Exploring Persian Music Scales through Interactive Visualizations

This study presents an advanced interactive digital tool for the visualization and analysis of Persian music scales, providing a groundbreaking approach to exploring their theoretical structure and pedagogical potential. The tool utilizes circular diagrams where scale intervals are mapped to angular degrees proportional to their cent values, offering an intuitive and precise representation of the scales' unique characteristics. By integrating elements of Persian and diatonic scale systems, this methodology facilitates comparative analysis and dynamic visualizations of key signatures, fostering deeper cross-cultural musical insights. Built on robust web-based technologies, the tool seamlessly combines principles of music theory, digital innovation, and educational design, making it a versatile resource for researchers, educators, and musicians seeking to engage with Persian musical traditions in a global context.

Introduction

The convergence of technology and musicology has opened up new frontiers for understanding, teaching, and preserving diverse musical traditions. Among these, Persian music, with its deep historical roots and modal complexity, offers a unique landscape for exploration. Emerging from the cultural and artistic heritage of the Persian Empire, Persian music has evolved over millennia, reflecting influences from ancient Zoroastrian chants, regional folk traditions, and interactions with neighboring civilizations, such as the Arab, Turkish, and Indian cultures. This rich historical backdrop has shaped a sophisticated musical system that continues to captivate musicians and scholars worldwide.

Central to Persian music is the Dastgah system—a framework of modes that serves as the foundation for composition and improvisation. Each Dastgah comprises a set of scales and sub-scales (Gushehs) that define its tonal and emotional character. These scales incorporate microtonal intervals, offering subtle nuances that are essential for expressing the intricate moods and narratives of Persian music. Unlike the equal-tempered tuning of Western music, Persian music's reliance on microtones creates a unique sonic identity, blending mathematical precision with artistic fluidity.

Historically, Persian music has been transmitted orally through master-disciple relationships, with theoretical foundations documented in treatises by scholars such as Farabi (Al-Farabi) and Safi al-Din al-Urmawi during the Islamic Golden Age. These works laid the groundwork for understanding the modal and intervallic structures that form the backbone of Persian music. However, traditional methods of notation and instruction remain less accessible to global audiences, particularly those trained in Western musical systems.

The absence of intuitive, visual tools for analyzing and teaching Persian scales has posed significant challenges for educators, students, and researchers seeking to engage with this tradition. Addressing this gap, this study introduces an interactive visualization tool that combines ancient theoretical concepts with modern digital innovation. By leveraging circular diagrams, the tool provides a dynamic platform for representing Persian scales as angular intervals, measured in cents. These angular representations align with the familiar framework of the diatonic scale, enabling meaningful comparisons between Persian and Western tonal systems.

This approach not only demystifies the complex intervallic structures of Persian music but also highlights shared tonal foundations that bridge these traditions. Through features such as real-time scale rotation, snapping to precise angular positions, and dynamic label updates, users can explore key signatures, transpose scales, and visualize tonal relationships in an engaging and intuitive manner. By incorporating web-based technologies ensures accessibility across devices, making it a versatile resource for musicians, educators, and researchers alike.

Beyond its pedagogical and analytical value, this project contributes to the ongoing dialogue between musical traditions, illuminating the ways in which Persian and Western systems converge and diverge. It offers a lens through which the historical, theoretical, and practical dimensions of Persian music can be explored, fostering a deeper appreciation for its unique characteristics and its enduring legacy.

This paper delves into the historical significance of Persian music, the theoretical framework underpinning the tool, and the methodologies used in its development. Through detailed visualizations and comparative analyses, it aims to provide a comprehensive resource for those seeking to engage with Persian music in both scholarly and practical contexts. Ultimately, this project aspires to serve as a bridge between musical traditions, offering a fresh perspective on the timeless beauty and complexity of Persian music.

Background and Theoretical Framework

Diatonic Scale Representation

The diatonic scale, foundational in Western music theory, consists of seven notes: Do, Re, Mi, Fa, Sol, La, and Si (C, D, E, F, G, A, B), which repeat cyclically. These notes are separated by specific intervals that follow a distinct pattern of whole tones (200 cents) and semitones (100 cents). When visualized in a circular format, the scale's structure aligns with angular positions, where each note corresponds to a specific degree of the circle. The graph presented (Figure 1) illustrates the diatonic scale in a polar layout, with each segment of the circle representing an interval between successive notes. Angular divisions of 60° represent the equal spacing of notes within the octave, while alternating colors (pink and gray) emphasize the tonal relationships and provide a clear distinction between segments. White radial lines divide the scale into its seven notes, labelled as Do, Re, Mi, Fa, Sol, La, and Si (C, D, E, F, G, A and B), offering a dynamic and visually intuitive representation of this widely used tonal framework.

