ENABLING FACTORIZED PIANO MUSIC MODELING
Year: 2019

Abstract:
Generating musical audio directly with neural networks is notoriously difficult because it requires coherently modeling structure at many different timescales. Fortunately, most music is also highly structured and can be represented as discrete note events played on musical instruments. Herein, we show that by using notes as an intermediate representation, we can train a suite of models capable of transcribing, composing, and synthesizing audio waveforms with coherent musical structure on timescales spanning six orders of magnitude (∼0.1 ms to ∼100 s), a process we call Wave2Midi2Wave. This large advance in the state of the art is enabled by our release of the new MAESTRO (MIDI and Audio Edited for Synchronous TRacks and Organization) dataset, composed of over 172 hours of virtuosic piano performances captured with fine alignment (≈3 ms) between note labels and audio waveforms. The networks and the dataset together present a promising approach toward creating new expressive and interpretable neural models of music.

heading: 1 INTRODUCTION
text: Since the beginning of the recent wave of deep learning research, there have been many attempts to create generative models of expressive musical audio de novo. These models would ideally generate audio that is both musically and sonically realistic to the point of being indistinguishable to a listener from music composed and performed by humans.
However, modeling music has proven extremely difficult due to dependencies across the wide range of timescales that give rise to the characteristics of pitch and timbre (short-term) as well as those of rhythm (medium-term) and song structure (long-term). On the other hand, much of music has a large hierarchy of discrete structure embedded in its generative process: a composer creates songs, sections, and notes, and a performer realizes those notes with discrete events on their instrument, creating sound. The division between notes and sound is in many ways analogous to the division between symbolic language and utterances in speech.
The WaveNet model by van den Oord et al. (2016) may be the first breakthrough in generating musical audio directly with a neural network. Using an autoregressive architecture, the authors trained a model on audio from piano performances that could then generate new piano audio sample-bysample. However, as opposed to their highly convincing speech examples, which were conditioned on linguistic features, the authors lacked a conditioning signal for their piano model. The result was audio that sounded very realistic at very short time scales (1 or 2 seconds), but that veered off into chaos beyond that.
Dieleman et al. (2018) made great strides towards providing longer term structure to WaveNet synthesis by implicitly modeling the discrete musical structure described above. This was achieved by training a hierarchy of VQ-VAE models at multiple time-scales, ending with a WaveNet decoder to generate piano audio as waveforms. While the results are impressive in their ability to capture long-term structure directly from audio waveforms, the resulting sound suffers from various artifacts at the fine-scale not present in the unconditional WaveNet, clearly distinguishing it from real musical audio. Also, while the model learns a version of discrete structure from the audio, it is not
directly reflective of the underlying generative process and thus not interpretable or manipulable by a musician or user.
Manzelli et al. (2018) propose a model that uses a WaveNet to generate solo cello music conditioned on MIDI notation. This overcomes the inability to manipulate the generated sequence. However, their model requires a large training corpus of labeled audio because they do not train a transcription model, and it is limited to monophonic sequences.
In this work, we seek to explicitly factorize the problem informed by our prior understanding of the generative process of performer and instrument:
P (audio) = Enotes [ P (audio|notes) ] (1)
which can be thought of as a generative model with a discrete latent code of musical notes. Since the latent representation is discrete, and the scale of the problem is too large to jointly train, we split the model into three separately trained modules that are each state-of-the-art in their respective domains:
1. Encoder, P (notes|audio): An Onsets and Frames (Hawthorne et al., 2018) transcription model to produce a symbolic representation (MIDI) from raw audio.
2. Prior, P (notes): A self-attention-based music language model (Huang et al., 2018) to generate new performances in MIDI format based on those transcribed in (1).
3. Decoder, P (audio|notes): A WaveNet (van den Oord et al., 2016) synthesis model to generate audio of the performances conditioned on MIDI generated in (2).
We call this process Wave2Midi2Wave.
One hindrance to training such a stack of models is the lack of large-scale annotated datasets like those that exist for images. We overcome this barrier by curating and publicly releasing alongside this work a piano performance dataset containing well-aligned audio and symbolic performances an order of magnitude larger than the previous benchmarks.
In addition to the high quality of the samples our method produces (see https://goo.gl/ magenta/maestro-examples), training a suite of models according to the natural musician/instrument division has a number of other advantages. First, the intermediate representation
used is more suitable for human interpretation and manipulation. Similarly, factorizing the model in this way provides better modularity: it is easy to independently swap out different performance and instrument models. Using an explicit performance representation with modern language models also allows us to model structure at much larger time scales, up to a minute or so of music. Finally, we can take advantage of the large amount of prior work in the areas of symbolic music generation and conditional audio generation. And by using a state-of-the-art music transcription model, we can make use of the same wealth of unlabeled audio recordings previously only usable for training end-to-end models by transcribing unlabeled audio recordings and feeding them into the rest of our model.

