Today at 3 pm, Glenna Batson will lead an exploration of folds and resistances. In her words:
What happens when awareness meets a curved line, a folding surface, a deepening crevice within the body’s interior and the surround? Is the quality of this first contact fixed or free? Is the conversation open or resistant? Is there a clear beginning and ending? It’s at this junction between folding and unfolding where new possibilities for negotiation arise – where a boundary can become more porous and transparent. In this session, movers will uncover the rub of resistance within themselves and open the conversation to new movement possibilities.
The soundscape for today’s playshop will be a piece from Audiorigami (Meditations on the Fold) interspersed with modular synthesis play in formless to form and back again. The Audiorigami track is called 11th Harmonic and consists of overlapping 11th harmonic intervals. This harmonic at extremely high frequencies has been shown to break up tumor cells! The Law of Octave allows us to bring the high frequency into the audible range, and benefit from the entangled resonance with the higher frequencies.
11th Harmonic is a kind of smudge soundscape. It has the capacity to clear stuck energy in a space, in a body, so is perfect for the suggested intentions Glenna has put forth. This piece has five or six movements, and the parts are layered in and shimmered over each other. This is an example of how I have created audiorigami to this point. Now there is new direction in the form of Ripplemaker – even the name suggests the Fold!
Ripplemaker is an iOs semi-modular synthesizer. Synthesizers play electrical signals or control voltages. These voltage-based signals are shaped by waveforms, oscillators, envelopes, filters and effects into sound sculptures. Modular synthesizers can illustrate the journey from the formless into form in amazingly beautiful ways! And the journey is accomplished through folds. The basic structure of this sound material is the waveform, and each waveform highlights the harmonic overtones in different ways. The waveshape is then propogated, expanded, attenuated, filtered, timbrally-morphed through oscillators, envelopes and filters. The journey is amazing and intense, so each mod synth excursion will be followed by a bit of room resonance and breath. Then 11th Harmonic will return.
Very excited to give this voice today at 3pm at ADF Studios. Please come and play with us!
The Law of the Octave is the first step in understanding how the frequencies of the Universe are vibrationally organized. The fact that any frequency, doubled or halved, is a re-expression of the original frequency suggests the beginning of some kind of fractal movement. We have a place to return to and begin again; a place that comes around again later. The next step in understanding how frequencies are organized involves adding the fundamental frequency to itself over and over again. This creates a beautiful and repetitive frequency pattern that expands The Law of the Octave into what is often referred to as Nature’s Chord.
Nature’s Chord is the same as the Harmonic Overtone series, which I have written about before. To get a really good idea how alchemical these tones are, you have to know their history. A long ago deep listener named Pythagoras was walking through town and heard the clanging hammers of metalsmiths. Then he really listened to the clanging and realized he was hearing high pitches when the small hammers were used and lower pitches when the large hammers were used. Then he tightened a string and noticed that dividing the string in particular ratio relationships created these beautiful harmonics.
With the string tightened to a particular tone when plucked – lets say an A (at 220 Hz), Pythagoras discovered that vibrating half the string gave an octave higher version of the same tone A (now at 440 Hz). When 2/3 of the string was vibrated the tone will be E, which is the fifth interval from A and vibrates at 660 Hz – 220+220+220. When the next 220 gets added, we are back at the octave. Simply amazing!
And on it goes, each iteration of the initial frequency, reveals another harmonic. After the A octave at 800 Hz comes the C# at 1100 Hz – this is a third above the fundamental tone. The Harmonic Overtone series has risen three octaves so far, and in that span has revealed the root chord structure for any music – the fundamental frequency, the third and the fifth. So, in our example, the A Major chord has been revealed through the harmonics inherent in the note we call A: A C# E.
Another overtone that comes out in the third octave is the flatted seventh. So, along with the root chord, we also get a nod to the seventh and its place in the most beautiful chord structures. The fourth octave reveals most of the remaining diatonic tones from the second, to the raised fourth, to the natural seventh. All of the tones we know in our most familiar musics are laid out in the first four octaves of the Harmonic Overtone series. The number of overtones per octave doubles with each successive octave, so the next octave after the fourth octave would have 16 overtones and the next 32. At these levels the harmonics are so varied, close together, and difficult to hear that discrete pitches disappear into a percussive wash of sound.
The amazing relevance of this chord to everythingyou hear is difficult to comprehend on first pass. The Law of the Octave and Nature’s Chord are undeniably present and absolutely inscrutable – wherever there is atmosphere, Nature’s Chord exists in potential. It is a preset pattern that awaits a disturbance to set it in motion. The disturbance moves the atmosphere and Nature’s Chord presents this disturbance to our ears in a beautiful harmonic package. The harmonic framework springs forth from the primary tones of all the sounds you hear. Each sound is characterized by the amount of and the “mix” of harmonics. Nature’s Chord is easily heard in strings, pipes, the voice – anything that can support a standing wave vibration and thus maintain a pitch. The mix gets less melodic when the waves are less harmonic and more dense. It is Nature’s Chord that renders what is known as timbre. Timbre is the “color” of sound and as easily recognized as red, blue, green, a knock on the door, your lover’s voice.
