MELONS: generating melody WITH LONG-TERM STRUCTURE USING transformers and structure graph

We employ the relations between pairwise bars to represent the musical structure. We take four beats as one bar and each beat equals to a quarter note. Based on the knowledge of musical composition theory, we classify the bar-level relations into three categories: repetition, development [18] and cadence [19]. After statistical analysis on more than 2500 pieces of pop music, we further decompose these three categories into eight frequently appeared types of structural relations, which are defined in Table 1. Fig. 1 shows an example of the relations in music score.

These relations have covered most common skills of pop music composition. They not only include complicated development methods, but can also reflect the progress of emotions (surround progression) and express the harmonious ending or breath of phrases (harmonious cadence). Moreover, these relations can be expressed by mathematical formulas¹¹1For more details, please refer to https://yiathena.github.io/MELONS/, which facilitates their auto detection.

We use a directed graph with multiple types of edges, which we call a structure graph, to describe the melody structure of a song. Bars and the relations between bars are represented as nodes and edges respectively, while types of the edges stand for types of the relations. As is shown in Table 1, the priority of relations is determined by the similarity between two bars. To avoid redundancies in the structure graph, each bar is matched with its previous bars from near to far to find out the relation of the highest priority. Fig. 2 illustrates the structure graph of the melody provided in Fig. 1.

The training and generation procedures of MELONS are shown in Fig. 3. We use the structure graph to bridge the gap between local pairwise relations and global music structure, and propose a multi-step melody generation framework to compose a full-song melody based on an 8-bar motif (which is the common length of a phrase).

Structure generation. We extract structure graphs from the original songs to construct the dataset for structure generation. Inspired by GraphRNN [20], we model the structure graph as a sequence of relations, and generate the relations of a song using an auto-regressive transformer model. We use a token triple like $(i,j,t)$ to represent the edge(relation) from a previous bar $j$ to the current bar $i$ with a relation type $t$. By arranging all edges of a structure graph in ascending order of the index of the current bar, we get a list of token triples like $\{(i_{1},j_{1},t_{1}),(i_{2},j_{2},t_{2}),\cdots,(i_{n},j_{n}.t_{n})\}$, which is a sequence form of the structure graph. We adopt the tokenize method proposed in [21] and predict the three tokens of an edge at one time step. As MELONS deals with full-song melody generation, we append an EOS relation at the end of each structure graph to mark the end of the song. At the inference time, edges in the structure graph would be generated autoregressively until the EOS is predicted, so the generated structure is not limited to a fixed length. Moreover, the subsequent relations are predicted conditioned on the music structure generated so far, leading to better cohesiveness.

Melody generation. The melody generation part consists of an unconditional music generation module and a conditional generation module. We adopt the event-based music token representation applied broadly for music generation [10, 22, 21, 2] in both two modules. The unconditional module is an auto-regressive Transformer model [21] trained on the original melodies. The conditional generation module adopts a similar architecture, but training data is reorganized to build a conditional scenario, like CTRL [23] for conditional text generation and MuseNet [24] for music. For each relation $(i,j,t)$ in a structure graph, we treat the melody of the $i^{th}$ bar as the target and train the model to generate the $i^{th}$ bar conditional on the related $j^{th}$ bar and the relation type $t$. The final sequence has the form of {[start of the melody context], (content of the melody context),[start of the related bar], (content of the related bar), [relation type], [start of the target bar], (content of the target bar)}. The melody context here is formed by the 8 bars prior to the $i^{th}$ bar. Tokens before the [start of the target bar] token would be given at the inference time. The three modules mentioned above are combined together in the generation procedure. The detailed generation algorithm is illustrated in Algorithm 1.

The datasets used in this work contain POP909 [25] and Wikifonia²²2http://www.wikifonia.org. They are public datasets of pop Chinese and Western songs, respectively. We keep melodies in 4/4 time signature as our training data and select 901 musical scores from POP909 and 1600 scores from Wikifonia with different pop music styles. We use a 9:1 method to allocate the training and testing set.

