Generative models for singing voice have been mostly concerned with the task of "singing voice synthesis," i.e., to produce singing voice waveforms given musical scores and text lyrics. In this work, we explore a novel yet challenging alternative: singing voice generation without pre-assigned scores and lyrics, in both training and inference time. In particular, we experiment with three different schemes: 1) free singer, where the model generates singing voices without taking any conditions; 2) accompanied singer, where the model generates singing voices over a waveform of instrumental music; and 3) solo singer, where the model improvises a chord sequence first and then uses that to generate voices. We outline the associated challenges and propose a pipeline to tackle these new tasks. This involves the development of source separation and transcription models for data preparation, adversarial networks for audio generation, and customized metrics for evaluation. The task of computationally producing singing voices is usually referred to as singing voice synthesis (SVS) in the literature (Cook, 1996) . Most researchers assume that the note sequence and the lyrics of the waveform to be generated are given as the model input, and aim to build synthesis engines that sound as natural and expressive as a real singer (Blaauw et al., 2019; Hono et al., 2019; Kaewtip et al., 2019; Lee et al., 2019a; Tamaru et al., 2019) . As such, the content of the produced singing voice is largely determined by the given model input, which is usually assigned by human. And, accordingly, progress in SVS has followed closely with that in text-to-speech (TTS) synthesis (Umbert et al., 2015; Shen et al., 2017; Gibiansky et al., 2017) . However, we argue that singing according to a pre-assigned musical score and lyrics is only a part of the human singing activities. For human beings, singing can also be a spontaneous activity. We learn to spontaneously sing when we were children (Dowling, 1984) . We do not need a score to sing when we are humming on the road or in the bathroom. The voices sung do not have to be intelligible. Jazz vocalists can improvise according to a chord progression, an accompaniment, or even nothing. We aim to explore such a new task in this paper: teaching a machine to sing with a training collection of singing voices, but without the corresponding musical scores and lyrics of the training data. Moreover, the machine has to sing without pre-assigned score and lyrics as well even in the inference (generation) time. This task is challenging in that, as the machine sees no lyrics at all, it hardly has any knowledge of the human language to pronounce or articulate either voiced or unvoiced sounds. And, as the machine sees no musical scores at all, it has to find its own way learning the language of music in creating plausible vocal melodies. It also makes the task different from TTS. Specifically, we consider three types of such score-and lyrics-free singing voice generation tasks, as shown in Figures 1(b) - (d) . A free singer sings with only random noises as the input. An accompanied singer learns to sing over a piece of instrumental music, which is given as an audio waveform (again without score information). Finally, a solo singer also sings with only noises as the input, but it uses the noises to firstly generate some kind of 'inner ideas' of what to sing. From a technical point of view, we can consider SVS as a strongly conditioned task for generating singing voices, as the target output is well specified by the input. In contrast, the proposed tasks are either unconditioned or weakly conditioned. This work therefore contributes to expanding the "spectrum" (in terms of the strength of conditional signals) of singing voice generation. Doing so has at least two implications. First, while our models are more difficult to train than SVS models, they enjoy more freedom in the generation output. Such freedom may be desirable considering the artistic nature of singing. Second, we can more easily use a larger training set to train our model- due to the difficulty in preparing time-aligned scores and lyrics, the training set employed in existing work on SVS usually consists of tens of songs only (Lee et al., 2019a) ; in contrast, in our case we do not need labeled and aligned data and can therefore use more than hundreds of songs for training. This may help establish a universal model based on which extensions can be made. The proposed accompanied singer also represents one of the first attempts to produce singing voice given an accompaniment. One intuitive approach to achieve this is to first generate a score according to an accompaniment in the symbolic domain and then synthesize the singing voices according to the score. The second step of synthesis is relatively well-established, but the first step of generating a score given an accompaniment is not explored yet. Extensive researches have been done in generating scores of one or several instruments (Hadjeres et al., 2017; Huang et al., 2019; Payne, 2019) . However, to the best of our knowledge, very few, if any, researches have been done on generating scores of singing voices given an accompaniment. Our approach bypasses the step of generating scores by directly generating the mel-spectrogram representation. We outline below the challenges associated with the proposed tasks and the solutions we investigate. First, the tasks are unsupervised as we do not provide any labels (e.g., annotations of phonemes, pitches, or onset times) for the training singing files. The machine has to learn the complex structure of music directly from audio signals. We explore the use of generative adversarial network (GAN) (Goodfellow et al., 2014) to address this issue, for its demonstrated effectiveness for SVS (Hono et al., 2019) and pitch-conditioned instrument note synthesis (Engel et al., 2019) . Specifically, we design a novel GAN-based architecture to learn