The Mirnov coil array, the horizontal soft x‐ray camera, and the ECE (electron cyclotron emission) grating polychromator are used to unfold the structure ofm≥2 coherent magnetic fluctuations (assumed to be tearing modes) observed in TFTR. The modes are found predominantly in the enhanced confinement, or supershot, regime, and when present seriously degrade confinement. The poloidal and toroidal mode numbers (mandn) are determined with the Mirnov coil array. The radial structure is found by calculating the theoretical radial eigenmode (based on the calculated current‐density profile) and scaling the resulting linear eigenmode with the measured fluctuation amplitude at the plasma edge. The presence of rotating magnetic islands is detected as fluctuations on both the chord‐averaged soft‐x‐ray emissivity measurements and the fast grating polychromator electron temperature measurements. The ECE and soft‐x‐ray systems are used to identify coherent modes as islands and confirm estimates of the islands’ location inferred from the Mirnov coil data and calculated current‐density profiles.