Xenharmlib (music theory library) adds support for Just Intonation

Xenharmlib, an evolving library dedicated to music theory analysis, has reached a major milestone with the release of version 0.4.0. This update significantly broadens the software’s capabilities by introducing full support for Just Intonation alongside a range of other regular temperament systems. The upgrade marks a considerable enhancement in how the library models tuning systems beyond the conventional equal temperament.

Historically, musical tuning has been dominated by equal division of the octave, notably the 12-tone equal temperament system that gained prominence from the 18th century onward. However, prior to this widespread adoption, many cultures and musical traditions employed tunings based on pure intervals created by ratios of small whole numbers — a concept known as Just Intonation. Xenharmlib now embraces this heritage by mathematically accommodating tunings that rely on these pure intervals.

The core architecture of Xenharmlib has undergone a profound restructuring to support multi-generator tunings. This shift enables the representation and analysis of a vast array of regular temperaments, transcending simple equal divisions. As a result, the library can accurately describe complex tuning systems used historically and cross-culturally, including Byzantine modal systems, Renaissance temperaments, Indian classical scales, Indonesian gamelan tunings, Arabic Maqam, and even the experimental microtonal work of 20th-century composers like Harry Partch and Ben Johnston.

One of the pivotal features introduced is the Prime Limit Tuning construct, which facilitates the creation of scales such as the Pythagorean 12-tone chromatic scale by stacking intervals defined as pure fifths. This approach captures the mathematical purity of interval relationships more faithfully than traditional software implementations, which often rely on scalar transposition methods that can distort interval sizes depending on the starting pitch. By opting for a regular transposition definition, Xenharmlib maintains consistency and opens analytical possibilities for compositions that utilize the full tuning space rather than a limited chromatic subset.

Moreover, the new multi-generator framework supports the custom design of temperaments, exemplified by the inclusion of the Quarter-Comma-Meantone Temperament. This temperament adjusts intervals to flatten the tritave by a fraction of a syntonic comma, demonstrating the library’s flexibility in tuning customization for theoretical and practical applications.

In addition to tuning enhancements, Xenharmlib 0.4.0 introduces interval arithmetic capabilities, which had been notably absent in earlier versions. This advancement enriches the analytical toolkit available for music theorists and researchers, allowing precise interval calculations within diverse tuning frameworks.

The update also expands harmonic primitives with two new constructs: Sequences and Interval Fans. Sequences enable the conceptual modeling of note progressions, complete with transformations like retrograde and inversion, which are essential for segment analysis. Interval Fans provide an abstract representation of relative pitch distances to a tonal center, serving as a valuable resource in post-tonal scale analysis.

Complementing these features, the library now supports the computation of interval class vectors, a critical tool in contemporary music analysis used to quantify interval content and relationships within scales. Additionally, all one-dimensional tuning and notation objects benefit from closest frequency approximation, enhancing the precision of scale representations and analyses.

Alongside these functional improvements, the documentation for Xenharmlib has been thoroughly overhauled. It now offers structured examples categorized by tuning and notation type, alongside dedicated explanations of harmonic primitives, making the library more accessible for users exploring complex musical temperaments.

While Xenharmlib’s current iteration encompasses the entirety of regular temperaments with the exception of certain irregular temperaments such as Werckmeister systems, it represents a comprehensive toolset for scholars and musicians seeking to explore the mathematical underpinnings of global tuning traditions and modern experimental music. Details on specific implementation methodologies and further feature additions remain limited but are expected to be documented in future updates.

This release positions Xenharmlib not just as a software library but as an expansive mathematical framework capable of bridging diverse musical worlds through precise tuning and analytical tools. Its ability to model and analyze a wide spectrum of tuning systems opens new avenues for research and composition in music theory and acoustics.