Starting from first principles, the optimum receiver for the detection of a harmonic set embedded in white Gaussian noise is derived. The receiver obtained also provides the maximum likelihood estimate of the fundamental frequency of the harmonic set. Three signal conditions are studied: (1) the harmonic amplitudes are known exactly, (2) the harmonic amplitudes are unknown, but have known, independent probability distributions, and (3) the harmonic amplitudes are unknown and have unknown, independent probability distributions. For cases (1) and (2) the optimum receivers are derived. For case (3) the receiver obtained cannot be claimed to be optimum; however, it does have intuitive appeal. In each case the receiver cross correlates the (transformed) spectral estimates with a periodic impulse train whose period corresponds to each possible fundamental frequency of the harmonic set. The receiver for case (3) has an additional interesting property in that it discards all spectral estimates less than a certain value. Some extensions to these results are discussed for situations where (a) the spectral estimates are obtained from data lengths much shorter than the observation interval, and (b) multiple similar harmonic sets may be present.