Sonic Spiral


The basis of this installation lies in the number sequence known as the Fibonacci series. The series starts on the number 1 and then adds the previous number to the current number to get a resultant number. It is laid out thusly: 1, 1, 2, 3, 5, 8, 13, 21, 34, 89, 144… The sequence continues infinitely. This seemingly simple sequence is found throughout the natural world (pine cones, the nautilus shell) and can even lay claim to being used by stockbrokers in the financial markets. A product of the Fibonacci series is the Fibonacci spiral shown above as well as the concept of the Golden Ratio. This ratio can be expressed as a number (1.6180339887) or algebraically as: Uses of the idea can be seen in Leonardo Da Vinci’s drawing of the Vitruvian Man (though he may not have known exactly of the concept, he understood it intuitively) and works by such composers as Bartok and Debussy.

The sonic component of the work begins with the idea of the harmonic series. When we sing a note, or an instrument produces sound, that particular sound wave is made up of composite sound waves all sounding together. These sound waves are known as the harmonic partials of the note, and each of them has an accompanying number value: 1st partial, 2nd partial, 3rd partial, etc. The lowest partial, the fundamental, typically yields the musical pitch of a note. In this installation, 55Hz is set as the fundamental (however this is not sounding, only implied) and partials used are based on the Fibonacci series. Thus the eight sounding frequencies (and their partial number) are: 110Hz (2) / 165Hz (3) / 275Hz (5) / 440Hz (8) / 715Hz (13) / 1155Hz (21) / 1870Hz (34) / 3025Hz (55).

John P. Hastings





Video documentation: