\chapter{Conclusion and Future Work}

In this chapter, the main findings of the research are summarized, and the implications of these findings in the context of computational music theory and the generation of \gls{mp}s are discussed. Additionally, possible directions for future research are proposed, highlighting the potential to extend and improve the methods developed in this study. The findings of this research provide a solid foundation for future explorations in the cross-cultural modulation between musical scales, opening new doors for both theoretical and applied research in computational music theory.

\section{Summary of Findings}

The main objective of this research was to propose a methodology for generating smooth \gls{sm} paths between Western and Persian musical scales. The methodology combined the \gls{som} with principles of music theory, enabling the clustering of musical scales based on their interval patterns, including \gls{mt} variations, and the generation of modulation paths that ensure a smooth and natural transition between scales. This study aimed to provide a computational approach that could handle both the structural aspects of Western music theory and the unique tonal qualities of Persian music.

The key findings of this research are as follows:

\begin{itemize}
    \item The \gls{som} successfully clustered Western and Persian scales based on their interval structures. It was capable of distinguishing between scales with traditional 12-tone equal temperament and those that incorporate \gls{mt} intervals, which are prevalent in Persian music. The model’s ability to handle these diverse scales was critical in enabling smooth modulations between musical traditions.
    \item \gls{mp}s between various scales were generated that adhered to known music theoretical practices. These paths were evaluated using both objective metrics (such as step differences and \gls{tpr}) and subjective feedback from users. The combination of these two evaluation methods provided a comprehensive understanding of the effectiveness of the generated \gls{mp}s.
    \item The generated \gls{mp}s were generally rated as smooth and natural, with transitions between related scales exhibiting the least abrupt changes. More divergent modulations, while still musically acceptable, were slightly less smooth, highlighting the trade-offs inherent in creating modulations between highly different musical systems.
    \item The methodology demonstrated the potential for cross-cultural applications, enabling modulations between Western and Persian music, as well as within each musical tradition. The ability to automatically generate these transitions without human intervention in identifying suitable modulations holds great promise for both music composition and theoretical exploration.
\end{itemize}

\section{Implications and Contributions}

This research contributes to the field of computational music theory by offering a novel approach to generating smooth \gls{sm} paths between different musical traditions. The combination of the \gls{som} with music theory principles provides a computational tool that is capable of handling both Western and non-Western (Persian) musical scales, including those with microtonal elements. By bridging the gap between different musical cultures, this research not only enhances our understanding of modulation but also provides a valuable tool for music composers and analysts.

The findings of this study have several important implications:

\begin{itemize}
    \item The ability to generate \gls{mp}s automatically opens new possibilities for music composition and arrangement. Composers and musicians can now experiment with smooth transitions between scales from different cultural traditions, enabling them to create more diverse and innovative compositions. This also facilitates the exploration of cross-cultural musical expression, blending elements from multiple traditions seamlessly.
    \item The method could be applied to the development of software tools for automated music composition, analysis, and music theory education. These tools would enable users to experiment with modulations between diverse musical scales and styles, empowering both students and professional musicians to better understand and utilize the relationships between musical scales from various traditions.
    \item The study also highlights the potential of using machine learning algorithms, such as the \gls{som}, for musical analysis. This suggests that such tools can capture complex musical relationships that are not immediately obvious through traditional theoretical analysis. The \gls{som} model offers a means to analyze musical scales in a way that could reveal hidden patterns, structures, and connections between musical traditions, providing new insights into the relationships between different musical systems.
\end{itemize}

\subsubsection{Applications and Future Enhancements}

The smooth modulation generator has wide-ranging applications in music composition, analysis, and performance. By providing structured modulation paths, the system enables musicians to explore novel harmonic transitions, microtonal variations, and unconventional modulation techniques. These applications can be particularly useful in a variety of musical contexts, such as:

\begin{itemize}
    \item \textbf{Compositional Assistance:} The smooth modulation generator assists composers by offering novel ways to experiment with key changes and modulation techniques. It helps streamline the process of creating modulations that are both musically logical and aesthetically pleasing, making it a valuable tool for composers seeking new ways to express harmonic transitions.
    \item \textbf{Performance Guidance:} The system can provide live performers with structured modulation suggestions, helping them navigate through complex key changes and enhancing their expressiveness during performance. This can be particularly helpful for musicians who are improvising or performing in real-time, offering them a roadmap for smooth, intuitive key transitions.
    \item \textbf{Music Theory Education:} The system can be used as an educational tool for teaching students about modulation and key changes. By providing visual and auditory feedback, it helps students understand the structural principles of modulation and gain a deeper understanding of how different keys and tonalities relate to one another. This hands-on approach to music theory can enhance the learning experience and make complex concepts more accessible.
\end{itemize}

Looking toward the future, the system can be enhanced in several ways to further improve its capabilities and expand its applicability across different musical domains. Future enhancements could include real-time modulation processing, allowing performers to adjust modulation paths dynamically during live performances. Integration with \gls{midi} controllers would provide musicians with an even more interactive and flexible tool, enabling them to manipulate modulation paths on the fly. Additionally, support for more advanced microtonal tuning systems would open up new possibilities for composers and performers working with non-traditional tunings. By refining the underlying algorithms and expanding the range of supported musical styles, the smooth modulation generator has the potential to become an indispensable tool for musicians across a wide variety of genres.


