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Several fully end-to-end text-to-speech (TTS) models have been proposed that have shown better performance compared to cascade models (i.e., training acoustic and vocoder models separately). However, they often generate unstable pitch contour with audible artifacts when the dataset contains emotional attributes, i.e., large diversity of pronunciation and prosody. To address this problem, we propose Period VITS, a novel end-to-end TTS model that incorporates an explicit periodicity generator. In the proposed method, we introduce a frame pitch predictor that predicts prosodic features, such as pitch and voicing flags, from the input text. From these features, the proposed periodicity generator produces a sample-level sinusoidal source that enables the waveform decoder to accurately reproduce the pitch. Finally, the entire model is jointly optimized in an end-to-end manner with variational inference and adversarial objectives. As a result, the decoder becomes capable of generating more stable, expressive, and natural output waveforms. The experimental results showed that the proposed model significantly outperforms baseline models in terms of naturalness, with improved pitch stability in the generated samples.