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In this paper, we provide a theoretical analysis of the amount of musical noise in iterative spectral subtraction, and its optimization method for the least musical noise generation. To achieve high-quality noise reduction with low musical noise, iterative spectral subtraction, i.e., iteratively applied weak nonlinear signal processing, has been proposed. Although the effectiveness of the method has been reported experimentally, there have been no theoretical studies. Therefore, in this paper, we formulate the generation process of musical noise by tracing the change in kurtosis of noise spectra, and conduct a comparison of the amount of musical noise for different parameter settings but the same achieved level of noise attenuation. Furthermore, we theoretically derive the optimal internal parameters that generate no musical noise. It is clarified that to find a fixed point in kurtosis yields the no-musical-noise property. Comparative experiments with commonly used noise reduction methods show the proposed method's efficacy.