Toward a New Harmonic Framework

There was a time when most people believed the universe and everything in it was made of music. The early Hindus were perhaps first to embrace this concept in their musical philosophy of Shabda, a Sanskrit word meaning “sound” or “speech.” Their Vedic texts, written in the form of sacred hymns, were said to embody the divine knowledge of sruti or “what is heard.” As this idea was adopted into Buddhist, Jainist and Tibetan teachings, it was known as the Audible Life Stream, Inner Sound, Sound Current and the Word. Spreading through much of the populations of India and China, many today still claim: “the Sound Current vibrating in all creation can be heard by the inner ears.”

The ancient Egyptians also celebrated the idea of a musical universe by employing harmonic proportions in the design of their pyramids and burial chambers. In the book Egyptian Sonics, acoustician John Stuart Reid found evidence the Egyptians had developed an advanced sonic science by the fourth Dynasty, circa 2520 BC. His acoustical experiments in the Kings Chamber of the Great Pyramid demonstrated that certain resonant frequencies would create vibratory patterns corresponding to some twenty hieroglyphs, suggesting that Egyptian writing may actually have its genesis in this early science of resonance.

Inheriting their wisdom from the Chaldean mystery school in lower Mesopotamia (modern day Iraq), the Hebrews developed their entire language around the harmonic properties of numbers and geometrical proportion. Their alphabet was based on the geometry of numbers, or gematria, from which the Torah was encoded. The Jewish people and later Gnostic sects then based their laws and social customs on these universal principles of harmony and balance.

In the 5th century BC, Greek philosopher Pythagoras united all of these teachings into one, founding his own mystery school to study the harmonic properties of nature. Discovering that different musical intervals corresponded to simple whole number proportions, he and his followers developed a unified philosophy of harmony in numbers, geometry, astronomy and organic forms. Finding the same harmonious patterns everywhere they looked – the seed patterns of fruit, orbits of planets and shape of the human body – an ancient scientific method known as musica universalis was established to guide the study of nature.

As this method was applied to the study of form, Greek philosopher Plato identified five perfect solids and developed a natural philosophy of archetypes to go with them. From this came Euclid’s Elements, describing the mathematics behind such archetypes, complete with rigorous logic and formal proofs. In the Hellenistic period that followed, Archimedes of Syracuse developed an early form of calculus known as infinitesimals while Ptolemy charted the periodic motions of the heavens. Behind all of these advancements in geometry, mathematics and astronomy could be found the guiding light of Pythagoras and his scientific method of musica universalis.

But this golden age of Greek science was not to last. With the Roman conquest in 146 BC, the study of nature became less important as the Romans focused on vast engineering projects to support their conquest of Europe. Beginning with Constantine in the 4th century AD, much of the pre-Christian knowledge was lost with the torching of the Royal Library of Alexandria by Archbishop Theophilus. Were it not for the work of Arab scholars, who had earlier translated and preserved many of the ancient works, all knowledge of the Greek’s science and mathematics would have been lost.

With the fall of Rome and the beginning of the Holy Roman Empire in 962 AD, the Dark Ages had begun. It was not until the European Renaissance in the 14th century that most of the important Greek works would be rediscovered and an interest in harmonic science would return.
Copernicus with his Sun-centric theory of the solar system was the first glimmer of a return to harmonic principles in astronomy. Then came Johannes Kepler’s Harmony of the World, proposing that Platonic forms in some way governed the spacing of the planets. While this turned out to be an oversimplification, he did accurately explain other phenomena of the solar system, such as the difference between maximum and minimum speeds of each planet’s orbit approximate harmonic proportions.

Around the same time, a prominent English physicist, astrologer and Rosicrucian mystic named Robert Fludd publicly debated Isaac Newton against adopting a purely empirical method for science. In De Musica Mundana, Fludd argued that the Pythagorean model of the universe was essentially correct and should be used to guide the study of nature, since the cosmos is indeed a kind of celestial monochord of vibratory energy from which all things arise. But in spite of this last attempt to hold onto musica universalis, Fludd’s harmonic ideals fell from favor and a new unguided science was born.

The Enlightenment or an Endarkenment?

Beginning first with Galileo, then Sir Francis Bacon and Sir Isaac Newton, a new “scientific method” was proposed and adopted in the 17th and early 18th centuries. It was a method that assumed no guidance from harmonic principles. Instead, it was presumed that observations and experiments alone would lead the world to truth and enlightenment.

Bacon was the first to propose the new empirical scientific method, designed to shield the mind from false notions that could distort the truth. Calling such notions “idols,” he proposed four kinds that must be avoided: those common to a given race, those peculiar to an individual, those resulting from the misuse of language and those resulting from the abuse of authority. All together, he argued that avoiding such idols would lead inductively to the discovery of forms and models that accurately describe natural phenomena and their genesis.