heading: 2 CONTRIBUTIONS OF THIS PAPER
text: Our contributions are as follows:
1. We combine a transcription model, a language model, and a MIDI-conditioned WaveNet model to produce a factorized approach to musical audio modeling capable of generating about one minute of coherent piano music.
2. We provide a new dataset of piano performance recordings and aligned MIDI, an order of magnitude larger than previous datasets.
3. Using an existing transcription model architecture trained on our new dataset, we achieve state-of-the-art results on a piano transcription benchmark.

heading: 3 DATASET
text: We partnered with organizers of the International Piano-e-Competition1 for the raw data used in this dataset. During each installment of the competition, virtuoso pianists perform on Yamaha Disklaviers which, in addition to being concert-quality acoustic grand pianos, utilize an integrated high-precision MIDI capture and playback system. Recorded MIDI data is of sufficient fidelity to allow the audition stage of the competition to be judged remotely by listening to contestant performances reproduced over the wire on another Disklavier instrument.
The dataset introduced in this paper, which we name MAESTRO (“MIDI and Audio Edited for Synchronous TRacks and Organization”), contains over a week of paired audio and MIDI recordings from nine years of International Piano-e-Competition events.2 The MIDI data includes key strike velocities and sustain pedal positions. Audio and MIDI files are aligned with ≈3 ms accuracy and sliced to individual musical pieces, which are annotated with composer, title, and year of performance. Uncompressed audio is of CD quality or higher (44.1–48 kHz 16-bit PCM stereo). A train/validation/test split configuration is also proposed, so that the same composition, even if performed by multiple contestants, does not appear in multiple subsets. Repertoire is mostly classical, including composers from the 17th to early 20th century. Table 1 contains aggregate statistics of the MAESTRO dataset.
We make the new dataset (MIDI, audio, metadata, and train/validation/test split configuration) available at https://g.co/magenta/maestro-datasetunder a Creative Commons Attribution Non-Commercial Share-Alike 4.0 license.
1http://piano-e-competition.com 2All results in this paper are from the v1.0.0 release of the dataset.
Several datasets of paired piano audio and MIDI have been published previously and have enabled significant advances in automatic piano transcription and related topics. We are making MAESTRO available because we believe it provides several advantages over existing datasets. Most significantly, as evident from table 2, MAESTRO is around an order of magnitude larger. Existing datasets also have different properties than MAESTRO that affect model training:
MusicNet (Thickstun et al., 2017) contains recordings of human performances, but separatelysourced scores. As discussed in Hawthorne et al. (2018), the alignment between audio and score is not fully accurate. One advantage of MusicNet is that it contains instruments other than piano (not counted in table 2) and a wider variety of recording environments. MAPS (Emiya et al., 2010) contains Disklavier recordings and synthesized audio created from MIDI files that were originally entered via sequencer. As such, the “performances” are not as natural as the MAESTRO performances captured from live performances. In addition, synthesized audio makes up a large fraction of the MAPS dataset. MAPS also contains syntheses and recordings of individual notes and chords, not counted in table 2. Saarland Music Data (SMD) (Müller et al., 2011) is similar to MAESTRO in that it contains recordings and aligned MIDI of human performances on a Disklavier, but is 30 times smaller.

heading: 3.1 ALIGNMENT
text: Our goal in processing the data from International Piano-e-Competition was to produce pairs of audio and MIDI files time-aligned to represent the same musical events. The data we received from the organizers was a combination of MIDI files recorded by Disklaviers themselves and WAV audio captured with conventional recording equipment. However, because the recording streams were independent, they differed widely in start times and durations, and they were also subject to jitter. Due to the large volume of content, we developed an automated process for aligning, slicing, and time-warping provided audio and MIDI to ensure a precise match between the two.
Our approach is based on globally minimizing the distance between CQT frames from the real audio and synthesized MIDI (using FluidSynth3). Obtaining a highly accurate alignment is non-trivial, and we provide full details in the appendix.

