3.1. Music Generation Framework Based on MuseGAN-GP

Automatic music generation technology has irreplaceable value in promoting artistic innovation and expanding the boundaries of human expression. MuseGAN can efficiently model complex polyphonic structures while maintaining the temporal coordination of voice parts, demonstrating unique advantages in the field of multitrack music generation. Therefore, based on MuseGAN, a music generation framework was constructed. Its structure is shown in Fig. 1.

As shown in Fig. 1, the MuseGAN framework employs a three-stage process: “bar-based latent space encoding, sequential structure generation, and multiscale adversarial discrimination.” The latent variables received by the generator include the global latent code \(z\) (serving as the foundation for diversity), temporal-step latent code \(z_t\), instrument track latent code \(z_i\), and fine-grained latent code \(z_{i,t}\). These are encoded by the bar encoder \(E\), which comprises a multilayer perceptron (MLP), into bar-level latent vectors for each measure. Subsequently, the temporal generator \(G_{\textit{temp}}\) uses these latent vectors to generate a complete multitrack PR \(x\) ¹⁸. Here, \(G_{\textit{bar},j}\) denotes the bar-level generation submodule corresponding to the \(j\)-th instrument. Finally, the multiscale discriminator performs “Real/Fake” classification between the generated and real samples to complete adversarial training. Prior to this, data preprocessing was performed, as shown in Fig. 2.

As shown in Fig. 2, the original multitrack musical instrument digital interface (MIDI) music was first segmented into independent measures based on tempo information. Each measure was quantized into a fixed time step (e.g., 48 steps) and encoded as a three-dimensional binary PR matrix \(\boldsymbol{P}_{\mathit{real}}\in \{0,1\}^{T\times N\times K}\), where \(T\) represents the time step, \(N=128\) denotes the pitch dimension, and \(K\) indicates the number of instrument tracks. After flattening this matrix into a one-dimensional vector, it constituted the true sample distribution input for the discriminator. This preprocessing step transforms the structured musical notations into numerical tensors processable by the model, which then participates in adversarial training alongside samples generated by the generator from the latent code \(\{z, z_{t}, z_{i}, z_{i,t}\}\). The input music sequence was encoded using a barcode structure, mapping each measure to a latent vector, as expressed in Eq. 1.

Here, \(\bar{x}^{(t)}\in \mathbb{R}^d\) is the latent vector representation corresponding to the \(t\)-th section (\(t=1,2,\dots,T\)), and \(T\) is the total number of sections contained in the music clip. Moreover, \(E\) is a bar-coding network composed of an MLP, and \(z\) is a random noise or conditional input used as the basis for generating diverse music ¹⁹. Based on the encoded bar latent vectors, a cross-sectional temporal dependency relationship was constructed to generate a complete PR, as expressed in Eq. 2.

Here, \(\boldsymbol{Y} \in [0, 1]^{T \times P \times V}\) is the generated three-dimensional PR matrix (time \(\times\) pitch \(\times\) instrument track). Among them, \(P\) is the number of pitch dimensions, usually 128 MIDI pitches, \(V\) is the number of independent instrument voices, and \(G_{\mathit{temp}}\) is a time-series generation operation. Adversarial training mechanisms were introduced to enhance the authenticity and detailed quality of the generated music, with input samples including real data (\(\boldsymbol{Y}_{\mathit{real}}\), from a multitrack music dataset) and generated data (\(\boldsymbol{Y}_{\mathit{fake}} = G(z)\), output by the generator). The training objective is a minimax game, as expressed in Eq. 3 ²⁰.

