This is for Mac only, not sure how you can do it in Windows:
The key is using a virtual device signal routing tool. The free one that I use is Blackhole. You will use this to route your default sound output device into Jamkazam.
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Download and install (this is an open source tool on Github). It will create a virtual sound interface device with 16 channels in and 16 out.
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In the Mac Midi setup for Audio Devices create a Multiple Output device (use the + sign at the bottom of the window to add a device) . Select the default system output device and the Blackhole device in the list presented in the panel and turn on “drift correction” checkbox for the Blackhole device. The default (or Built in) output must be selected first.
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Create an “aggregate device” in the same Mac Midi Audio Devices setup and select input entries for the Scarlet 2i2 and the Blackhole device (in that order). In my setup I set the Clock Source to be Blackhole and set Drift Correction on for the 2i2. This is a bit of a gray area to me but this works in my setup.
-Make sure all the devices in this setup have the same sampling rate specified (e.g. 48K).
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Now go to Jamkazam Audio Setup and select the aggregate device as your input. Select the 2i2 as the output. Save this configuration.
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Start a Jamkazam session and you will be able to hear your Strum Machine in the mix (and so will anyone else in your session). The sound will also still be coming from your Mac speakers so you will need to mute them when using this configuration so that they don’t get picked up in your microphone. You can do this in the same Audio Devices setup utility by selecting Built in Output and checking the box to mute Master.
This is a fairly terse tutorial for a somewhat involved configuration but I can provide some more detail if you need it. Didn’t want to write an encyclopedia only to find out you are using a Windows PC