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I have a signal that I would like to play back from different directions with slight delays. However, when I do this, I'm getting an undesirable not-very-nice-sounding phasy effect, caused by phase cancellation I suppose.

Now I know about phase cancellation and why it's there (and why this exact set-up causes it), but I was wondering if there's a way to avoid it. All the stuff I found about that deals with this problem discussed two sources (in which they suggest inverting the phase of one signal), but that solution doesn't work when you have multiple (like ~5 similar signals). Is there a way around this to make this sound nicer, and to process the signals to get the minimum of phase cancellation?

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Delays on a signal smaller that 20-30 ms normally produce "comb filtering" artifacts when combined together with the direct signal because the waveforms add or subtract (in the situation of inverted phase) from each other. You can't avoid that behavior. The same result will emerge for delays that are multiple of the tempo and differentiate by the same amount of samples.

To address that issue you can feed different physical outputs so to produce a Haas effect.

https://en.wikipedia.org/wiki/Precedence_effect

To use a single signal path perhaps you can try to modulate the delay lines so to get a non constant comb filtering effect similar to a chorus.

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