Halting sound immediately upon muting

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You can use the Routings page for audio mutes (using on DT here, assuming DN is the same)…

Digitakt tips and tricks

Although its primary purpose is for OB recording use, the Audio Routings’ Route To Main page (press […] and scroll to bottom, turn off Use Global Settings to enable) can also be used as an alternative Mute feature, handy for toggling audio without affecting the midi triggers – e.g. long samples can be mute-toggled mid-way through (not possible with regular Mutes). It can also mute the FX by toggling Del and Rev buttons (they’re green like the trigger buttons)