In MELONS, we choose the linear Transformer [26] as the backbone architecture for sequence modeling, considering its linear complexity in attention calculation. The structure generation module consists of 4 self-attention layers with 4 heads and 256 hidden states. The inner layer size of the feed-forward part is set to 1024. The melody generation modules consist of 6 self-attention layers with 8 heads and 512 hidden states, with the inner layer size set to 2048. We adopt the compound word (CP) method [21] for sequence representation and tokenization. The structure generation module employs a token set including three types of tokens: index of the current bar, index of the related bar and relation type, and the embedding size is 128, 128 and 32 respectively. The unconditional melody generation module uses a token set $(type,beat,tempo,pitch,duration)$ to serialize melodies, with embedding size as $(16,128,64,256,128)$. We additionally use $track(size=16)$ to mark the different sections in the conditional generation module, and use $relationtype(size=32)$ to impose the control. The embedding sizes are chosen based on the vocabulary sizes of different token types, and the embedded tokens describing the same object would be concatenated together and linearly projected to the same size of the corresponding module’s hidden state. We use the Adam optimizer [27] with a learning rate of $10^{-4}$ for all these models. We apply dropout with a rate of 0.1 during training.

In order to verify the versatility of the relationship we define in Table 1, we additionally collect 1160 pop music in different styles and regions from the Internet, and also collect thousands of melodies generated by the MELONS. We automatically extract all relations of each dataset. Then we perform statistical analysis on relations in each dataset. The proportion is defined as the ratio of the number of bars with a certain relation to the total number of bars. Table 2 shows the statistical results of the proportions. We can see that the distribution of the relations across the four dataset are roughly close (correlation coefficients $>0.98$ for all pairs). This demonstrates the universality and stability of our proposed structure representations.

We also want to see whether our melody generation network can produce target bars with correct relations under specified conditions. After comparing the structure graphs extracted from the generated melodies with the graphs used as conditions, we get the ratio of correctly generated bars of each relation. Among all the relations, rhythmic sequence owns the highest accuracy$(92.88\%)$ while transposition shows the lowest performance$(77.33\%)$.

We compare the performance of MELONS with another two systems including CP-Transformer (SOTA method for unconditional music generation without control on structure) and PopMNet with different configurations. The structure graph used as the condition for the melody generation network can either be extracted from the real music (marked as R) or generated by the structure generation net (no mark). The relations in the structure graph can be either a simple repetition and rhythm sequence as PopMNet suggested (marked as B) or the more sophisticated relation set as described in  2.1 (no mark). We also include human created melodies for reference.

For the listening test, we randomly select 10 motifs from the testing set and generate sets of melodies corresponding to the above experimental systems³³3Audio samples of generated melodies are available at https://yiathena.github.io/MELONS/. We invite 12 listeners who are professionals in music to evaluate 80 samples. The subjects are asked to rate the melodies on a five-point scale varying from very bad to excellent on the following four metrics: 1) Structure: Does the melody have clear structure? 2) Richness: Does the melody have rich content? 3) Pleasure: Does the melody sound melodious? 4) Overall: What is the overall quality of the melody?

Table 3 shows the average mean opinion scores on the four evaluation metrics. The distributions of the results of the four metrics are relatively similar, which to a certain extent illustrates the significance of musical structure in the overall evaluation of music. Hence, we only show the box plots on the overall metric in Fig. 4. T-tests with Holm-Bonferroni correction ($\alpha=0.05$) were also conducted for all evaluation metrics.

The results demonstrate the effectiveness of our proposed approach. MELONS and MELONS-R outperform the other systems on all metrics by a large margin ($p<1e-6$ for all evaluation metrics). Among all the systems, CP-transformer archives the lowest evaluation. This indicates that, remarkably, melody generation can benefit from structural information. Furthermore, the performance of MELONS systems which use the sophisticated structure graph is obviously better than those using the basic structure graph proposed by PopMNet, which shows the superiority of our proposed structure representation. We also see that MELONS-B related systems are better than the PopMNet related systems, indicating that MELONS could generate better melodies when using the same structural information as prior knowledge. There is still an obvious gap between generated melodies and human created music, leaving large room for improvement. We notice that differences between models using the generated structure graph and those using the real structure graph are not significant. This suggests that music structure generated by MELONS has close quality compared to artificially designed music forms. Thus our future work will focus more on improving the melody generation model.