to generate the mel-spectrogram of singing voice, and then use WaveRNN (Kalchbrenner et al., 2018) , a single-layer recurrent neural network, as the vocoder to generate the audio waveform. Rather than considering the mel-spectrograms as a fixedsize image as done in recent work on audio generation (Engel et al., 2019; Marafioti et al., 2019) , we use gated recurrent units (GRUs) and dilated convolutions (van den Oord et al., 2016) in both the generator and discriminator, to model both the local and sequential patterns in music and to facilitate the generation of variable-length waveforms. Second, for training the free singer, unaccompanied vocal tracks are needed. As for the accompanied singer, we need additionally an accompaniment track for each vocal track. However, public-domain multi-track music data is hard to find. We choose to implement a vocal source separation model with state-of-the-art separation quality (Liu & Yang, 2019) for data preparation. The proposed pipeline for training and evaluating an accompanied singer is illustrated in Figure 2 . The advantage of having a vocal separation model is that we can use as many audio files as we have to compile the training data. The downside is that the singing voice generation models may suffer from the artifacts (Cano et al., 2018) of the source separation model, which is moderate but not negligible. Third, for the accompanied singer, there is no single "ground truth" and the relationship between the model input and output may be one-to-many. This is because there are plenty of valid ways to Figure 2 : A pipeline for building the accompanied singer. We use source separation to get separated singing voice and accompaniment from professionally recorded audio files. Then, we use the separated tracks to train the generators and discriminators in the GAN. In inference time, we feed an unseen accompaniment to the trained singer model and let it "sing." sing over an accompaniment track. For diversity and artistic freedom, we cannot ask the machine to generate any specific singing voice in response to an accompaniment track, even if we have paired data of vocal and accompaniment tracks. We investigate using conditional GAN (Mirza & Osindero, 2014) to retain the possibility of generating singing voices with multiple modes. Fourth, as the proposed tasks are new, there are no established ways for performance evaluation. According to our setting, we desire our machine to generate audio waveforms with high quality and diversity, vocal-like timbre, plausible pitch contour, emotion expression, and, for the accompanied singer, that are in harmony with the given accompaniment track. But, the singing does not have to be intelligible. We propose customized objective and subjective metrics to evaluate our models in these aspects. For example, we adapt the melody harmonization model proposed by Lim et al. (2017) to measure the matchness between the generated vocal track and the given accompaniment track. Finally, reproducibility is a major issue, especially for a subjective task. We intend to use publiclyavailable copyright-free instrumental music as the conditional signals for testing the accompanied singer, so that other researchers can use the same testing conditions for model comparison in the future. We will also release the testing conditions for the solo singer, the generated singing voices for all our models, as well as open source our code through a public git repository [URL removed]. We focus on Jazz music in this work. Samples of the generated singing voices can be found at https://bit.ly/2mIvoIc. Our models have many possible use cases. For example, we can use the accompanied singer as a backing vocalist. In addition, we can use the free singer as a sound source-to demonstrate this, we make a song by hand in the style of Jazz Hiphop by sampling the output of our free singer. This song can be listened to at https://bit.ly/2QkUJoJ. In this paper, we have introduced a novel task of singing voice generation that does not use musical scores and lyrics. Specifically, we proposed three singing schemes with different input conditions: free singer, accompanied singer, and solo singer. We have also proposed a BEGAN based architecture that uses GRUs and grouped dilated convolutions to learn to generate singing voices in an adversarial way. For evaluating such models, we proposed several objective metrics and implemented a model to measure the compatibility between a given accompaniment track and the generated vocal track. The evaluation shows that the audio quality of the generated voices still leave much room for improvement, but in terms of humanness and emotion expression our models work fine. Score and lyrics-free singing voice generation is a new task, and this work represents only a first step tackling it. There are many interesting ideas to pursue. For example, we have chosen to extract pitch-related information only from the accompaniment track for the accompanied singer, but a more interesting way is to let the model learns to extract relevant information itself. In the near future, we plan to investigate advanced settings that allow for timbre and expression control, and experiment with other network architectures, such as coupling a fine-grained auto-regressive model with a multiscale generation procedure as done in MelNet (Vasquez & Lewis, 2019) , using a discriminator that examines different chunks of the generated audio as done in PatchGAN for the vision domain (Isola et al., 2017) , or using multiple discriminators that evaluate the generated audio based on multi-frequency random windows as done in GAN-TTS (Bińkowski et al., 2019) The generator in G3BEGAN is implemented with a stack of two G3 blocks. Please see Table 4 for details of the network architecture.
Our models generate singing voices without lyrics and scores. They take accompaniment as input and output singing voices.
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