In summary, MuseGAN’s three-stage generation process constitutes a hierarchical mapping from latent space to multi-track symbolic sequences. The bar encoder \(E\) maps the conditional input \(z\) (Eq. 1) into a sequence of bar latent vectors. The temporal generator \(G_{\mathit{temp}}\) generates a three-dimensional PR matrix \(\boldsymbol{Y}\) (Eq. 2) based on this sequence to model cross-bar temporal dependencies. The multi-scale discriminator forces the generator to approximate the true music distribution from local to global levels through adversarial evaluation at multiple temporal resolutions (Eq. 3), thereby achieving structurally coherent multi-track synthesis. However, MuseGAN has shortcomings in modeling multitrack coordination, and training is prone to gradient anomalies, leading to voice imbalance. GP can effectively constrain the gradient norm of the discriminator, thereby significantly improving the stability of adversarial training ²¹. Therefore, this study introduced GP to optimize the discriminator of MuseGAN; its principles are shown in Fig. 3.

As shown in Fig. 3, this strategy forces the discriminator to satisfy the local Lipschitz continuity conditions by applying gradient constraints in the real data neighborhood, thereby avoiding gradient explosion or disappearance ²². The perturbation data sampling operation is \(\hat{Y} = Y + \delta\), where \(Y\) is the real multitrack PR sample (PR format), \(\delta\) is a random disturbance (\(\delta \sim \mathscr{N}(0,\mathit{cI})\)) that follows a Gaussian distribution, and \(c\) is the disturbance strength hyperparameter (based on the empirical values \(c = 0. 1\)) ²³. This study employed GPs based on Gaussian noise-induced local perturbations rather than linear interpolation between samples. This approach stems from the continuous and structured manifold properties of music data in feature space. Gaussian noise enables the construction of smoother constraint points within the local neighborhood of genuine samples and better aligns with the data distribution. This strategy provides a more stable regularization path for the Lipschitz constraints and is better suited to the geometric characteristics of multitrack music data. This avoids instability issues in the gradient estimation that may arise from linear interpolation traversing regions with low probability density. Subsequently, the GP term was calculated using Eq. 4.

Here, \(\nabla_{\hat{Y}}D(\hat{Y})\) is the gradient of the discriminator output to the perturbation input, \(\Vert\cdot\Vert_2\) represents the L2 norm of the gradient vector, and \(\lambda\) is the penalty coefficient (based on the empirical values \(\lambda = 1.0\)) ²⁴. The GP employed in this study is a relaxed variant of the original WGAN-GP objective (in which the gradient norm approaches 1). Theoretically, this formulation penalizes the square of the gradient norm, causing it to converge to 0. This optimizes a discriminator with a smaller Lipschitz constant and a smoother function. In practice, compared to the strict 1-Lipschitz constraint of the original form, this relaxed form (approaching 0) provides a more stable Lipschitz boundary by suppressing gradient magnitudes, making it better suited for the complex local distribution characteristics of polyphonic music. Next, this study reconstructed the discriminator loss function while keeping the generator loss unchanged, as expressed in Eq. 5.

Here, \(\mathscr{L}_{D}^{\mathit{GP}}\) represents the reconstructed discriminator loss, and \(\mathscr{L}_G\) denotes the generator loss. By constraining the gradient changes in the discriminator near the real data manifold, the voice coordination and training stability of the multi-track music generation model can be improved. GP stabilizes the dynamics of adversarial training by constraining the Lipschitz constant of the discriminator near the true data manifold. Complex joint dependencies exist among the vocal part distributions in multitrack music, where traditional adversarial training often suffers from gradient conflicts. GP enforces bounded and smooth gradients for the discriminator, coordinating gradient estimates across all vocal part distributions. This introduces a smooth and consistent optimization landscape for the adversarial learning of multitrack joint distributions, effectively suppressing vocal-part imbalances. The music generation framework based on MuseGAN-GP is illustrated in Fig. 4.

As shown in Fig. 4, MuseGAN-GP strengthens the discriminator optimization path based on the original framework and adds a GP calculation module. This framework retains the multitrack generation capabilities of the bar encoder and timing generator. The discriminator simultaneously receives real, generated, and perturbed samples, calculates penalty terms through the gradient constraint module, and integrates them into the discrimination loss, significantly improving the training stability and voice coordination.

