Mapping the Neighborhood of Microtonal Music Scales Using Self-Organizing Maps

This study introduces a novel method for discovering similarities among music scales by mapping them in a two-dimensional space, leveraging a Self-Organizing Map (SOM). Scales are modelled considering microtonal variations typical of the Radif in Iranian music and capturing the role of the Shahed note as emotional anchor. Eight distinct scale interval patterns from Western and Persian music theories based on tonic, dominant notes, and microtones are considered in the SOM construction process.A key application of this mapping is enabling smooth modulation between scales. Using Bresenham's Algorithm, modulation pathways can be computed based on the generated SOM, allowing for gradual transitions that are hardly perceptible by the listener.A quantitative analysis measured the smoothness of transitions and the coherence of the proposed modulation pathways, considering 40 modulation transitions appearing in classic and contemporary music pieces: a comparison of the modulation pathways, obtained by querying our SOM, to the corresponding scale transitions appearing in the original scores yielded an average hit rate of 0.83. Moreover, a user survey with 79 participants confirmed that the system effectively aligns with traditional modulation practices descending from classical theories of harmony, while introducing innovative transitions.