Depending on what you are using for the initial video, if a camcorder there may be line level inputs where you could hook up your mixer directly, so sync with the video will be perfect. There are also iOS or Android compatible inexpensive audio interfaces that can allow you to hook up your phone to your mixer output while you record video.

These all bypass the need to wild sync any recorded audio to your video, but it’s not that big a chore. You will help yourself doing the old clapboard trick that film people do, simply clap your hands once before you start the music, and that will give you a nice clear transient on both the video audio and the mixer recording. You can then zoom in in the editor and line both claps up as tight as you can go, and that will give you perfectly synced audio, at least for the duration of a single song.

You might have bigger issues if you try to record a whole show, especially if using a tape camcorder, trying to keep synced for half an hour or more. But digital video is pretty stable. Just keep an eye out for any drift in sync between the nice tight start of the recording and the end…

You certainly don’t need to worry about multitrack audio as long as you simply want to record your live performance…
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An arranger is just a tool. What matters is what you build with it..!