Recently, I was studying voices on a sonogram and saw the overtone series in each person’s speaking voice. Most everyone has a fundamental tone around which their vocal inflection patterns dance. Here is a photo of a voice in the key of F:
The bottom line is F, the next line up is the re-expressed octave F, the next line is C the fifth overtone for F, the next the octave again and so on. Look in the upper right corner and you can see the “pitch bin” for where the cursor is pointing: F F C – Nature’s Chord made flesh!
All of this information has me wanting to explore the power of Nature’s Chord. Several contemporary classical music composers have used this chord as a theme for compositions. Terry Riley’s In C is composed of the prominent notes from the harmonic overtone series of the tone C. John Adam’s Sila the Breath of the World is built on the overtone series of Bb. Moondog, a NYC street composer, was fascinated with the overtone series and used it in his piece called Creation. Here is what he had to say about the overtone series in an interview:
How could you send a message that would never be destructible? Only in sound waves. Waves are indestructible. Wherever there’s a planet that has atmosphere, these overtones could be heard. Scientists are looking in telescopes and microscopes and they don’t realize that this is here, right here. The secret is all around us and nobody recognizes it.
I am exploring tones and harmonics and octaves and fractals, oh my! Last year, I developed a piece for the Human Origami workshops based on the disruptive power of the 11th harmonic. I am expanding that piece and putting it into the iBoD repertoire. Invoking the Law of the Octave, the disruptive 11th Harmonic stirs the energy wherever a tone and its fifth are played. And the further apart they are, the closer you can get to that four octave span that produces the 11th harmonic, the more powerful the vibe!
So here is an early version of 11th Harmonic – the first in a series of works inspired by Nature’s Chord!
To form an octave is to double or halve a given frequency.The Cosmic Octave Cousto
When asked what one piece of information represented the most important knowledge humans possess, Richard Feynman, the remarkable mathemetician/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 orbit a nucleus. And atoms are primarily “empty” space. Yet this moving, spacious world of Everything appears to human beings as material form. 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. (The actual measurement is from peak to peak = one cycle) Put a bunch of oscillations together in a periodic sequence, and you have frequency. Frequencies, along with resonance, consonance, dissonance, 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 frequency oscillations. Oscillations are the pervasive movement pattern that weaves 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. If this is true, then frequency is a portal into and through all of existence. And this portal is accessible and useful due to the Law of the Octave.
A vibrational frequency is known through a measurement called hertz. Hertz expresses the number of oscillations per second. One oscillation per second is 1 Hz, twenty-five oscillations per second is 25 Hz, and so on. Vibrational frequencies reveal the world to us through our senses. Everything we hear, vibrates at 20 Hz to 20,000 Hz, which is the audible spectrum. Everything we see is vibrating between 400 Trillion Hz and 750 Trillion Hz, which is the visible spectrum of the electro-magnetic field. The entire electro-magnetic field is a vibrational gift basket of frequency bandwidths that give us telegraph, radio, television, mobile phones, internet, and the electricity to power it all. And then when we go deep into the building blocks of matter, what do we get? – more oscillations.
According to the Law of the Octave – every frequency is entangled with its half and its double. Any known frequency can be calibrated as an audible frequency or visual frequency or x-ray frequency, simply by dividing higher frequencies by 2 and multiplying lower frequencies by 2. In the book The Cosmic Octave, Hans Cousto argues that the octave is a unit of measurement that can be useful in understanding and working with our very existence. Using a simple mathematical formula, Cousto converts all manner of measureable phenomenon to audible tones. (More on that in a future post.)
The audible frequency range demonstrates clearly how The Law of Octave works. A frequency of 440 Hz is the infamous Concert A- multiply 440 x 2 and 880 is also an A tone. The frequency is higher, denser, more oscillations per second, but it is the same expression as the 440 – it also is an A. Divide 440 by 2 and you have 220 Hz – also an expression of an A note. This suggests a repetitive pattern that is renewed each time it doubles or halves. This is a moment of return, an opportunity to begin again. I am wondering about The Law of the Octave as a jumping off point in the design of all kinds of fractals (mostly sound fractals).
And this is just the beginning, as there are other factors informing my fractal understanding, including Nature’s Chord, the Golden Mean, and Fibonacci numbers.
For now, The Law of the Octave and its relationship to the movements of the Universe are enough to ponder.