3.2. Cross-Modal Quality Optimization Based on VGGish and WD and Establishment of MAG-GPWD Method

The MuseGAN-GP established through research optimizes multitrack symbol generation through GP, achieving improved voice coordination and training stability. However, MuseGAN-GP lacks an audio perceptual quality constraint mechanism to optimize the authenticity of the timbre and the dynamic reverberation effects. VGGish extracts the perceptual features of the Mel frequency spectrum through a DCNN, effectively characterizing auditory attributes such as timbre and harmony ²⁵. Therefore, this study constructed an audio feature extraction module based on VGGish, the structure of which is shown in Fig. 5.

The network consisted of four convolutional blocks and two fully connected layers. The input was a \(96\times 64\) Mel frequency spectrum, and the output was a 128-dimensional deep feature vector ²⁶. It performed convolutional feature extraction through \(F^{(l)} = \mathrm{ReLU}(W_{c}^{(l)} \ast X^{(l-1)} + b_{c}^{(l)})\), where \(l\) is the convolutional layer number (1–4); \(X^{(0)}\) is the input Mel spectrogram (size 96 frames \(\times\) 64 frequency bands); \(\{W_{c}^{(l)}, b_{c}^{(l)}\}\) is the convolution kernel weight and bias parameter of the \(l\)-th layer; and \(\ast\) stands for the two-dimensional convolution operation. Spatial pooling compression was then performed, as expressed in Eq. 6.

Here, \(k\) is the position of the pooling layer (after each convolutional block); \(\Omega\) represents a \(2 \times 2\) local receptive field; and \(\max(\cdot)\) denotes the maximum pooling operation, which was used to reduce spatial dimensions and enhance feature robustness. Thus, the fully connected embedding was completed, as expressed in Eq. 7.

Here, \(\mathit{vec}(\cdot)\) represents the flattening of the feature map into a one-dimensional vector, and \(\{\boldsymbol{W}_{\mathit{fc}1}, \boldsymbol{W}_{\mathit{fc}2}\}\) is the fully connected layer weight matrix (\({4096 \times N}\) dimensions). Finally, the feature vector is output as \(\phi = \sigma(W_{\mathit{emb}} \cdot h_{2} + b_{\mathit{emb}})\), where \(\phi \in \mathbb{R}^{128}\) ultimately outputs a 128-dimensional audio embedding vector, and \(\sigma(\cdot)\) is the Sigmoid activation function used for normalizing feature representations ²⁷.

However, the VGGish feature space lacks distribution-alignment ability and cannot effectively quantify the distance between the generated audio and the true distribution. The WD provides a continuous and differentiable measure of distribution differences that can accurately characterize geometric structural relationships in the feature space ²⁸. Therefore, this study introduced WD into VGGish to optimize the alignment of audio feature distributions, as shown in Fig. 6.

As shown in Fig. 6, this distance establishes a quantitative bridge for cross-modal distribution matching by calculating the optimal transmission cost of the feature vector statistics ²⁹. The study sampled the feature distribution, and the feature distribution \(D_{\mathit{real}}\) of the real audio samples is expressed in Eq. 8.

Here, \(Y_{\mathit{audio}}\) is the real audio sample, and \(N\) is the number of batch samples of the feature distribution of real audio samples. The audio sample feature distribution \(D_{\mathit{fake}}\) was generated, as expressed in Eq. 9.

Here, \(\mathscr{S}\) is a MIDI synthesizer, and \(M\) is the number of batch samples used to generate the distribution of audio sample features. Subsequently, statistical calculations were performed, including mean vector and covariance matrix calculations, as expressed in Eq. 10 ³⁰.

Here, \(\mu \in \mathbb{R}^{128}\) is the feature mean vector, and \(\Sigma \in \mathbb{R}^{128 \times 128}\) is the characteristic covariance matrix. In addition, the second-order WD can be approximated using Eq. 11.