Ali-Naqi Vaziri and The 24 Equally-Tempered Division of the Octave (EDO)

In the 20th century, Ali-Naqi Vaziri (1887–1979), a renowned composer, educator, and musician, introduced the concept of a 24-tone equally-tempered quarter-tone scale, building upon al-Urmawī’s theory of al-Advār from 700 years earlier. Vaziri was among the first Iranian musicians to study music in Europe. During his time in France, he mastered the principles of harmony and composition while also learning piano and violin. In his seminal book, "Musiqi-e Naẓari," published in 1934, he proposed that all traditional musical modes could be represented within a scale of 24 equally spaced quarter-tones in an octave. He also developed two unique microtonal accidentals, influenced by Western music notation: "Sori," which raises a tone by a quarter step, and "Korun," which lowers it by a quarter step.

Vaziri’s innovative approach established a bridge between Persian and Western musical traditions. By creating a system that incorporated microtones into a Western-style framework, he made Persian music more accessible for teaching and cross-cultural collaboration. His efforts to standardize Persian musical notation and his introduction of new symbols for microtonal intervals continue to influence musicians and scholars.

Persian Music Scales Representation

Persian music is based on the modal system of Dastgah, which consists of multiple scales and sub-scales (Gushehs). Each scale comprises a specific sequence of intervals, often incorporating microtones that differentiate Persian music from Western traditions. The most prominent scales include Shur, Segah, Homayoun, Nava, and others, each with distinct emotional and cultural connotations. Traditional representations of Persian scales often rely on notation that is less intuitive for individuals trained in Western systems. The lack of visual and interactive tools limits accessibility, particularly for cross-cultural education. This project addresses these limitations by offering a digital approach to scale representation.

Interval Representation

Persian music is built on a complex system of modal structures, known as "Dastgah," which are characterized by specific tonal intervals. In Persian music, intervals are measured in cents, with microtonal variations that deviate from the 100-cent steps of equal temperament. These intervals were mapped to angular degrees within a circular diagram: 

This angular representation aligns with the diatonic circle, enabling comparisons between Persian and Western systems. Such a representation simplifies the identification of key signatures and visualizes the theoretical connections between scales. Each Persian scale is represented with angular divisions corresponding to its intervals in cents. The following table 1 provides detailed information about the scales implemented in the tool.

To effectively illustrate these intervals, we created pie chart representations of the most prominent scales in Persian music, including Shur, Segah, Nava, Homayoun, Chahargah, Esfahan, and Mahur. Each scale is visualized as a circular graph divided into angular segments that correspond to the tonal distances between notes, measured in cents. Color coding is employed to differentiate interval types, with Pink representing 150-cent intervals (semi-stable notes), Gray for 200-cent intervals (neutral or transitional notes), Black for 100-cent intervals (high-tension notes), and Green for 250-cent intervals (dynamic or leading tones). This method highlights the inherent structural differences between the scales while providing a clear and intuitive visual representation of their modal characteristics. These visualizations serve as an analytical tool to better understand the tonal hierarchy and melodic progression within Persian music.

Persian musical scales are distinguished by their microtonal intervals, which form the foundation of their modal system and differ significantly from the equal-tempered framework of Western music. These microtonal intervals are quantitatively represented as angular degrees in a circular visualization, providing a precise and intuitive means for their analysis.

The Segah scale exemplifies this microtonal complexity through its 250-cent interval, corresponding to 75° on the circular model. This interval falls between the diatonic minor second (100 cents) and major second (200 cents) in Western music, producing a distinct tonal character that is both audibly and visually identifiable. Similarly, the Esfahan scale features an 850-cent interval, mapped to 255°, which serves as a microtonal counterpart to the Western augmented sixth, emphasizing the scale’s unique tonal identity.

To further enhance the interpretability of these scales, color-coded segments are used in the visualizations. Pink segments highlight intervals that are unique to the Persian scale, underscoring their role in defining the modal identity. In contrast, gray and black segments represent intervals that overlap with the diatonic framework, illustrating structural connections between Persian and Western tonal systems. This methodology provides a systematic approach for examining the microtonal architecture of Persian scales and their relationship to broader musical traditions.