As a result, the Greek harmonic science that had sparked the Renaissance was abandoned to avoid the religious connections it had with the Church. It seems harmonic principles, long a central concern to sacred music and closely controlled since 1234 AD by Church canon law, was now considered a false idol to be avoided. Harmonic theory and religion were simply too intertwined to be unraveled at the time.

Yet in hindsight, the wholesale removal of a harmonic foundation from the methods of science may have seriously impeded scientific progress. Some argue that this decision led to a disorganized and fragmented study of nature, resulting in the tentative, incompatible and rather dogmatic scientific formulae known as the Standard Model. Contrary to Sir Francis’ original intent, the rejection of harmonic science may have opened the door for even bigger idols to sway the cause of science.

Today, acceptance of contradictory theories have led to wildly different models for even the most common phenomena, not the least of which is gravity, the structure of the vacuum and human perception. Without a unified foundation, the language of science has become increasingly arcane, heavily barnacled and decidedly obtuse, a veritable Tower of Babel, making it difficult for anyone outside of a given field of specialty to comprehend and integrate much of the scientific research now available.

At the same time, there is a rising chorus of scientists around the world who complain of unreasonable and unfair barriers to the publishing of their work. Journal review boards, controlled by older generations bent on defending their life’s work, often reject studies that do not conform to already accepted models, even in the face of compelling evidence showing errors in such established models. But, this is not all that now haunts Bacon’s scientific method.

New idols must be worshipped by science that did not exist prior to the Industrial Revolution. These are the idols of economics and politics. Markets now demand a continuing flow of new technologies to fuel the global economic engine, redirecting the focus of university education and research away from the search for real understanding. To make matters worse, more and more of our best scientists are being recruited right out of college by the military industrial complex to build more powerful weapons and devastating war machines. It seems that Bacon’s idols have become bigger and more powerful than he could have ever imagined.

So, even as the worldwide standard of living has risen from waves of innovations in productivity, entertainment and creature comfort, we are really no closer to an agreement on how the major components of nature fit together than we were 300 years ago. There is no understanding of how the quantum microcosm contributes to the development of life; no agreement on what causes gravity; no interest in the geometric properties encoded in DNA (or life in general) and no explanation for what caused life to evolve along the particular path it did, to name but a few. And while we can tell through MRI imaging which parts of the brain are activated by different stimulus, there remains no accepted model for how the brain actually thinks or how conscious self-awareness could emerge from inanimate matter.

Welcome to The Endarkenment, an age where the quest for the big picture has no currency – a time when seeking enlightenment in the study of nature has become not only irrelevant, but laughable. A time when field specialization and isolation have brought us to an artificial and overly complex view of things where we no longer see or even care about how the pieces fit together. We embrace the differences and eschew the commonalities. We think we get it, but we really don’t.

The time has come to reevaluate and update our methods of science. We must seek a new approach where natural study can once again be guided by laws common to all fields of study. This method must be powerful enough to overcome Bacon’s false idols while loosening the strict dogma of the Standard Model. It is time to reintegrate the fields of science and, in so doing, begin the process of reintegrating our fragmented society.

But to do this, we must first reconcile ourselves with the past. We must find a way to mend the worldviews of Pythagoras and Planck, Plato and Bohm, Euclid and Lisi. Only through reconciliation can we hope to find our way forward.

A New Harmonic Framework

First off, let’s agree that the ancients were essentially right – all things are in vibration. From the smallest particle to the whole of the cosmos, everything we see comes from the resonance of electromagnetic waves and the formation of atomic particles. This is the harmonic framework of our physical reality.

It all starts with spirals. As pressure builds, vortices form; as vortices form, closed cycles appear; and as these cycles stabilize, energy crystallizes into harmonic forms. Repeating at every level of reality, the fractal formations of galaxies, solar systems, planetary systems, biological-botanical systems, molecular systems and atomic systems all emerge from layer upon layer of coherent vibration. Yet each system is part of a whole, sharing a common source of energy and descending from a set of universal laws. These are the laws of the ancients – the laws found inside a periodic standing wave.

A standing wave occurs whenever vibration is trapped inside a container and reflects back upon itself, becoming stationary as it oscillates in place. This occurs because the energy in the standing wave travels in opposite directions, adding together into a single, coherent waveform. As this process begins to stabilize, whole number harmonic frequencies emerge to piggyback on the fundamental frequency of the container. This natural process, known as resonance, quickly generates an entire harmonic series of wave frequencies that share the energy of the fundamental.

The Harmonic Series is a series of wave frequencies produced as a single wave vibrates and subdivides in halves, thirds, fourths, fifths and so on, inside a container. This natural process generates the whole number set of harmonics h = {1, 2, 3, 4, 5, …, ∞}. Also known as “overtones” in music, harmonics are responsible for the various timbral qualities of an instrument.