Here, \(\mathscr{W}_2\) is a second-order WD, and \({\mathrm{Tr}}(\cdot)\) represents the trace operation of the matrix. Based on the WD calculated above, the loss function can be defined as \(L_{\mathit{WD}} = \mathscr{W}_{2}^{2}(D_{\mathit{real}}, D_{\mathit{fake}})\). This loss function has the characteristics of differentiability and continuity and is suitable for gradient backpropagation processes ³¹. Compared to the Jensen–Shannon (JS) divergence, WD’s core theoretical advantage of WDs stems from their geometric essence based on optimal transport. Even when the support sets of the symbol and audio feature distributions do not intersect, WD provides an effective continuous metric, whereas JS divergence fails because of vanishing gradients. For cross-modal matching, the WD characterizes the geometric differences between distributions by minimizing the transport cost. Its second-moment form (Eq. 11) aligns covariance structures, while matching means, enabling more structured distribution matching that captures holistic correlations across modalities. By applying WD constraints, the VGGish feature distribution of the generated audio can be accurately aligned with the statistical characteristics of real audio libraries, thereby overcoming the local optimal problem in traditional similarity measurement methods and achieving more efficient feature alignment and cross-modal learning. In summary, this study combined WD-constrained VGGish with the MuseGAN-GP music generation framework to establish the MAG-GPWD method, the structure of which is shown in Fig. 7.

As shown in Fig. 7, the MAG-GPWD works in conjunction with symbol generation and audio optimization modules. The symbol generation module adopts the MuseGAN-GP framework to ensure the coordination of voice parts in multitrack music through GP. The audio optimization module converts the generated symbols into audio, extracts features using VGGish, and aligns the feature distribution with a real audio library using the WD constraint. The two modules achieve end-to-end optimization through a joint loss function while improving structural rationality and auditory authenticity.

4.1. Robust Testing of Music Generation

In the simulation test, the corresponding experimental environment was established based on the application scenario of the music generation model, which was divided into hardware and software environments. The specific environmental configurations are listed in Table 1.

The study used PyTorch 2.2 to build a multi-track symbol GAN and Wasserstein distribution alignment module, realizing the MAG-GPWD model architecture and integrating the GeomLoss library to optimize the cross-modal feature alignment process. It supports multitrack piano roller blind symbol input and high-fidelity audio perception optimization. The parameter settings are consistent with those reported in previous research. During training, both the generator and discriminator of MuseGAN employed the Adam optimizer with a unified learning rate of \(2\times 10^{-4}\). The first-order moment estimation decay coefficient \(\beta_1\) was set to 0.5, whereas the second-order moment estimation decay coefficient \(\beta_2\) was set to 0.999. The model underwent 500 training epochs with a batch size of 64 to balance training stability and computational efficiency. The study used the MAESTRO Dataset v3.0 as the training and validation sets (divided into \(8{\,}{:}{\,}1\) layers by a performer). This dataset contains 1286 precise MIDI-audio synchronization samples of professional piano performances, covering seven genres including Baroque, Classical, and Romanticism. It included 417 high-difficulty polyphonic segments as a structural complexity test set and a benchmark evaluation subset, MAESTRO-Expressive (including 198 performance samples with touch-key force/sustain pedal dynamic fine annotation) ³². The study extracted bar start and end time markers from MIDI files in the MAESTRO v3.0 dataset, segmenting the music stream into bar-based segments. Each bar was uniformly quantized into 48 time steps (corresponding to the 48th-note resolution) and mapped to a \(48\times 128\times K\) binary PR tensor, where \(K\) was determined by the actual number of instrument tracks in the segment. For example, a single bar from a quartet segment in the dataset becomes a 3D tensor with four channels (\(K=4\)), where the values are set to 1 at the corresponding time step and pitch position and 0 elsewhere. The tensors from all the bars were flattened to form the training set, which was used to constrain the discriminator and engage in adversarial learning with samples driven by the latent codes generated by the generator.

