Mountain glaciers represent one of the largest repositories of fresh water in alpine regions globally. However, little is known about the processes by which water moves through these systems. Analysis of data from a deployment of seismometers located near an ice marginal lake in the Swiss Alps reveals, for the first time, that harmonic tremor occurs within mountain glaciers and that individual icequakes at the glacier base can exhibit harmonic properties. These observations suggest that there is a complex network of fluid-induced fracture processes at the glacier base. Modeling changes in the observed harmonic frequencies indicates that the spectral characteristics of seismic data can provide important information about hydraulic fracture geometry and fluid pressure at depth, leading to important insights into subglacial hydrologic processes. Future modeling of these processes may lead to improved glacial outburst flood hazard predictions.