Synthesized polyphonic sound completely different from the “real” one

Question

I am making a software audio synthesizer and so far i've managed to play a single tone at once.

My goal was to make it polyphonic, i.e when i press 2 keys both are active and produce sound (i'm aware that a speaker can only output one waveform at a time).

From what i've read so far, to achieve a pseudo-polyphonic effect what you are supposed do, is to add the tones to each other with different amplitudes.

The code i have is too big to post in it's entirety but i've tested it and it's correct (it implements what i described above, as for whenever it's the correct thing to do i'm not so sure anymore)

Here is some pseudo-code of my mixing

sample = 0.8 * sin(2pi * freq[key1] * time) + 0.2 * sin(2pi * freq[key2] * time)

The issue i have with this approach is that when i tried to play C C# it resulted in a wierd wobble like sound with distortions, it appears to make the entire waveform oscillate at around 3-5 Hz.

I'm also aware that this is the "correct" behavior because i graphed a scenario like this and the waveform is very similar to what i'm experiencing here.

I know this is the beat effect and that's what happens when you add two tones close in frequency but that's not what happens when you press 2 keys on a piano, which means this approach is incorrect.

Just for test i made a second version that uses stereo configuration and when a second key is pressed it plays the second tone on a different channel and it produces the exact effect i was looking for.

Here is a comparison

• Normal https://files.catbox.moe/2mq7zw.wav
• Stereo https://files.catbox.moe/rqn2hr.wav

Any help would be appreciated, but don't say it's impossible because all of the serious synthesizers can achieve this effect

Answer 1

You seem insistent that "YOUR CODE IS CORRECT" but looking at the wave forms in your links, I can't see anything that corresponds to what you say you are doing.

For example both files are actually stereo even though you say one is mono, but both have almost the audio in one channel. Your "stereo" version does NOT "play the second tone on a different channel". It plays both tones (mixed) on both channels.

I suggest you go back a bit and PROVE that your code is doing exactly what you think it does, one step at a time.

Answer 2

Most probably the problem is that your pure sine waves don't have any harmonics, and that's why the beating is so extreme. Any real instrument will have some harmonics, and when you play a sine wave out of a physical loudspeaker, it adds harmonics as well, in the form of distortion. This should be evident on your recording (made with a smartphone mic?), because that's not a clean sine wave at all. If you stereo-separate, each note gets its own separate speaker with separate distortion and set of harmonics. But if you sum first in the digital domain, then it's the beating sound that gets the distortion.

You can add harmonics to the sine waves by raising each sample/sine value to a power, before adding them together.

note1sample = pow(sin(2*pi*freq1), 8.0)
note2sample = pow(sin(2*pi*freq2), 8.0)
output = note1sample + note2sample

For more of the same effect, add more harmonics. https://dsp.stackexchange.com/questions/51759/harmonic-distortion-of-sine-signal-plotting-resulting-spectrum

Mixing i.e. summing (addition) is a linear operation, but distortion is non-linear. In non-linear systems, the order of operations changes the output, but in linear systems the ordering doesn't matter. It's easy to understand with the math operations above: A + B = B + A, the same thing. But when you add the pow() function, it's different. pow(A) + pow(B) is not the same as pow(A+B).

Here's a video how to recreate the phenomenon in Ableton's Operator synth

First there's just sine waves, and then harmonics are added one by one. With enough harmonics added, the beating is less obvious, and you can distinguish the notes better.

Here's the same with an envelope and then changing the wave from sine to triangle

And finally, the A and A# sine waves are separated to individual channels and run through overdrive effects, first individually, and then through a common master overdrive. I think this corresponds to what happened with your test. The overdrive simulates the speaker distortion. When both sines go through the same distortion, the beating is greatly amplified, but when each sine has its own distortion, the pitches can be distinguished much better.

Answer 3

Close tones result beats as you already know (all tones, really). When adding two notes on same channel, the output waveform is rendered as the sum; the beat effect occurs in the file. When making the stereo file, each sine conserves its integrity. Your ears distinguishes them nicely, and the beat effect is much less perceived, since it occurs physically through air from different position of speakers and acoustics. In this case the waves are not already committed together to cause a chop/annihilation/beat.

The discussion about your method is off topic.

Top track: 440 Hz. Middle track: 445 Hz. Bottom track: both mixed together into a mono file (they were first halved amplitude).

The frequency modulation effect happened at 445 - 440 = 5 Hz. At each second, the wave forms will cancel each other completely 5 times. Reversal can be achieved by subtracting a waveform, however, this will work defectively once a master mix has been applied.

In a stereo file, each sine wave is through a distinct channel. The effect will still happen in air, though, but will be more or less significant according to node positions. Also, having two ears, in this case, makes less likely to be perceived.

All samples given were sines. More complex timbres are made of many harmonics, which can be understood as many sines added together. In nature, usually resonances occur in perfect proportions in the harmonic spectrum (as Pythagoras has demonstrated): 2/1, 3/1, 4/1, 5/1 and so on. Since different timbres have different harmonic signatures, not all sub-vibrations will participate for a 'beat' effect, and timbres will cancel out only phase differences from each other.