This study compared the methods proposed in references ^12,13 and ^16,17 with MAG-GPWD (GPWD), including recurrent-feature enhanced MuseGAN (RFMG), GP-driven hybrid learning encoder (GHLE), VGGish-based hybrid music evaluation framework (VHEF), and WD-optimized multi-voice GAN (WOMG). These are cutting-edge approaches reported during 2022–2025, covering core areas such as symbol temporal enhancement, voice coordination optimization, cross-modal perception alignment, and distribution-driven generation, and can effectively measure the comprehensive performance of research models. To ensure fairness in the comparative experiments, all benchmark models were trained on a unified hardware platform and a deep learning framework. Comparable hyperparameters such as training iterations, batch size, optimizer type, and learning rate were strictly aligned with the model under study. For the model-specific structural parameters (e.g., hidden layer dimensions), the recommended configurations from previous studies were adopted, with training conducted under identical computational resources to guarantee the validity of the performance comparisons. This study validated the voice coordination of the method by comparing the track conflict ratio (TCR) and gradient norm variance (GNV), as shown in Fig. 8.

As shown in Fig. 8(a), the mean TCR of the GPWD model is 0.60%, which is significantly better than that of RFMG (1.66%), GHLE (1.20%), VHEF (1.93%), and WOMG (1.31%; \(p<0.001\)). This is because the GP mechanism constrains the discriminator gradient norm to eliminate voice imbalances in multitrack generation. Although the minimum value of GHLE (fusion GP encoding architecture) at 0.84% was close to the maximum value of GPWD at 0.85% (\(p>0.05\)), GPWD reached a global minimum value of 0.35% for Task 0, and there was no way to break through this limit. As shown in Fig. 8(b), the GNV mean of the GPWD model is \(1.13\times 10^{-3}\), which is better than that of RFMG (\(2.27\times 10^{-3}\)), GHLE (\(2.73\times 10^{-3}\)), VHEF (\(3.66\times 10^{-3}\)), and WOMG (\(1.94\times 10^{-3}\); \(p<0.001\)). This is attributed to the Lipschitz continuity condition forcing stable training process. Although the minimum value of WOMG (WD optimization) of \(1.3\times 10^{-3}\) is better than the maximum value of GHLE of \(3.2\times 10^{-3}\) (\(p<0.01\)), GPWD reached the global minimum value of \(0.5\times 10^{-3}\) in Task 30. To verify the distribution alignment performance of the method, a comparison was made between cross-modal WD (CMWD) distance and feature alignment error (FAE), as shown in Fig. 9.

As shown in Fig. 9(a), the mean CMWD of the GPWD model is 0.28, which is significantly better than that of RFMG (0.63), GHLE (0.49), VHEF (0.58), and WOMG (0.42; \(p<0.001\)). This is attributed to the feature distribution alignment mechanism driven by the WD, which precisely matches the second-order statistics of the symbol-audio space. WOMG (WD optimized voice) had a significantly lower minimum value of 0.30 compared to the maximum value of 0.74 (\(p<0.01\)) of VHEF owing to the lack of VGGish perceptual modeling. As shown in Fig. 9(b), the mean FAE of the GPWD model is 0.17, which is better than that of RFMG (0.39), GHLE (0.29), VHEF (0.49), and WOMG (0.24; \(p<0.001\)). This is attributed to the second-order WD constraint, which forces the alignment of the feature mean and covariance structure. Recurrent feature generation (RFMG) had a minimum value of 0.30 significantly higher than the maximum value of 0.40 (\(p<0.01\)) of GHLE owing to the lack of integrated distribution alignment. Subsequently, the temporal structure entropy (TSE) was compared to verify the structural diversity of music generated by the proposed method, as shown in Fig. 10.