Like the musical tone of a simple reed flute, all matter results from the same physics of resonance that brings harmony to music. While the container for a flute is its pipe, planets resonate harmoniously into place from the hot plasma contained inside the gravity bubble of a star. Similarly, living things resonate into harmonic forms inside the container of their cell, egg or body. The atoms that make up those living cells then resonate inside their own micro bubble of space, bonding harmonically into larger molecules, compounds and mesoscopic structures. The quantum world beneath is no different, emerging from spiraling “torsion” fields that form spherical standing waves whose harmonic intersections form the nodes we call particles.

But resonance alone is not the whole story. There is something else quietly at work inside these standing waves that makes coherent resonance possible. This is the phenomenon known as harmonic damping.

If standing waves are the stuff of the visible world of structure, harmonic damping is the invisible force of stability, order and balance. Discovered in the 1930’s by Soviet physicist Lev Landau, plasma waves were found to exchange energy at “avoided crossings” called “adiabatic transfers.” Known as Landau-Zener Theory or simply Landau damping, this idea quickly spread to become the cornerstone of quantum mechanics and has since been applied to explain such phenomena as superconducting, superfluidity and coherent states of matter like Bose-Einstein condensate.
As it occurs in the very special case of standing waves, the principles of Landau damping explain how wave energy transfers across gaps called damping wells to form harmonics. In particular, the damping wells in standing waves exist at fixed locations identified by the natural constant known as the golden ratio.

The Golden Ratio, documented in the 3rd century BC, but known thousands of years earlier, occurs when a line is divided in such a way that it can be nested infinitely into itself at the same proportion. We can easily visualize this as the proportion between line segments in a pentagram, commonly expressed as: φ = (1 + √5) / 2 ≈ 1.618033 and its inverse 1/φ = (√5 - 1) / 2 ≈ 0.618033. In a variety of studies, the golden ratio has been found to represent the maximum damping location in standing wave phenomena.

This is not a trivial point. The Landau damping effect of the golden ratio can explain many properties found throughout nature – from the average spacing of planets to the branching patterns of life to the lattice alignment of atoms in crystals as they spin in the same direction. It is due to this effect that rectangular speakers and auditoriums are often built near golden ratios of 0.62 x 1.62 x 1 in order to suppress wave reflection and echoes. Indeed, it is the damping effect of the golden ratio that enable standing waves in all mediums to nest deeper and deeper within themselves, creating endless fractal formations.

Landau damping theory also suggests that as standing waves form within a container, those frequencies near the damping well of a golden ratio or its inverse will be suppressed while those furthest away will remain as whole number harmonics. Thus, we find that the golden ratio is responsible for creating the space between harmonics and carving out the slack needed for harmonics to coexist within the same space. We can define this “anti-harmonic” or fractional set of frequencies using the infinite set of numbers in the Fibonacci series, a subset of the harmonic series.

The Fibonacci Series, named after Leonardo “Phi” Bonacci of Pisa but first documented by the Sanskrit grammarian Pingala in the Chandah-shastra around 450 BC, represents a “mountain of cadence” that “grows” by adding adjacent pairs of numbers starting with 1 + 1. This growth process continues to produce the infinite series {1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …}.

The relevance of this series to standing wave formation is apparent when each adjacent pair of ascending Fibonacci numbers is taken as a proportion, creating numbers closer and closer to the golden ratio, represented by the Greek letter φ or Phi.

For instance, the adjacent Fibonacci proportions 13/8, 21/13 and 34/21 are roughly equal to 1.625, 1.6153 and 1.6190, respectively. As the process continues, the Fibonacci series approximates the golden ratio of about 1.6180339887 by spiraling closer and closer to it, but never actually reaching it. In this way, all of the Fibonacci frequencies are increasingly damped and suppressed from the standing wave as they converge ever nearer to the golden ratio, leaving only whole number harmonics in the space between (Fig. 1).


Figure 1. Harmonic damping stabilizing a standing wave

Thus, we see that Fibonacci proportions in a standing wave are just as important as whole number harmonic proportions. They produce a silent spiraling background field in the waveform that stabilizes the process of resonance, enabling the formation of “sympathetic” harmonics. And, at the center of these deadening Fibonacci vortices lays the golden ratio and its inverse – two infinite and constant damping wells present in every standing wave cycle where energy is exchanged. Without this natural ordering property at every scale of nature, standing waves, their harmonics and physical structures of all kinds would simply cease to exist.

