Efficacy of binaural auditory beats in cognition, anxiety, and pain perception: a meta-analysis (García-Argibay et al., 2019)
The most useful single reference in the field: a meta-analysis pooling controlled binaural beat studies across cognition, anxiety, and pain outcomes. It found a modest overall effect, with longer exposure and beats presented without masking sound tending to work better. It's also candid about the field's problems — small samples and wildly inconsistent protocols. If you read one paper before forming an opinion, read this one.
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