As shown in Fig. 10(a), the mean TSE of the GPWD model is 0.818, which is significantly better than that of GHLE (0.742), WOMG (0.716), RFMG (0.615), and VHEF (0.553; \(p<0.001\)). The extreme value breakthrough of 0.97 in Task 15 validated the excitation of innovative patterns by second-order statistical matching in the feature space, while the maximum value of 0.85 in GHLE (GP encoding architecture) was close to the minimum value of 0.72 of GPWD (\(p>0.05\)). As observed from Fig. 10(b), the average absolute deviation of the TSE in the GPWD is 0.068, which is significantly lower than that of RFMG (0.089), GHLE (0.074), VHEF (0.092), and WOMG (0.085; \(p<0.01\)). This is attributed to the GP mechanism forcing smooth training trajectories. The deviation of 0.068 observed for Task 27 confirmed the Lipschitz constraint suppression mode fluctuation, whereas the minimum value of 0.085 of WOMG (WD optimization) was better than that of VHEF of 0.143 (\(p<0.001\)). To verify the effectiveness of the research selection method, ablation experiments were conducted to ablate or replace the selected basic methods listed in Table 2.

According to Table 2, the TCR of the complete MAG-GPWD model is \(0.61{\pm}0.15\), which is significantly lower than that of the A1 group with GP disabled at \(1.24{\pm}0.25\) (\(p<0.001\)) and the R4 group with music transformer replaced at \(1.50{\pm}0.35\) (\(p<0.001\)). These results verify the core role of GP gradient constraint in eliminating voice conflicts. The CMWD was \(0.28{\pm}0.06\), which was 49%–52% lower than that of the R2 group with JS divergence replacement at \(0.55{\pm}0.15\) (\(p<0.01\)) and the A2 group with WD disabled at \(0.58{\pm}0.12\) (\(p<0.001\)), demonstrating the irreplaceability of WD distribution alignment in cross-modal matching. The TSE reached \(0.818{\pm}0.05\), which is higher than that of the spectral normalization replacement R1 group of \(0.746{\pm}0.09\) (\(p<0.05\)) and the GP disabled A1 group of \(0.752{\pm}0.08\) (\(p<0.01\)). These results reflect the synergistic enhancement mechanism of GP-WD on structural diversity. The TCR of R3 group replaced by OpenL3 was \(0.65{\pm}0.18\) (\(p>0.05\)), indicating that the music-specific characterization of VGGish can be replaced, but its CMWD increased to \(0.40{\pm}0.10\) (\(p<0.01\)), revealing its cross-modal alignment weakness. Moreover, while the introduction of GP increased the number of iterations required for model convergence by approximately 12%, it significantly enhanced the training stability and vocal harmony coordination. The single-inference latency of each configuration model remained below 50 ms (\(42{\pm}5\) ms for the full model), thereby meeting the low-latency requirements for real-time music generation. Consequently, the proposed approach achieved stable music creation suitable for real-time interactive scenarios through gradient constraints while maintaining highly efficient forward generation capabilities.

4.2. Professional Creative Environment Testing

Simulation verification can efficiently evaluate the core performance of algorithms (such as voice coordination and structural entropy), eliminate differences in performance equipment and interference from recording environments, and significantly reduce the cost of creative trial-and-error. However, it cannot simulate human emotional interactions and real-time artistic feedback in real creations, ignoring compatibility issues across software and hardware platforms, and there is a risk of distortion in the deep evaluation of artistic expressions. Actual testing can demonstrate the performance of a model in a professional composition environment and verify the feasibility of implementing a multi-track music generation scheme. Therefore, this study selected GHLE and WOMG, which have the best simulation performance, as the comparison methods and deployed them on the National Digital Music Innovation and Research Cloud Platform. This platform integrates creative matrices from various global genres, continuously injecting 10 ms precision MIDI instruction streams (including touch force/pedal dynamics) and 96 kHz high-fidelity acoustic feature streams. This study compared harmonic rule compliance (HRC) and polyphonic complexity retention (PCR) to verify the structural compliance of the music generated by the proposed method, as shown in Fig. 11.

