at times $0, \frac{1}{f_1}, \frac{2}{f_1}, \frac{3}{f_1},\dots$ and also at times $\frac{1}{f_2}, \frac{2}{f_2}, \frac{3}{f_2},\dots$. This will sound to the ear exactly like the two notes being played at once, because that's essentially what it is.

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  • $\begingroup$ That looks great! However, I had tried alternating between notes really quickly, and I have to say, it didn't sound good. Then again, I was using a pretty crappy speaker (coil of wire + magnet), so perhaps the sound quality degradation at high frequencies was from that rather than from the technique. $\endgroup$ – sredmond Jan 23 '14 at 5:44
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    $\begingroup$ As a general rule it works better with higher pitched notes - you might try transposing your chords up an octave or two and see if that helps. $\endgroup$ – Nathaniel Jan 23 '14 at 5:56
  • $\begingroup$ I had another idea, and updated my post. $\endgroup$ – Nathaniel Jan 23 '14 at 6:04
  • $\begingroup$ That video is mostly talk. To simply hear the sound you can click here youtu.be/fgvlOxZysvs?t=208 $\endgroup$ – chasly from UK Dec 1 '18 at 16:08
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It's a neat question, but I think it has a simple intuitive answer: when you play a chord normally on a guitar or something else, you really are just plucking the individual notes in order, very quickly, which is definitely recognizable as a chord.

Of course, with a guitar, the strings keep resonating, so the sound pulse has a finite (large) width, and they certainly overlap. So your problem doesn't seem to be that you have to play the notes at different times, but that each individual note isn't played for very long.

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    $\begingroup$ Very true... With the guitar, though, the resonating string still generates, say, 440 Hz sound even after I'm done plucking it, whereas with the Tesla coil, it stops creating 440Hz air vibrations as soon as I remove the pulses to the transistor's base. $\endgroup$ – sredmond Jan 23 '14 at 5:30

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