Although Essential Tremor is one of the most common movement disorders, current treatment options are relatively limited. Peripheral tremor suppression methods have shown potential, but we do not currently know which muscles are most responsible for patients' tremor, making it difficult to optimize suppression methods. The purpose of this study was to quantify the relationships between the tremorogenic activity in muscles throughout the upper limb. Muscle activity was recorded from the 15 major superficial upper-limb muscles in 24 subjects with Essential Tremor while they held various postures or made upper-limb movements. We calculated the coherence in the tremor band (4-12 Hz) between the activity of all muscle pairs and the time-varying phase difference between sufficiently coherent muscle pairs. Overall, the observed pattern somewhat mirrored functional relationships: agonistic muscle pairs were most coherent and in phase, whereas antagonist and unrelated muscle pairs exhibited less coherence and were either consistently in phase, consistently antiphase, consistently out of phase (unrelated pairs only), or else inconsistent. Patients exhibited significantly more coherence than control subjects (p<0.001) in the vast majority of muscle pairs (95 out of 105). Furthermore, differences between patients and controls were most pronounced among agonists; thus, the coherence pattern existing in control subjects was accentuated in patients with ET. We conclude that tremor-band activity is broadly distributed among the muscles of the upper limb, challenging efforts to determine which muscles are most responsible for a patient's tremor.