We propose a semi-supervised singing synthesizer, which is able to learn new voices from audio data only, without any annotations such as phonetic segmentation. Our system is an encoder-decoder model with two encoders, linguistic and acoustic, and one (acoustic) decoder. In a first step, the system is trained in a supervised manner, using a labelled multi-singer dataset. Here, we ensure that the embeddings produced by both encoders are similar, so that we can later use the model with either acoustic or linguistic input features. To learn a new voice in an unsupervised manner, the pretrained acoustic encoder is used to train a decoder for the target singer. Finally, at inference, the pretrained linguistic encoder is used together with the decoder of the new voice, to produce acoustic features from linguistic input. We evaluate our system with a listening test and show that the results are comparable to those obtained with an equivalent supervised approach.