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Why the term « harmony »: music, sciences

Why the term “harmony” ?


This very relevant question was asked by Nguyen Minh Tâm, the Artistic Director of the Percussions de Strasbourg group for whom I am currently composing the Symphony – ballet Cenas da Amazônia. I was very happy that he validated the term harmony after my explanations, that I present here in a few sentences.

Musical definition: rhythm-space harmony is a set of spatio-temporal principles that regulate the use and combination of simultaneous sounds when they are emitted from different locations in a hall, and their sequencing at specific times so that it develops an evolving spatial and rhythmic equilibrium in the 3-dimensional physical space.

Musical and scientific foundations for the term “harmony”


In music, classical-romantic harmony is defined as the “set of principles which regulate the use and combination of simultaneous sounds” [consonants], or even the “art and science of the formation and chords sequence[1] ”.

In scientific language, the consonant chords used by classical-romantic harmony are superimpositions of pitch frequencies which have physical consonance relations between them. In acoustic sciences, physical consonance is defined as “sounds which fundamental frequencies are in a simple arithmetic relation to one another[2].” This natural arithmetic characteristic has been known since Pythagoras, and it also exists in rhythm-space harmony, in another form.

Until the 20th century, the definition of the musical term “harmony” only applied to the vertical dimension of simultaneous sounds in the musical writing, meaning applied to superimposed consonant sounds, emitted from the same place in the room and at the same rhythmic moment.

Rhythm-space harmony is also a “set of principles which regulate the use and combination of simultaneous sounds, and its sequence”. But this time the principles apply to the horizontal rhythmic (temporal) and spatial (physical space) dimension of the musical architecture. They apply to “the use and combination of simultaneous sounds” when these sounds are emitted from several different places in the room, at rhythmic moments of the same bar or of the same “beat”, and to their sequence with other spatialized rhythms.

Like traditional harmony, rhythm-space harmony maintains a “simple arithmetic relation” between the simultaneous sounds. This simple arithmetic relation links the musical rhythms to the spatial position of their sound sources (the position of instrumentalists or loud speakers in the room). It exits in the 2 “horizontal” dimensions of rhythm-space harmony musical writing, the rhythmic temporal one, and the spatial physical one.

This is what I observed in the Amazon rainforest: a natural rhythm-space harmony, which first appeared to me while listening to antiphonal song toads from the Amazon. The laws of proxemics have been known since the middle of the 20th century, they decide the position of each animal in relation to the others in physical space. They also decide, according to my observations, its rhythmic position in time when it emits a sound [3]. A regular pulse (with its relative pulses) synchronizes all the complex sounds of biophony, this neurosciences subject has been in discussion with some scientists since 2009 .

In the “rhythmic temporal” dimension of music, it is the very definition of rhythm which is arithmetic: the relation between the durations of the sounds of a rhythm is mathematical. Each division or multiplication of the chosen unit of time is in “simple arithmetic relation” with this same musical unit of time. For example, a whole note is divided into 2 half notes, a quarter note is equal to 3 eighth notes of a triplet, or 2 eighth notes in binary. The set of rhythmic multiplications or divisions is a multiple or divisor of simple whole numbers, 1, 2, 3, 4, or 5, which rarely go beyond 7.

In the dimension of the physical space, the 3 dimensions (height, width, length) of a room are considered. These 3 dimensions are themselves divided into 2: top-bottom, left-right, front- behind. And the composers using the language of rhythm-space harmony will decide the distances between the sound sources, so that they are in “simple arithmetic relation” to each other.

The “simple arithmetic relation” characterizing traditional harmony and physical consonance is then found in at least 2 dimensions, in rhythm and in space, to build the rhythm-space harmony, allowing to reconstruct the rhythm-space balance in movement in the hall at each moment.

The time-space principles of rhythm-space harmony admit all musical systems, including classical-romantic harmony in its verticality, serial, modal music, etc. They do not alter the classical-romantic harmony if it is present in the composition. This one can continue the same regardless of the location of its sound emission, coming from the stage “in front” or from elsewhere in the room. The rhythm-space harmony adds dimensions and rules to the music produced from the stage in front of the listeners. It adds “left-right-top-bottom-behind” to it, and the sequence of sounds is then developed, following the rules of a “time-space balance”.

Subsequently, questions of timbre, acoustics and human auditory perception determine other rules which are superimposed on these. They are based on the possibility, or not, of a good perception of the sound localization in the room by the human ear, and of its interest, or not, in the general musical context. Like the orchestration rules, some configurations are better than others, and have imposed themselves on me during the composition of my works of rhythm-space harmony, until recently creating popular rhythms in 3D.

For all these reasons, the term “harmony” seemed to me the best to name this musical construction.

[1] Larousse dictionary.
[2] Pythagoras discovered that there was a relation between the length of a stretched string that is made to vibrate and the pitch of the sound emitted: by placing a bridge on a monochord (or a guitar fret) which did not allow to stretch only half the string, the pitch obtained was one octave higher. The frequency, ie the pitch of a fundamental sound is inversely proportional to the length of the vibrating string. In acoustics, a harmonic partial is a component of a periodic sound, which frequency is an integer multiple of a fundamental frequency.
[3] Aesthetics of composition, Reflections and trans-disciplinary researches for the 21st century, Isabelle Sabrié, 2012. Untranslated, unpublished.