Existing approaches for multi-pitch detection have still been highly complex. In this paper, the harmonic shift algorithm (HSA) for multi-pitch detection is illustrated. The HSA is a noncoherent blind detection scheme, exploiting the constant-Q transform (CQT). The only requirement for the successful application of the HSA is that all the sources are harmonic sources. Due to this simplicity, the HSA is considered viable for both single-pitch and multi-pitch detection, making its attractive for the application in other areas of signal processing. When illustrating the performance capabilities of the HSA, we demonstrate that it outperforms the state of the art regarding the computational complexity providing detection precision, accuracy and a recall factor comparable with existing schemes.