Mapping Key Signatures

The key signature of each Persian scale is achieved by aligning the angular intervals of the scale with the tonic note, represented as the starting point (0°) on the circular diagram. Each subsequent interval is represented as an angular position, calculated based on its cent value. For example: In the Shur scale, the intervals are spaced at 150, 300, 500, 700, 800, and 1000 cents. These are mapped to angular positions of 45°, 90°, 150°, 210°, 240°, and 300°, respectively. When the tonic is positioned at 0°, the arrangement of these intervals creates a distinct tonal identity for the scale.

The rotation feature allows users to explore how the scale adapts to different tonic notes. By snapping to angular markers, the tool ensures precise alignment, dynamically updating the key signature and corresponding labels for each interval. This functionality simulates transposition, enabling users to visualize the scale in different tonal contexts. For example, in Figure 3, rotating the diatonic scale by 60° positions "Re" as the new tonic, creating a new key signature while maintaining the scale's interval structure.

The visual alignment of Persian scales with the diatonic circle highlights shared features and deviations. For instance: The Homayoun scale closely aligns with the diatonic minor scale, with intervals like 150 (45°), 400 (120°), and 700 cents (210°). However, it incorporates microtonal shifts, such as 800 cents (240°), which distinguish it from its diatonic counterpart.

The dynamic label updates further enhance the understanding of key signatures, providing immediate feedback on the scale's configuration. This interactive feature makes the tool particularly valuable for pedagogical use, allowing students to explore the modal structures of Persian scales in different tonal contexts.

Results and Discussion

The interactive visualization tool developed in this study represents a significant advancement in the analysis and understanding of Persian music scales. By employing angular representations of intervals and integrating interactive features, the tool bridges the theoretical complexities of Persian music with the accessibility of modern digital platforms. The results are discussed below, focusing on the theoretical insights, visualization of tonal relationships, and the broader implications for musicology and education.

Theoretical Insights

The interactive tool offers a robust framework for examining the intricate modal structures of Persian music in a format that is both intuitive and precise. Angular representations of intervals, measured in cents, provide a quantifiable and visually interpretable means of mapping the microtonal characteristics of Persian scales. This method reveals several key theoretical insights:

Microtonal Distinctions: Persian scales such as Segah and Chahargah are defined by unique intervals that deviate significantly from the equal-tempered diatonic framework of Western music. For example, the Segah scale includes a 250-cent interval, mapped to 75° on the circular diagram. This interval, falling between the diatonic minor second (100 cents) and major second (200 cents), exemplifies the microtonal richness of Persian music. Similarly, the Esfahan scale’s 850-cent interval (255°) highlights its tonal distinctiveness, emphasizing the need for tailored visualization methods.

Structural Parallels and Divergences: The tool demonstrates how scales such as Mahur align closely with the diatonic major scale, sharing intervals such as 200 cents (60°) and 400 cents (120°). In contrast, scales like Homayoun and Segah incorporate microtonal shifts that distinguish their modal identities while preserving a structural relationship to the diatonic framework. These findings underscore the potential for cross-cultural musical analysis facilitated by the tool.

Tonal Hierarchies and Progressions: Color-coded segments in the visualizations emphasize the hierarchical relationships within each scale. Pink segments highlight intervals that are unique to Persian music, underscoring their modal significance. Black and green segments represent tension points and dynamic tones, respectively, providing a nuanced understanding of the tonal architecture.

Visualizing Tonal Relationships

The circular visualization of intervals offers a powerful lens through which the tonal relationships of Persian scales can be examined. The integration of interactive features enhances the pedagogical and analytical utility of the tool:

Dynamic Interaction: The tool's real-time rotation functionality enables users to explore how scales adapt to different tonic notes. For instance, rotating the Shur scale by 60° repositions the tonic to a new angular marker, dynamically updating the key signature while maintaining the scale's interval structure. This feature simulates transposition, providing valuable insights into the flexibility and adaptability of Persian modal systems.

Comparative Analysis: The alignment of Persian scales with the diatonic circle highlights areas of convergence and divergence. For example, the Homayoun scale aligns with the diatonic minor scale at intervals such as 150 (45°), 400 (120°), and 700 cents (210°) but diverges with microtonal intervals like 800 cents (240°). Such comparisons reveal the shared tonal foundations and unique characteristics of Persian music, fostering a deeper understanding of its modal identity.

Real-Time Feedback: Dynamic label updates provide immediate feedback on the angular positions and cent values of intervals as scales are rotated. This feature not only facilitates theoretical exploration but also aids in practical applications such as composition and improvisation.