According to Fig. 11(a), the mean HRC of the GPWD model is 0.90, which is significantly better than that of GHLE (0.80) and WOMG (0.82; \(p<0.01\)). This is attributed to the GP mechanism forcing chord progressions to conform to harmony rules (such as prohibiting parallel fifths). GHLE (GP encoding architecture) reached 0.84 in Task 10, which is close to that of GPWD in Task 30 (0.87; \(p>0.05\)), but GPWD reached the global highest value of 0.96 in Task 20. As shown in Fig. 11(b), the PCR mean of the GPWD model is as high as 0.87, which is better than that of GHLE (0.77) and WOMG (0.77; \(p<0.001\)). This is attributed to the feature alignment driven by the WD to maintain voice independence. Although the value of WOMG (0.83) in Task 10 was close to that of GPWD (0.84) in Task 20 (\(p>0.05\)), it was lower than the value of GPWD (0.88) in Task 10. To verify the auditory perception authenticity of the generated music, a study was conducted to compare the dynamic expressiveness score (DES) and perceived audio similarity (PAS) (calculated using ViSQOL v3.0), as shown in Fig. 12.

As shown in Fig. 12(a), the DES mean of the GPWD model is 4.66, which is significantly better than that of GHLE (4.24) and WOMG (4.01; \(p<0.001\)). This is because of the feature distribution alignment driven by the WD, which accurately restores the force gradient and the technique of continuous playing. However, GHLE (GP encoding architecture) achieved 4.5 in Task 1, which is close to that achieved by GPWD in Task 7 (4.7; \(p>0.05\)), whereas WOMG (WD optimization) only achieved 3.8 in Task 3 because of the lack of GP (\(p<0.01\)). As shown in Fig. 12(b), the mean PAS of the GPWD model is 0.89, which is better than that of GHLE (0.79) and WOMG (0.81; \(p<0.001\)). This is attributed to the collaborative optimization of the VGGish perceptual features and WD constraints to ensure timbre fidelity. GHLE (theoretical reinforcement learning) reached 0.76 in Task 12 (\(p<0.01\)) owing to cross-modal mismatch and 0.77 in Task 6, which was significantly lower than that of WOMG in Task 28 (0.85; \(p<0.05\)). Subsequently, different methods were used to generate six styles of music, including Baroque (B), Classicism (C), Romanticism (R), Jazz Blues (J), Pop Rock (P), and Electronic Dance (E), and their style transfer fidelity (STF) was compared to verify the artistic expression of the methods.

As shown in Fig. 13(a), the average STF of GPWD is 91.7%, which is significantly higher than that of GHLE (76.0%) and WOMG’s (62.8%; \(p < 0.001\)). This is because of its dual-module collaborative mechanism, wherein the MuseGAN-GP framework constrains the coordination of multi-track voices through GP, effectively preventing the mixing of stylistic elements, such as Baroque (94%) and Jazz Blues (95%). As shown in Fig. 13(b), the average STF of GHLE (GP-encoding architecture) is 76.0%. Although its independent transformer track encoder combined with GP-driven music theory reinforcement learning improved voice rule compliance (such as Baroque 78%), it was difficult to distinguish similar harmonic styles because of the lack of audio perception modeling and distribution alignment (without WD/VGGish). As shown in Fig. 13(c), the STF of the WOMG model (WD-optimized) is the lowest, with an average of only 62.8%, which is significantly lower than that of GPWD (91.7%) and GHLE (76.0%; \(p<0.001\)). Although the model used WD to optimize voice distribution matching (Monte Carlo tree search), the lack of a GP mechanism led to training instability (e.g., electronic dance music accuracy of 65%), and there was no VGGish audio feature extractor that could capture the dynamic characteristics of style (pop rock accuracy of 58%). Although the GPWD model demonstrates high fidelity in structured genres such as baroque and jazz blues (Fig. 13(a)), it performs relatively poorly in styles such as electronic dance music (EDM), which relies heavily on synthesized timbres and complex rhythmic loops (achieving approximately 88% accuracy). Taking the failed EDM sample as an example, its limitations primarily stem from the inability of the predefined MIDI synthesizer to accurately simulate the dynamic range and envelope variations of electronic timbres, resulting in monotonous sounding-generated audio.

