Fundamental Folds: Octaves and Overtones

When asked what one piece of information represented the most important knowledge humans possess, Richard Feynman, the remarkable mathematician/physicist, replied:

Everything is made of atoms.

Indeed! What an amazing discovery! While the atomic structure and molecular composition vary from one object to the next, from one human to the next, from one star to the next, still – Everything is made of atoms!

But wait! There is more! Atoms are comprised of electrons that move around a nucleus. And atoms seem to be primarily “empty” space. Yet this moving, spacious world of Everything appears to human beings as solid matter. Even our earth suits have an animate integrity. What holds all of this together?  Within these “building blocks” lies a deeper cohesion, a durational measurement, a simple, but pervasive infrastructure for all of Creation – the oscillation.

An initiating gesture, rising to a peak, falling past the midline to trough, and rising back to the midline beginning – motion across/around a central axis – a cycle, one complete oscillation. (And this refers back to the Dance Polonaise of the embryonic spine that Glenna wrote about in the blog The Folding Continuum.) String a bunch of oscillations together in a periodic sequence, and you have frequency. Frequencies, along with resonance, consonance, dissonance, and interference, hold the world together AND move us through our experiences. While our reality appears solid and stable, it is actually in constant flux driven by changes in frequency oscillations. Oscillations are the pervasive movement pattern that weave together what we call “reality”. From the quantum, to the electromagnetic, to the world of form, all of existence is waving at and through us.

One way that oscillating frequencies manifest is as sonic folds in atmospheres. Fundamental sonic folds are created through a harmonic template that is actually embedded in the atmosphere. This template amplifies/attenuates and mixes frequencies into an audible world for our ear/brain. The Law of the Octave and the Acoustic Scale hold that every frequency event triggers more events at whole number relations to the intiating frequency. Doubling or halving a frequency gives you the same frequency expression again as an octave. In addition, there is an on-going rising reiteration of the initiating frequency, which manifests an entire scale. This scale reveals itself in a series of harmonics that appear in higher and higher octaves. This framework is responsible for every sound we hear!

For a more detailed explanation please follow this link:


The scale that is enveloped in the atmosphere is often referred to as Nature’s Scale or the Acoustic Scale due to its appearance whenever the atmosphere is disturbed. This scale seems to be what Deleuze is describing when he talks about “accords”. Accords are described as “…the relation of a state…with the differential relations of infinitely small units that are integrated into this state.” He goes on to note that “To hear the noise of the sea is tantamount to striking a chord.” a seeming reference to the presence of the Acoustic Scale and its role in creating our perception and cognition of the sounding world.


Here is a sonic sketch of Deleuze’s metaphor in action. An audio loop of waves crashing on rocks is processed through a Multi-Band Compressor, a notch filter and audio-to-midi harmonics slicing. With the help of my own ears and a spectrum analyzer, several pitches are identified as fundamental to the sound of the waves (in this recording). C# and G# emerge as strong tones. What you will hear is the sound of the waves that are then stripped of all but the highest harmonics (which emphasize the G#). In addition, I layer in C# and G# on a long bell-like tone in order to amplify the chord in the wave.

The harmonics of a sound like “waves crashing on rocks” are complex and the tonal character of the sound is obscured by the density of enharmonic frequencies. But, remember, it is this mix arising from the Acoustic Scale framework, that allows you to recognize that you are hearing “waves crashing on rocks”.

By Jude Casseday



Al-Khalili, Jim (2007). Everything is Made of Atoms. The Guardian


Cousto, Hans (2000).  The Cosmic Octave. LifeRhythm Press.


Deleuze, Gilles (1993), The Fold: Leibniz and the Baroque, trans. Tom Conley, Minneapolis: University of Minnesota Press.


Hewitt, Dr. Michael (2013). Musical Scales of the World,


Strauss, Jonathon (1991). Gilles Deleuze The FoldYale French Studies, No.80, Baroque Topographies, Literature/History/Philosophy, 227-247.