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In this paper, a pitch-adaptive waveform generative model named Quasi-Periodic WaveNet (QPNet) is proposed to improve the limited pitch controllability of vanilla WaveNet (WN) using pitch-dependent dilated convolution neural networks (PDCNNs). Specifically, as a probabilistic autoregressive generation model with stacked dilated convolution layers, WN achieves high-fidelity audio waveform generation. However, the pure-data-driven nature and the lack of prior knowledge of audio signals degrade the pitch controllability of WN. For instance, it is difficult for WN to precisely generate the periodic components of audio signals when the given auxiliary fundamental frequency ($F_{0}$) features are outside the $F_{0}$ range observed in the training data. To address this problem, QPNet with two novel designs is proposed. First, the PDCNN component is applied to dynamically change the network architecture of WN according to the given auxiliary $F_{0}$ features. Second, a cascaded network structure is utilized to simultaneously model the long- and short-term dependencies of quasi-periodic signals such as speech. The performances of single-tone sinusoid and speech generations are evaluated. The experimental results show the effectiveness of the PDCNNs for unseen auxiliary $F_{0}$ features and the effectiveness of the cascaded structure for speech generation.