Is there a way I can continuously play one event clip after another in the event browser without having to drag them into a project?
Not directly but you could select them all and make them into a Compound Clip and then play that as one long string out.
I assume by making a "Compound" clip you are saying to drag all clips into a new Project. If not, please explain what you mean by making a compound clip. Thanks.
It simply creates a new clip in the Event Browser that is a combination of all the clips you selected. The order the clips will play is in the order you select them. It's non-destructive so give it a try with just two or three clips.
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