Research Activity: Numbers-Based Musical Harmony

In the West, the study of musical harmony through ratios of integers goes back as far as Pythagoras, some 2,500 years ago. This approach, which was superseded in the 19th century by the subdivision of the octave into twelve equal parts, is now enjoying renewed interest. Simon Martin‘s postdoctoral fellowship is geared toward developing this field of research through artistic creation, theoretical publications, and presentations for various audiences.


In Concert: Musique d’art (2021)

For his creation, Simon Martin used only harmonic pitches that are multiples of 2, 3 and 7. The 2nd harmonic corresponds to the fundamental vibration of the instrument, i.e. the air column when no piston is depressed. Tightening the lips by blowing into the mouthpiece causes the air column to vibrate in harmonic mode, resulting in frequencies in integer multiples (2, 3, 4, 5, 7…) of increasing pitch. Depressing the pistons transposes the fundamental frequency of the air column and gives access to new series of harmonics. The combination of fingering and the control of the harmonics by the lips thus makes it possible to play musical scales. However, musicians usually try to avoid the 7th harmonic, which has a different intonation from conventional western scales. Martin uses it in his creation for its characteristic colour and acoustic effects.

Link to the Video

– On Projections libérantes’s Website.


In Conference: Numbers-Based Musical Harmony

Link to the Video

*Available in French with English subtitles.


Publication – Treatise: Numbers-Based Musical Harmony

The Treatise proposes a complete and coherent harmonic modulation method. Beginning with simple basic notions, it builds toward the use of a vast repertoire of modulating harmonic sequences described strictly with integers available in the Supplements.