\section{Limitations of the Study}

While the proposed methodology has shown promising results, there are several limitations that need to be addressed in future research:

\begin{itemize}
    \item \textbf{Scope of Scales}: The current study focused on a relatively limited set of Western and Persian scales. Expanding the dataset to include other world music traditions, such as Indian or Arabic scales, could provide a broader perspective on the modulation process and further validate the approach. A more diverse set of scales would also enable a deeper understanding of how the \gls{som} handles musical systems with varying tonal structures and cultural contexts.
    \item \textbf{Modulation Path Complexity}: Although the \gls{som} was able to generate smooth transitions between scales, the complexity of the paths could be further refined. Future work could explore incorporating more sophisticated algorithms, such as deep learning models, to better handle complex modulation scenarios. These models could capture finer nuances of musical relationships and produce more sophisticated and expressive modulation paths.
    \item \textbf{Subjective Evaluation}: While user feedback provided useful insights into the emotional and tonal impact of the modulation paths, the small sample size and the subjective nature of the feedback could introduce biases. A more extensive user study with a larger and more diverse group of participants would provide more reliable feedback and ensure that the results are generalizable to a wider audience. Additionally, more detailed demographic information could help understand how different listeners perceive modulations between musical traditions.
\end{itemize}

\section{Future Research Directions}

Several directions for future research could build upon the results of this study. These directions offer the potential to enhance the methodology, broaden its application, and address some of the limitations identified in this research:

\begin{itemize}
    \item \textbf{Integration of Rhythmic and Harmonic Elements}: The current research focused primarily on melodic modulations between scales. Future work could incorporate rhythmic and harmonic elements into the modulation process to create more complete and expressive musical transitions. For instance, the incorporation of chord progressions and rhythmic patterns could improve the musical coherence of the transitions and make them more fitting for real-world musical composition.
    \item \textbf{Advanced Machine Learning Models}: While the \gls{som} demonstrated the ability to cluster scales effectively, more advanced machine learning techniques, such as deep neural networks, could be explored to improve the generation of modulation paths. These models could better account for subtle musical features, such as articulation, phrasing, and texture, and produce more nuanced modulation transitions that reflect these complexities.
    \item \textbf{Personalization and Adaptability}: Future research could explore how the system could be personalized for individual users or adapt to specific musical styles. This could involve incorporating user preferences or learning from user interactions to generate modulation paths that align with their particular aesthetic tastes or compositional style. Personalization could also enhance the system’s usefulness for educational purposes, as it would be able to cater to the musical tastes and learning goals of different students.
    \item \textbf{Cross-Cultural Applications}: Given the cross-cultural nature of the study, further research could explore how the methodology can be applied to other non-Western music traditions. This could include investigating the modulation practices in African, Latin American, or Eastern European musical traditions and how these could be integrated into the modulation path generation process. Additionally, such research could reveal new insights into how different musical systems approach modulations and the role of cultural context in shaping musical transitions.
\end{itemize}

\section{Conclusion}

This research successfully presented a novel methodology for generating smooth \gls{sm} paths between Western and Persian musical scales. By combining the \gls{som} with music theory principles, the study demonstrated the potential for computational models to capture complex musical relationships and generate smooth, musically coherent modulations. The ability to model both Western and non-Western scales, including microtonal systems, opens exciting new possibilities for cross-cultural musical exploration.

The results of this study open up exciting possibilities for both theoretical and practical applications in the field of computational music theory. The ability to automatically generate \gls{mp}s between different musical scales can serve as a valuable tool for composers, musicologists, and educators, providing them with a deeper understanding of the relationships between scales and the potential for cross-cultural musical exploration. Moreover, the approach lays the groundwork for the development of advanced musical tools that can automate the process of creating new musical works that are both theoretically sound and musically expressive.

While the methodology has shown promising results, further work is needed to refine and expand upon the approach, including exploring more complex modulation scenarios, incorporating additional musical elements, and validating the results through larger user studies. Future research will continue to push the boundaries of computational music theory, offering new insights into the structure and expressive potential of music across cultures. The continued integration of machine learning with music theory principles will likely lead to innovative solutions for musical analysis, composition, and education in the future.
