Explain the mechanics of Shor's algorithm for integer factorization to an audience of senior computer scientists who have no background in quantum mechanics. Your explanation must: 1) Use musical harmony or wave interference as a metaphor for quantum superposition and entanglement. 2) Contrast the time complexity of the classical trial division method versus the quantum period-finding approach. 3) Detail the role of the Quantum Fourier Transform (QFT) in the process without relying on dense mathematical notation. 4) Discuss the practical implications of current quantum error correction limitations on running this algorithm for large RSA keys.