\chapter{Introduction}
\section*{Introduction}

Music is a universal medium for expressing emotions, ideas, and stories, achieved through a combination of melody, harmony, rhythm, and tonal dynamics \cite{1}. Across cultures and historical periods, music has played an essential role in human expression, serving as a means of storytelling, emotional release, and cultural identity \cite{2}. One of its most fascinating aspects is its ability to evoke a wide range of emotions, creating a profound connection between the listener and the composition. Whether through a melancholic melody, an uplifting harmonic progression, or a dynamic rhythmic pattern, music has the power to influence mood and perception \cite{3}. Among the many techniques composers use to shape a piece's emotional and structural narrative, modulation, the transition between musical keys, stands out as an essential tool. \cite{4}. This technique allows composers to guide listeners through contrasting emotional landscapes while maintaining coherence and enhancing the overall complexity of the composition.

In any musical work, preserving the tonal integrity of the key is fundamental to creating a harmonious experience \cite{5}. The choice of key defines the tonal center, influencing the emotional character of a piece and the relationships between notes and chords. However, composers often choose to modulate, or change the key, deliberately to introduce contrast, expand expressive possibilities, and sustain listener interest \cite{6}. modulation is particularly effective when executed seamlessly, allowing the transition to unfold naturally without disrupting the flow of the composition. When done skillfully, key changes can create a sense of movement and evolution, leading the listener through different tonal environments while preserving musical unity \cite{7}.

In the context of Persian classical music, modulation is deeply rooted in the tradition of the Radif, a structured system of melodic patterns passed down through generations \cite{8}. The Radif provides a framework for both composition and improvisation, guiding musicians in their exploration of different tonal spaces \cite{9}. A defining feature of Persian music is its extensive use of \acrfull{mt}, which contribute to its rich tonal palette and unique expressive qualities \cite{10}. These microtonal inflections allow for nuanced modulations that might not conform to the rigid structures found in Western tonal music. In Persian music, modulation often revolves around the axis notes, known as the Shahed, which serves as a melodic anchor and establishes a sense of resolution and emphasis \cite{11}. The Shahed is a crucial element in defining the emotional direction of a piece, acting as a reference point for modulation between different scales or modes \cite{12}.

Traditionally, musicians have relied on intuition and empirical knowledge to navigate \acrfull{mp}, drawing on their understanding of the relationships between the tonic, dominant, and axis notes of different keys \cite{13}. These relationships are influenced by the intervallic similarities between modes, facilitating smooth and coherent transitions \cite{14}. Despite the significance of modulation in both composition and performance, a systematic and \acrfull{ct} of \glspl{mp} has remained largely unexplored \cite{15}. The absence of a formalized, data-driven approach has left much of the modulations process to the subjective interpretation and experience of musicians \cite{16}. While this allows for artistic freedom, it also means that modulation techniques are not always structured or easily accessible for study.

This research seeks to bridge the gap between tradition and modernity by employing \glspl{ct} methods to analyze \glspl{mp} across Persian and Western classical music scales \cite{17}. The primary objective is to construct a two-dimensional map of musical modes that visually represents their neighborhood relationships and provides a structured framework for modulation \cite{18}. By utilizing \acrfull{som}, a type of \acrfull{ai} neural network, this study clusters modes based on their interval patterns, tonal characteristics, and shared modulation possibilities \cite{19}. The resulting visualization not only offers theoretical insights into the relationships between different modes but also serves as a practical tool for musicians and composers \cite{20}. This approach enables a systematic exploration of \glspl{sm} pathways, expanding the expressive possibilities of music while preserving the richness of both Persian and Western classical traditions \cite{21}. By integrating \glspl{ct} with traditional music theory, this research aims to provide a novel perspective on modulation, offering both theoretical advancements and practical applications in composition and performance \cite{22}.

\section*{Thesis Structure}

This thesis is structured in a way that facilitates a comprehensive exploration of the research objectives, methods, and findings. The document is divided into the following chapters:

\begin{enumerate}
    \item \textbf{Introduction:} The first chapter introduces the research problem, objectives, and scope of the study. It provides an overview of the importance of modulation in music, particularly within the context of Persian and Western music scales, and presents the research questions that guide the thesis.
    
    \item \textbf{Literature Review:} Chapter 2 presents an extensive review of the relevant literature. This includes a discussion on modulation in music theory, the use of \acrfull{mt} in Persian classical music, and the application of Self-Organizing Maps (SOM) in music theory and pattern recognition. The literature review also covers the principles behind the SOM algorithm and its application in other domains.
    
    \item \textbf{Methodology:} In Chapter 3, the methodology used for this research is described in detail. This chapter covers the data collection process, including the musical scales and interval patterns considered in the study. It also explains the use of the SOM algorithm for clustering musical scales and generating modulation paths, as well as the technical aspects of the algorithm, such as the initialization of nodes and the calculation of modulation paths.
    
    \item \textbf{Results and Discussion:} Chapter 4 presents the results of the SOM algorithm applied to Persian and Western music scales. The generated map of musical scales is analyzed, and the modulation paths between different scales are discussed. The findings are also compared with existing theories on musical modulation. The chapter further includes a qualitative evaluation of the AI-generated modulation paths through field surveys and user feedback. This evaluation covers the criteria for assessing the smoothness, emotional impact, and effectiveness of the modulation transitions.
    
    \item \textbf{Conclusion and Future Work:} The final chapter summarizes the main findings of the research and discusses their implications for music theory and composition. It also suggests potential areas for future research, including the refinement of the modulation system and its application to other musical traditions.
\end{enumerate}
