Music art is a form of conveying cultural information and humanistic emotions. From ancient times to the present, the form of music has undergone great changes. The change of music form is closely related to the change in dynasties, the development of the market economy, and the change in humanistic spirit. Today, the development of music has reached a relatively prosperous stage, which is closely related to the rapid development of the market economy. At the heart of the quantitative analysis is the study of associations between data. However, it will be a difficult task to analyze the relationship between the development scale of the market economy and the form of music innovation only by artificial means. This research mainly uses a convolutional neural network and long and short-term memory neural network technology to quantitatively analyze the relationship between the development scale of the market economy and the form of music innovation, which is mainly a quantitative analysis of classical music, pop music, and rap music. The research results show that convolutional neural networks and long short-term memory neural networks have sufficient capabilities to quantitatively analyze the relationship between the market development scale and the form of music innovation. Neural networks with LSTM layers have lower errors in predicting market economic correlates than neural network methods without LSTM layers. The error is reduced by 0.27%. For the prediction of innovative forms of music, the largest prediction error is only 2.93%, which is closely related to the variability of popular music. The linear correlation indices for the predictions of the three forms of musical innovation also all exceed 0.955.