A progressive series of five new coils is described. The first coil solves problems of transmit-field inefficiency and inhomogeneity for heart and body imaging, with a close-fitting, 16-channel TEM conformal array design with efficient shield-capacitance decoupling. The second coil progresses directly from the first with automatic tuning and matching, an innovation of huge importance for multi-channel transmit coils. The third coil combines the second, auto-tuned multi-channel transmitter with a 32-channel receiver for best transmit-efficiency, control, receive-sensitivity and parallel-imaging performance. The final two coils extend the innovative technology of the first three coils to multi-nuclear (31P—1H) designs to make practical human-cardiac imaging and spectroscopy possible for the first time at 7 T.