To evaluate the artistic expression quality of the generated music comprehensively and address the limitations of purely objective metrics, a double-blind subjective evaluation experiment was conducted. The experiment invited a panel of 12 professional musicians and 24 general listeners to score the same set of multistyle music samples generated by the GPWD, GHLE, and WOMG models on a 100-point scale across four dimensions: melodic fluency, harmonic coherence, emotional conveyance, and overall artistic quality. Table 3 presents the results of the study.

Table 3 indicates that the GPWD model achieved the highest scores across all artistic dimensions (overall artistic quality: 85.1 for professional judges; 88.0 for general listeners), significantly outperforming both GHLE and WOMG (\(p<0.01\)). Professional musicians generally scored lower than general listeners, with the greatest disparity observed in the emotional expression dimension (e.g., a 3.5-point difference for GPWD), highlighting the cognitive differences between the evaluation groups. This discrepancy indicates that professional judges prioritize harmonic complexity and profound emotional interpretation, whereas general listeners are influenced more by melodic fluidity and the overall auditory experience. Correlation analysis revealed Pearson coefficients of 0.82 and 0.79 (\(p<0.001\)) between subjective overall artistic scores and objective metrics STF and DES, respectively. This strong correlation confirms the effective complementarity of the subjective and objective evaluation systems. Overall, subjective evaluation not only supplements the emotional dimensions unaccounted for by quantitative metrics but also reveals group differences. These insights provide crucial guidance for optimizing the model across distinct scenarios: professional composition (emphasizing rule compliance and expressive depth) and mass entertainment (prioritizing melodic appeal and immediate impact).

In addition, to verify the effectiveness of the parameter selection in the study, the statistical order of the GP coefficients \(\lambda\) and WD, as well as the hidden space dimension of bar coding, were selected for the parameter sensitivity analysis, as presented in Table 4.

Evidently, the validation of the core parameters of the MAG-GPWD model showed that the selected intermediate-value configuration (\(\lambda=1\), second-order WD, and \(d =64\)) had the best comprehensive performance. When the GP coefficient \(\lambda=1\), the GNV was the lowest (only \(1.15\times 10^{-3}\)). When \(\lambda=0.1\), it increased to \(2.31\times 10^{-3}\) (\(p<0.01\)). When \(\lambda=10\), it reached \(2.54\times 10^{-3}\), with \(p<0.001\). These results confirm that the GP module ensures training stability through precise constraint discriminator gradients. The FAE of second-order WD was 0.19, which is significantly lower than that of the first-order WD (0.26; \(p<0.01\)) and third-order WD (0.23; \(p<0.05\)), indicating that the cross-modal optimization module relies on covariance statistics to achieve accurate distribution matching. When the hidden-space dimension \(d\) was 64, the TSE reached 0.810. When \(d =32\), it was 0.742 (\(p<0.001\)). When \(d =128\), it was 0.792 (\(p<0.05\)). To verify the strip encoder, balancing its representational ability with the risk of overfitting is necessary.

Furthermore, this study verified the similarity between model-generated and real music in terms of macrostructure and dynamic changes by comparing waveform patterns in the time domain. These results are presented in Fig. 14. Fig. 14(a) shows that the real music signal exhibited continuous natural amplitude variations and a wide dynamic range. The clear section transitions and rich dynamic layers within the waveform reflect the structural complexity of authentic performances. Fig. 14(a) shows that the GPWD-generated signal maintains high consistency with the real waveform in terms of the overall amplitude envelope, with largely aligned undulating trends. This indicates that the model successfully captured the macro-level temporal patterns and dynamic contour characteristics of the original music. However, at the micro level, the generated waveform exhibits higher local smoothness and slightly softer transient responses, resulting in some loss of fine dynamic details. This precisely reflects the design advantage of the proposed model in prioritizing overall structural authenticity and auditory coherence. This result validates the effectiveness of GPWD in reproducing the core structure of music. The generated output maintains temporal continuity while providing a clear technical pathway for the subsequent optimization of transient detail preservation.