heading: 3.2 DATASET SPLITTING
text: For all experiments in this paper, we use a single train/validation/test split designed to satisfy the following criteria:
• No composition should appear in more than one split. • Train/validation/test should make up roughly 80/10/10 percent of the dataset (in time),
respectively. These proportions should be true globally and also within each composer. Maintaining these proportions is not always possible because some composers have too few compositions in the dataset.
• The validation and test splits should contain a variety of compositions. Extremely popular compositions performed by many performers should be placed in the training split.
For comparison with our results, we recommend using the splits which we have provided. We do not necessarily expect these splits to be suitable for all purposes; future researchers are free to use alternate experimental methodologies.
3http://www.fluidsynth.org/

heading: 4 PIANO TRANSCRIPTION
text: The large MAESTRO dataset enables training an automatic piano music transcription model that achieves a new state of the art. We base our model on Onsets and Frames, with several modifications informed by a coarse hyperparameter search using the validation split. For full details of the base model architecture and training procedure, refer to Hawthorne et al. (2018).
One important modification was adding an offset detection head, inspired by Kelz et al. (2018). The offset head feeds into the frame detector but is not directly used during decoding. The offset labels are defined to be the 32ms following the end of each note.
We also increased the size of the bidirectional LSTM layers from 128 to 256 units, changed the number of filters in the convolutional layers from 32/32/64 to 48/48/96, and increased the units in the fully connected layer from 512 to 768. We also stopped gradient propagation into the onset subnetwork from the frame network, disabled weighted frame loss, and switched to HTK frequency spacing (Young et al., 2006) for the mel-frequency spectrogram input. In general, we found that the best ways to get higher performance with the larger dataset were to make the model larger and simpler.
The final important change we made was to start using audio augmentation during training using an approach similar to the one described in McFee et al. (2017). During training, every input sample was modified using random parameters for the SoX 4 audio tool using pysox (Bittner et al., 2016). The parameters, ranges, and random sampling methods are described in table 3. We found that this was particularly important when evaluating on the MAPS dataset, likely because the audio augmentation made the model more robust to differences in recording environment and piano qualities. The differences in training results are summarized in table 6. When evaluating against the MAESTRO dataset, we found that audio augmentation made results slightly worse, so results in table 5 are presented without audio augmentation.
After training on the MAESTRO training split for 670k steps, we achieved state of the art results described in table 4 for the MAPS dataset. We also present our results on the train, validation, and test splits of the MAESTRO dataset as a new baseline score in table 5. Note that for calculating the scores of the train split, we use the full duration of the files without splitting them into 20-second chunks as is done during training.
In sections 5 and 6, we demonstrate how using this transcription model enables training language and synthesis models on a large set of unlabeled piano data. To do this, we transcribe the audio in the MAESTRO training set, although in theory any large set of unlabeled piano music would work. We
4http://sox.sourceforge.net/
call this new, transcribed version of the training set MAESTRO-T. While it is true that the audio transcribed for MAESTRO-T was also used to train the transcription model, table 5 shows that the model performance is not significantly different between the training split and the validation or test splits, and we needed the larger split to enable training the other models.

heading: 5 MUSIC TRANSFORMER TRAINING
text: For our generative language model, we use the decoder portion of a Transformer (Vaswani et al., 2017) with relative self-attention, which has previously shown compelling results in generating music with longer-term coherence (Huang et al., 2018). We trained two models, one on MIDI data from the MAESTRO dataset and another on MIDI transcriptions inferred by Onsets and Frames from audio in MAESTRO, referred to as MAESTRO-T in section 4. For full details of the model architecture and training procedure, refer to Huang et al. (2018).
We used the same training procedure for both datasets. We trained on random crops of 2048 events and employed transposition and time compression/stretching data augmentation. The transpositions were uniformly sampled in the range of a minor third below and above the original piece. The time stretches were at discrete amounts and uniformly sampled from the set {0.95, 0.975, 1.0, 1.025, 1.05}. We evaluated both of the models on their respective validation splits.
Samples outputs from the Music Transformer model can be heard in the Online Supplement (https://goo.gl/magenta/maestro-examples).

