Title image

Scientific foundations

Like classical harmony, rhythm-space harmony is based on natural physical laws. If the  physical consonance laws of acoustics are founding classical harmony, the rules of  proxemics are founding rhythm-space harmony.

Proxemics is “a scientific discipline which studies the significant organization of the space of different animal species and in particular of the human species [1]”. Proxemics has been observed by statistical scientific studies during the 20th century [2], then by brain amygdala neurosciences in 2009 [3].

More simply, what is it? An example. Proxemics determines that when you enter a train car in which a single unknown person is sitting at one end of the train car, statistically in more than 80% of cases, you will sit as far as possible from that person, at the other end of the train car. If you sat down next to this unknown person, the rest of the train car continuing empty, it would make this person feeling defensive, like “what does this person want from me?” and probably wanting to move away. For this person, it is comparable to a forced entry into her or his intimacy, an entry into her or his physical “territory”, which was the entire train car before our arrival. And if there are 2 unknown people seated at each end of the train car, the entering human will most of the time sit in the middle, at an equal distance from these 2 people.

These are the “laws” of the occupation of physical space by a group of living beings, that we obey most of the time without realizing it. These proxemic “interpersonal distance” rules have first been observed in animals [4], then in humans.

And it is exactly from this that rhythm-space harmony was born! It was while listening to antiphonal song toads in Manaus-Amazonas-Brazil, where I have been living since 2007, that I suddenly noticed the particular rhythm-space distances between them, between their physical positions and between their sounds. On the one hand, the interpersonal physical distances between the toads seemed to place them in precise locations depending on each other (like the humans in the train car), and on the other hand the precise, rhythmic temporal interpersonal distances [5] between the sounds emitted by these same toads, seemed to correspond to their position in physical space.

It was as if a “symphony” of toads already composed and perfectly balanced in equal multipoles, was played around me! I suddenly observed the existence of a natural multipolar sound balance, a rhythm-space one, between these toads. Then I observed it between all living species, including the human species.

It was only after a lot of researches, that I learned the existence of proxemics, a discipline that I knew nothing about. I started to build a musical architecture in 3D which puts in “simple arithmetic relation” [6] the space positions of the instrumental groups in the music hall, according to the  musical rhythms, in my compositions. I let the inspiration guiding me, and I gradually tested the best rhythm-space configurations, with several loudspeakers located in specific places of the hall, and finally several  work creations presented to the public, in multichannel through loudspeakers or with musicians of the Amazonas Filarmônica orchestra, placed in specific locations of the famous “Jungle Opera”, the Teatro Amazonas.

In 2020, neuroscience has shown that brain amygdala actually decides the position in space of human individuals, providing a scientific basis for statistical evidence. At this time my intuition about a “simple arithmetic ratio” that could build mathematics of physical and temporal proxemics is not demonstrated. I do not know if some science experiments could try to highlight it, at least statistically, it is probably a task as complex as the variety of human relations. However, who has never walked on floor tiles, on the ground, having fun placing his feet in precise places on the floor tiles, as if an unknown balance or invisible rules demanded to respect a “balance” in the middle of the floor tiles ? Or who has never experienced the train car phenomenon described above?

In the same way as we “calculate” musical rhythms with a great precision while singing a melody, without realizing that we are calculating (at three-quarter of the next beat, I will sing the second syllable of the word during one quarter, etc. .), in the same way, it is my hypothesis, we do “calculate” the position of our body in space according to the other present beings or objects, without being conscious of it. And I seriously do think that there are mathematics, even complex, of proxemics [7].

Anyway, the “simple arithmetic relation” that I have heard and noticed in Nature, is the choice made to build the rhythm-space harmony organizing my musics, founded on proxemics.

[1] https://www.cnrtl.fr/definition/prox%C3%A9mie
[2] The hidden dimension, Edward T Hall, Garden City,N.Y, Doubleday 1966.
[3] Kennedy, Daniel P et al. “Personal space regulation by the human amygdala.”
Nature neuroscience vol. 12,10 (2009): 1226-7. doi:10.1038/nn.2381. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2753689/
[4] Hediger, Psychology and behaviours of animals in zoo and circuses, 1954
[5] Esthétique de composition, Réflexions et recherches transdisciplinaires pour le XXIème siècle, Isabelle Sabrié, 2012. Inédit, tous droits protégés.
[6] Les musiciens ou les groupes de musiciens sont placés à égale distance les uns des autres, ou à 2 fois, 3 fois une distance physique de base choisie en fonction des dimensions de la salle. La construction des rythmes en 3D suit d´autres règles précises. D´autres “relations arithmétiques simples” se rencontrent dans les structures musicales courantes. Pythagore a découvert qu’il existait un rapport entre la longueur d’une corde tendue que l’on fait vibrer et la hauteur du son émis : en plaçant un chevalet sur un monocorde (ou une frette de guitare) qui ne permettait de tendre que la moitié de la corde, la hauteur du son obtenue était l´octave supérieure. La fréquence, c’est à dire la hauteur d’un son fondamental est inversement proportionnelle  à la longueur de la corde en vibration. En acoustique, un partiel harmonique est une composante d’un son périodique, dont la fréquence est un multiple entier d’une fréquence fondamentale.
[7] Par exemple, Les mouvements de foules obéissent aux lois de la mécanique des fluides.