A birdsong involves multiple traits that may have evolved under sexual selection pressure. There are two types of song traits: performance-related and elaboration-related traits. These two aspects of songs are partially independent, reflecting neural development and physical condition, respectively, but some song traits might interact with each other because they share the same mechanism for song production. Understanding the evolution of multiple ornaments requires knowledge of correlations among ornaments in the same individual. We explored the potential relationships between the following five song measures. We measured song duration and note rate as performance-related traits; and average note types, linearity index score, and entropy as elaboration-related traits for the analysis. First, we found a significant relationship between linearity and entropy, indicating that syntactical complexity was consistently measured in both different variables. However, note type repertoire was not significantly associated with the two measures of syntactical complexity. Different song nuclei are responsible for each aspect of hierarchically organized song structures. Specifically, a lower-order song nucleus (RA) codes note type, while higher-order song nuclei (HVC and Nif) program transition patterns. Considering that female Bengalese Finches prefer syntactically complex songs, sexual selection, especially female choice, has played a role in shaping brains; however, the sexual selection pressure for each song nucleus may differ in its intensity. Our investigation also revealed that those birds having a larger repertoire of note types tended to sing at lower speeds and require longer song bouts to sing syntactically complex songs. Hence, these results indicate that there are trade-offs and correlations between distinct aspects of performance-related and elaboration-related traits.