heading: 6 PIANO SYNTHESIS
text: Most commercially available systems that are able to synthesize a MIDI sequence into a piano audio signal are concatenative: they stitch together snippets of audio from a large library of recordings of individual notes. While this stitching process can be quite ingenious, it does not optimally capture the various interactions between notes, whether they are played simultaneously or in sequence. An alternative but less popular strategy is to simulate a physical model of the instrument. Constructing an accurate model constitutes a considerable engineering effort and is a field of research by itself (Bank et al., 2010; Valimaki et al., 2012).
WaveNet (van den Oord et al., 2016) is able to synthesize realistic instrument sounds directly in the waveform domain, but it is not as adept at capturing musical structure at timescales of seconds or longer. However, if we provide a MIDI sequence to a WaveNet model as conditioning information, we eliminate the need for capturing large scale structure, and the model can focus on local structure instead, i.e., instrument timbre and local interactions between notes. Conditional WaveNets are also used for text-to-speech (TTS), and have been shown to excel at generating realistic speech signals conditioned on linguistic features extracted from textual data. This indicates that the same setup could work well for music audio synthesis from MIDI sequences.
Our WaveNet model uses a similar autoregressive architecture to van den Oord et al. (2016), but with a larger receptive field: 6 (instead of 3) sequential stacks with 10 residual block layers each. We found that a deeper context stack, namely 2 stacks with 6 layers each arranged in a series, worked better for this task. We also updated the model to produce 16-bit output using a mixture of logistics as described in van den Oord et al. (2018).
The input to the context stack is an onset “piano roll” representation, a size-88 vector signaling the onset of any keys on the keyboard, with 4ms bins (250Hz). Each element of the vector is a float that represents the strike velocity of a piano key in the 4ms frame, scaled to the range [0, 1]. When there is no onset for a key at a given time, the value is 0.
We initially trained three models:
Unconditioned Trained only with the audio from the combined MAESTRO training/validation splits with no conditioning signal. Ground Trained with the ground truth audio/MIDI pairs from the combined MAESTRO training/validation splits. Transcribed Trained with ground truth audio and MIDI inferred from the audio using the Onsets and Frames method, referred to as MAESTRO-T in section 4.
The resulting losses after 1M training steps were 3.72, 3.70 and 3.84, respectively. Due to teacher forcing, these numbers do not reflect the quality of conditioning, so we rely on human judgment for evaluation, which we address in the following section.
It is interesting to note that the WaveNet model recreates non-piano subtleties of the recording, including the response of the room, breathing of the player, and shuffling of listeners in their seats. These results are encouraging and indicate that such methods could also capture the sound of more dynamic instruments (such as string and wind instruments) for which convincing synthesis/sampling methods lag behind piano.
Due to the heterogeneity of the ground truth audio quality in terms of microphone placement, ambient noise, etc., we sometime notice “timbral shifts” during longer outputs from these models. We therefore additionally trained a model conditioned on a one-hot year vector at each timestep (similar to speaker conditioning in TTS), which succeeds in producing consistent timbres and ambient qualities during long outputs (see Online Supplement).
A side effect of arbitrary windowing of the training data across note boundaries is a sonic crash that often occurs at the beginning of generated outputs. To sidestep this issue, we simply trim the first 2 seconds of all model outputs reported in this paper, and in the Online Supplement (https: //goo.gl/magenta/maestro-examples).

