New periodic table for the analysis and composition of musical pieces

From sodium, potassium, hydrogen or nickel to tones, semitones, chords and eighth notes. Luis Nuño, professor at the Universitat Politècnica de València (UPV), has taken another step in the fusion of two of his great passions: mathematics and music. If a few years ago he surprised with his musical abaci -a tool that allows learning music in a simpler way- now his reference is Mendeleev. The result of more than a year of research, Nuño has created a new musical Periodic Table, especially useful for students of this artistic discipline and also for composers. His work has been published in the Journal of Mathematics and Music.

“This periodic table facilitates the analysis of musical works, especially post-tonal, but also of other styles, since it allows us to visualize which regions of the table are used and what types of movements or trajectories are followed. Likewise, it serves to design the structure of a composition based on criteria of similarity and contrast between the classes used”, explains Luis Nuño, also a researcher at the Institute of Information and Communication Technologies (ITACA) of the Universitat Politècnica de València (UPV).

Nuño’s table bears different similarities with the periodic table of chemical elements: “the number of columns is the same, as is the number of rows, since in the periodic table there are seven periods and two more rows for lanthanides and actinides”, points out Luis Nuño.

The basis of the work is the description of all the possible combinations that can be made with 12 notes: a total of 4096 combinations, reduced by “transposition” and “inversion”, and considering from groups of 0 notes to groups of 12 notes. Nuño points out that in his Periodic Table “each period corresponds to a certain number of notes, where the first element or class is the one that has its notes as close together as possible (in chromatic sequence) and the last one that has them as far apart as possible . The table also includes several symbols that indicate certain symmetry properties, while the “complementary” classes and those that keep the so-called “Z relationship” are clearly shown, ”explains Luis Nuño.

Regarding its usefulness to analyze musical pieces and even to create different compositional structures, the UPV professor points out that each musical style (classic, contemporary, flamenco, Pop, Jazz, etc.) focuses on a part of the table. In addition, it makes it easier to establish mathematical relationships in compositions, related to set theory, such as union, intersection, inclusion, etc.

Reference

Luis Nuño (2020): A detailed list and a periodic table of set classes, Journal of Mathematics and Music, DOI: 10.1080 / 17459737.2020.1775902

Source: UPV’s Information Office