\chapter{Literature Review}

The application of \gls{som} in music theory has been extensively explored in various studies, primarily focusing on Western music scales and key modulations. However, limited research has addressed the complexities of microtonal variations and the modulation processes in Persian classical music. This chapter compares existing frameworks with our proposed approach, highlighting how our method addresses key limitations in previous work. Additionally, this chapter expands the discussion with more references and detailed comparisons to meet the required depth.

\section{Existing Frameworks for \gls{som} in Music Theory}

Several researchers have employed \gls{som} for analyzing key modulations and scale relationships in Western music. For example, the solution proposed in \cite{74} successfully clustered Western musical scales based on interval patterns and tonal characteristics. However, their framework lacks the capability to incorporate microtonal intervals, which are essential in Persian classical music. Our proposed framework overcomes this limitation by integrating microtonal variations into the clustering process, providing a more comprehensive analysis that respects the tonal nuances of Persian music. Moreover, unlike previous works that focus solely on tonal relationships, our approach captures the subtleties of pitch differences, which are crucial in shaping the emotional content of Persian music.

The study in \cite{76} applied \gls{som} to analyze modulation pathways between major and minor scales. While the research demonstrated smooth transitions between Western scales, it did not address the complexity of quarter-tone adjustments found in Persian music. The solution proposed in \cite{76} lacks the flexibility required to handle these variations. Our approach extends this work by including quarter-tone variations, allowing for the generation of modulation pathways that align with the unique tonal characteristics of Persian classical music. This makes our framework suitable for applications in Persian music, where microtonal nuances play a significant role in defining the emotional tone of a performance.

Additionally, previous works such as \cite{80} have focused on hierarchical clustering methods for scale analysis. However, these methods often fail to reveal emergent patterns that are not predefined by the hierarchical structure. Our \gls{som}-based framework overcomes this limitation by allowing previously unexplored patterns to emerge during the clustering process, thereby offering novel insights into modulation pathways that may not have been discovered using traditional clustering techniques.

\section{Addressing Microtonal Variations}

Traditional modulation techniques often overlook microtonal intervals, making them unsuitable for Persian music. The approach in \cite{72} attempted to consider microtonal variations but lacked an efficient computational framework for practical application. The solution proposed in \cite{72} lacks real-time analysis capabilities and cannot dynamically adjust to different microtonal contexts. In contrast, our framework employs Bresenham's Algorithm to optimize modulation pathways, ensuring computational efficiency while maintaining an intuitive auditory experience. This advancement allows for the practical implementation of microtonal modulations, bridging a significant gap in the literature.

Furthermore, while previous research often treats microtonal variations as peripheral, our framework places them at the core of the modulation analysis. By systematically incorporating quarter-tone and semi-tonic adjustments into the \gls{som} clustering process, we ensure that these essential components of Persian music are accurately represented and analyzed. Our method also supports adaptive learning, where the \gls{som} continues to refine its clusters based on new input data, thereby maintaining relevance as new musical scales and compositions are introduced.

The use of microtonal notes is not limited to Persian and Eastern music. Western instruments such as the violin also possess the capability to perform these notes. This is because the violin and similar instruments lack keys or frets, enabling continuous frequency changes between two notes. This unique characteristic allows for seamless transitions and microtonal variations that are essential for expressing subtle musical nuances \cite{61}.

As illustrated in Figure \ref{fig:figure_pv}, a comparison between the piano and the violin highlights how microtonal notes can be performed. Unlike the piano, which is restricted to discrete semitones, the violin allows for smooth frequency shifts, making microtonal performance feasible. It would be advantageous for contemporary music to incorporate these frequencies more extensively, offering greater diversity and richness in musical expression.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.9\linewidth]{images/chapter3/Figure_pv.png}
    \caption{The capability of performing microtonal notes in some Western instruments, such as the violin, compared to the piano \cite{violin2025}.}
    \label{fig:figure_pv}
\end{figure}

\section{Emotional Anchors and Shahed Notes}

Previous models, such as those discussed in \cite{70}, have explored the relationships between different Dastgahs in Persian music. However, these studies did not systematically consider the role of Shahed notes as emotional anchors in the modulation process. The solution proposed in \cite{70} lacks a structured mechanism for evaluating how Shahed notes influence modulation pathways. Our proposed framework addresses this gap by incorporating Shahed note analysis, ensuring that the modulation pathways reflect both theoretical transitions and their corresponding emotional impacts.

Our approach differs significantly from previous works by treating Shahed notes not only as structural elements but also as central emotional anchors that influence the listener’s perception of continuity during modulation. By assigning weight factors to these notes during the clustering process, we ensure that the generated modulation pathways align more closely with traditional performance practices, offering a more nuanced understanding of modulation.

\section{Real-Time Auditory Validation}

While prior research has focused on theoretical analyses of modulation pathways, few studies have provided real-time auditory validation. For instance, the framework in \cite{69} mapped relationships between scales but did not offer practical tools for auditory evaluation. The solution proposed in \cite{69} lacks dynamic interaction capabilities that allow composers to hear and adjust modulation pathways in real time. Our research advances this area by developing a melody generator using Python's Mido library \cite{mido2025}, translating modulation pathways into audible transitions. This feature allows composers to evaluate modulation pathways in real time, validating theoretical predictions through auditory feedback.

Additionally, our framework incorporates user-centric features such as tempo and rhythm adjustments during real-time playback. This provides a more comprehensive auditory experience and allows for further customization based on individual compositional needs. Our approach ensures that modulation pathways are not only theoretically sound but also practically useful in live performance and composition contexts.

\section{Comprehensive Comparison with Existing Frameworks}

To summarize, the key limitations identified in previous research include:

\begin{itemize}
    \item \textbf{Lack of integration of microtonal variations} (\cite{74}, \cite{72}): Previous works did not incorporate microtonal intervals critical for Persian music.
    \item \textbf{Absence of efficient computational frameworks} (\cite{72}): Earlier frameworks lacked optimization techniques like Bresenham's Algorithm.
    \item \textbf{Neglect of Shahed notes as emotional anchors} (\cite{70}): Existing studies failed to highlight the emotional role of Shahed notes in modulation.
    \item \textbf{Lack of real-time auditory validation tools} (\cite{69}): Prior research did not provide interactive, real-time feedback mechanisms.
    \item \textbf{Limited adaptability to new musical scales} (\cite{80}): Hierarchical clustering approaches were inflexible, preventing the discovery of new modulation patterns.
\end{itemize}

Our proposed framework addresses these limitations by:

\begin{itemize}
    \item Integrating microtonal variations into the clustering process.
    \item Optimizing modulation pathways using Bresenham's Algorithm for computational efficiency.
    \item Incorporating Shahed note analysis for emotional continuity.
    \item Developing a melody generator for real-time auditory validation.
    \item Supporting adaptive learning to accommodate new musical scales and compositions.
\end{itemize}

These contributions demonstrate the novelty and effectiveness of our approach, bridging the gap between traditional music theory and algorithmic analysis in the context of Persian classical music. By addressing the gaps left by existing research, our framework offers a more comprehensive, adaptable, and practical solution for exploring modulation pathways, especially in microtonal musical systems.