Bridging Musical Traditions

The tool’s ability to juxtapose Persian and Western scales in a single framework represents a significant step toward bridging these musical traditions. While scales like Mahur (the Persian major scale) align closely with their Western counterparts, others like Segah and Esfahan highlight the microtonal nuances that define Persian music. These visualizations provide a systematic approach for exploring the intersections and distinctions between these traditions, promoting cross-cultural dialogue and appreciation. Furthermore, the tool underscores the role of microtonal intervals in defining the expressive qualities of Persian music. For instance, the 250-cent interval in Segah imparts a distinct tonal character that cannot be replicated within the constraints of equal temperament. Such insights have implications for performance practice, composition, and music education, emphasizing the importance of preserving and understanding these microtonal traditions.

Pedagogical and Research Implications

The pedagogical value of the tool lies in its ability to make abstract theoretical concepts tangible. By visualizing scales in an interactive format, the tool provides an engaging platform for students to explore Persian music. Key features such as transposition, dynamic labeling, and color-coded intervals allow users to internalize the modal structures and tonal hierarchies of Persian scales more effectively than traditional notation systems.

For educators, the tool serves as a versatile teaching resource that can be adapted for use in diverse learning environments. Its interactive nature facilitates real-time demonstrations of theoretical principles, making it particularly valuable for cross-cultural music education. Researchers, on the other hand, can leverage the tool for comparative studies of modal systems, exploring the structural relationships between Persian and other non-Western musical traditions.

Future Implications

The success of this tool in visualizing Persian scales suggests its potential for broader applications. By incorporating additional modal systems such as Arabic Maqamat, Indian ragas, and Turkish Makam, the methodology could be extended to encompass a wide range of musical traditions. Adding audio functionality would further enhance the tool's pedagogical value, allowing users to hear the intervals as they explore them visually. Such developments would position the tool as a comprehensive resource for global musicology, fostering a deeper appreciation of the world’s diverse musical heritage.

Conclusion

This project introduces an innovative tool for visualizing and teaching Persian music scales, bridging the gap between theoretical complexity and practical accessibility. By integrating angular representations, dynamic interactivity, and comparative analysis with Western scales, the tool highlights both the unique microtonal features and shared tonal foundations of Persian music.

With applications in musicology, education, and performance, the tool fosters cross-cultural understanding and deeper engagement with Persian music traditions. Its adaptability for other musical systems and potential for enhancements, such as audio integration, establish it as a model for future global music education projects.

Supplementary Information

Exploring Persian Music Scales through Interactive Visualizations

Pouya Hosseini

Contact: hoseini.ph@gmail.com

Website: Persian Music Scales

LinkedIn: Pouya Hosseini

The supplementary materials provide a comprehensive overview of the methodologies, data, and technical resources that support the development and functionality of the interactive visualization tool for Persian music scales. These resources aim to ensure the reproducibility of the project and facilitate further exploration and adaptation by researchers, educators, and developers.

Code Repository

The full source code of the tool is hosted on GitHub, ensuring transparency and accessibility. The repository includes:

Modular JavaScript code implementing the circular visualization logic.

HTML and CSS files for the user interface.

Detailed documentation explaining the code structure, algorithms, and customization options.

The repository is accessible at: GitHub Repository Link.

Database of Persian Scales

The database contains the cent values and angular representations for all Persian scales featured in the tool, including Shur, Segah, Nava, Homayoun, Chahargah, Esfahan, and Mahur. It also includes detailed color-coding rules and cent intervals used in the visualization. This structured data allows users to modify or expand the tool to include additional scales or tuning systems. The database is integrated within the GitHub repository for easy access and download.

Usage Instructions

Step-by-step guides and examples are included in the repository to help users:

Set up the tool locally or on a web server.

Modify existing scales or add new ones.

Integrate the tool into educational or research settings.

Technical Specifications

The tool is built using HTML5, CSS, and JavaScript for compatibility across devices.

The D3.js library is utilized for creating scalable vector graphics and implementing interactive features such as rotation and snapping.

SVG ensures high-quality visual rendering on all screen sizes, including mobile devices.

Future Development

The repository is designed to support future enhancements, such as the addition of audio playback for intervals, integration with other music systems, and expanded pedagogical features. Contributions from the research and developer community are encouraged, with clear guidelines provided for submitting pull requests.

License

The tool is open-source and distributed under the MIT License, allowing users to adapt and distribute the tool while attributing the original creators.

By providing open access to the code, database, and documentation, this project fosters collaboration and innovation in music education and research. The GitHub repository serves as a central hub for disseminating knowledge and ensuring the long-term impact of this work on the global music community.