Insomnia is the most prevalent sleep disorder and is associated with significant psychosocial and somatic pathology. Effective noninvasive interventions for insomnia are lacking. High-resolution, relational, resonance-based, electroencephalic mirroring (HIRREM), is a noninvasive, brain feedback technology to facilitate relaxation and auto-calibration of neural oscillations by using auditory tones to reflect brain frequencies in near real time. An open label, randomized, crossover pilot trial showed that HIRREM was safe and effective, with significant benefits for individuals with moderate to severe insomnia, based on differential change with symptoms of insomnia (Insomnia Severity Index, ISI). This study will extend those results in a larger cohort using a single blind, placebo controlled study design.