heading: 7 LISTENING TESTS
text: Since our ultimate goal is to create realistic musical audio, we carried out a listening study to determine the perceived quality of our method. To separately assess the effects of transcription, language modeling, and synthesis on the listeners’ responses, we presented users with two 20-second clips5 drawn from the following sets, each relying on an additional model from our factorization:
Ground Truth Recordings Clips randomly selected from the MAESTRO validation audio split. 5While it would be beneficial to do a listening study on longer samples, running a listening study on those samples at scale was not feasible.
WaveNet Unconditioned Clips generated by the Unconditioned WaveNet model described in section 6. WaveNet Ground/Test Clips generated by the Ground WaveNet model described in section 6, conditioned on random 20-second MIDI subsequences from the MAESTRO test split. WaveNet Transcribed/Test Clips generated by the Transcribed WaveNet model described in section 6, conditioned on random 20-second subsequences from the MAESTRO test split. WaveNet Transcribed/Transformer Clips generated by the Transcribed WaveNet model described in section 6, conditioned on random 20-second subsequences from the Music Transformer model described in section 5 that was trained on MAESTRO-T.
The final set of samples demonstrates the full end-to-end ability of taking unlabeled piano performances, inferring MIDI labels via transcription, generating new performances with a language model trained on the inferred MIDI, and rendering new audio as though it were played on a similar piano—all without any information other than raw audio recordings of piano performances.
Participants were asked which clip they thought sounded more like a recording of somebody playing a musical piece on a real piano, on a Likert scale. 640 ratings were collected, with each source involved in 128 pair-wise comparisons. Figure 2 shows the number of comparisons in which performances from each source were selected as more realistic.
A Kruskal-Wallis H test of the ratings showed that there is at least one statistically significant difference between the models: χ2(2) = 67.63, p < 0.001. A post-hoc analysis using the Wilcoxon signed-rank test with Bonferroni correction showed that there was not a statistically significant difference in participant ratings between real recordings and samples from the WaveNet Ground/Test and WaveNet Transcribed/Test models with p > 0.01/10.
Audio of some of the examples used in the listening tests is available in the Online Supplement (https://goo.gl/magenta/maestro-examples).

heading: 8 CONCLUSION
text: We have demonstrated the Wave2Midi2Wave system of models for factorized piano music modeling, all enabled by the new MAESTRO dataset. In this paper we have demonstrated all capabilities on the same dataset, but thanks to the new state-of-the-art piano transcription capabilities, any large set of piano recordings could be used,6 which we plan to do in future work. After transcribing the recordings, the transcriptions could be used to train a WaveNet and a Music Transformer model, and then new compositions could be generated with the Transformer and rendered with the WaveNet. These new compositions would have similar musical characteristics to the music in the original dataset, and the audio renderings would have similar acoustical characteristics to the source piano.
The most promising future work would be to extend this approach to other instruments or even multiple simultaneous instruments. Finding a suitable training dataset and achieving sufficient transcription performance will likely be the limiting factors.
6The performance of the transcription model on the separate MAPS dataset in table 4 shows that the model effectively generalizes beyond just the MAESTRO recordings.
The new dataset (MIDI, audio, metadata, and train/validation/test split configurations) is available at https://g.co/magenta/maestro-datasetunder a Creative Commons Attribution NonCommercial Share-Alike 4.0 license. The Online Supplement, including audio examples, is available at https://goo.gl/magenta/maestro-examples.

heading: ACKNOWLEDGMENTS
text: We would like to thank Michael E. Jones and Stella Sick for their help in coordinating the release of the source data and Colin Raffel for his careful review and comments on this paper.

Review summaries:
The paper addresses the challenge of using neural networks to generate original and expressive piano music.  The available techniques today for audio or music generation are not able to sufficient handle the many levels at which music needs to modeled.  The result is that while individual music sounds (or notes) can be generated at one level using tools like WaveNet, they don't come together to create a coherent work of music at the higher level.  The paper proposes to address this problem by imposing a MIDI representation (piano roll) in the neural modeling of music audio that serves as an intermediate (and interpretable) representation between the analysis (music audio -> MIDI) and synthesis (MIDI -> music audio) in the pipeline of piano music generation.  In order to develop and validate the proposed learning architecture, the authors have created a large data set of aligned piano music (raw audio along with MIDI representation).  Using this data set for training, validation and test, the paper reports on listening tests that showed slightly less favorable results for the generated music.  A few questions and comments are as follows.  MIDI itself is a rich language with ability to drive the generation of music using rich sets of customizable sound fonts.  Given this, it is not clear that it is necessary to reproduce this function using neural network generation of sounds.  The further limitation of the proposed approach seems to be the challenge of decoding raw music audio with chords, multiple overlayed notes or multiple tracks.  MIDI as a representation can support multiple tracks, so it is not necessarily the bottleneck.  How much does the data augmentation (audio augmentation) help?