In this paper, we present Period Singer, a novel end-to-end singing voice synthesis (SVS) model that utilizes variational inference for periodic and aperiodic components, aimed at producing natural-sounding waveforms. Recent end-to-end SVS models have demonstrated the capability of synthesizing high-fidelity singing voices. However, owing to deterministic pitch conditioning, they do not fully address the one-to-many problem. To address this problem, we present the Period Singer architecture, which integrates variational autoencoders for the periodic and aperiodic components. Additionally, our methodology eliminates the dependency on an external aligner by estimating the phoneme alignment through a monotonic alignment search within note boundaries. Our empirical evaluations show that Period Singer outperforms existing end-to-end SVS models on Mandarin and Korean datasets. The efficacy of the proposed method was further corroborated by ablation studies.