We now find in the containment and reflection of waves the universal method by which energy self-organizes into coherent particles out of a chaotic spread spectrum of energy. The golden ratio – often considered of little real importance to science – is actually what keeps atoms from flying apart, yet simultaneously bonds them together. At the cosmological scale, it is the golden ratio that sets the size, spacing, orbital frequency and other attributes of the planets within the Sun’s resonating current sheet. And in life forms, the golden ratio is responsible for every crevice, curve, hole and flexible joint as organisms self-organize from the atomic realm up. It is this one constant of nature that makes it possible for the resonant structure of our bodies to articulate, move and do work.

When organized around a central polar axis, standing waves composed primarily of water and carbon-12 resonate together into the familiar shapes of life, first exploding outward as spheres but then spiraling back inward as the damping force becomes too strong. Trapped inside a gravity bubble of space, compressed by atmosphere and water, living cells have little choice but to resonate into a multitude of nested cardioid forms (Fig. 2).


Figure 2. The universal harmonic pattern of life.

That’s it – harmony is everywhere and in everything. It is the simple balance of resonance and damping intrinsic to spacetime, present from the first moment of the universe. This is the physics of a standing wave that offers a new framework for science, if only our methods would allow it.

Toward a Harmonically Guided Science

Early natural philosophers had no need of Bacon’s scientific method to protect them from undue influence and bias – they were innocent from the beginning. Their societies looked with fresh eyes at the planetary movements in the sky, mineral crystals on the ground and geometry of life all around them, seeing only commonalities. Wherever they gazed, they found the truth staring back at them – the universe truly is made of music.

In those days, the tools of science were drums, gongs and flutes. The scientist’s method was to sprinkle sand on a drumhead, intone a simple chant and then watch wide-eyed as geometric patterns appeared on its surface. Taken as the first symbols of language and ideas, the physics of a standing wave was the model upon which early civilization achieved its coherence. Just as we now celebrate music as the universal language of culture, the study of resonance and damping was once revered as the universal language of science.

It is through this simple and most beautiful worldview of our forebears that we might now envision a new future for science. Perhaps it is time to bring back harmonic study to our schools, as it once was long ago. And while we are at it, perhaps we should consider adding harmonic principles back into the scientific method, recalibrating all scientific research to the universal model of a standing wave. Maybe it is even time to include a new field of harmonic science – a field whose job it is to look for the commonalities and reconnect the fragments of modern science into a meaningful whole.

Let us envision an educational system where every student takes at least one year of general harmonic studies. We may find it helps guide more students toward science through their love of music. At the same time, those already scientifically inclined may find greater passion for their field of study as it became infused with the values of Art.

But no matter their chosen field, we might expect these students to develop a more integrated worldview from harmonic theory and a musical worldview of the universe. Maybe our youth would begin to see the broader impact of their decisions, bringing more ethical and socially responsible solutions to market. Just this small adjustment to the educational system could change the world.

With harmonic principles central to a new scientific method and integrative field of harmonic science, researchers could become more efficient by avoiding dead-end paths. New generations of scientists guided by harmonic models would seek deeper causality in the phenomena they study, more often finding their answers in adjacent fields. When this was not enough, a new field of harmonic science could pose questions, recommend avenues of research and encourage research across fields to solve key problems.

As astronomers came to embrace harmonic processes once again, we could expect many of the competing cosmological theories to be put aside as models grounded in harmonic laws take center stage. Quantum mechanics, itself already founded on harmonic principles, would at last become the accepted foundation of astrophysics. Soon, astronomers would feel free to discuss the universe in musical terms, triggering a domino effect into other fields.

With the Standard Model adjusted to guide research toward integration, the life sciences would experience a revolution not seen since Charles Darwin. Biologists would feel compelled to recognize and study the role of atomic resonance in guiding evolution, therein realigning anthropological and genetic models with quantum and cosmological models. Beginning as only a trickle of information to the outside world, the message would eventually get out that life is just an enfoldment of the same harmonic processes at work all around us. A new vision of life as a beautiful musical crystal could suddenly blossom into the social consciousness, elevating self-image and bringing a new sense of interconnection and responsibility back to society.

As medical scientists also came to accept the human body as the resonating liquid crystal it really is, increased research into bio-currents and directed wave resonance treatments would surely come, bringing unimaginable medical breakthroughs to replace many of the drug therapies so heavily promoted by today’s pharmaceutical industries. Change would also come to the cognitive sciences, refocusing research on brain resonance and non-local quantum effects, therein establishing new models of perception and a more natural approach to machine intelligence.
No field of science would remain unchanged. Reconciliation with ancient harmonic wisdom could lead to revised interpretations of history, a rereading of the archeological records and new social theories proposing harmonic physics as the central theme behind the development of social order. The economic and political sciences would change as well, gradually shifting Western institutions toward less polarized, more moderate policies. This, in turn, could bring a surge of R&D funding to alternative and yet-undiscovered energy sources to relieve the world’s oil dependence. Out of this, the ecosciences would flourish beyond anything we can imagine now.

If we are to have a true understanding of nature and achieve a sustainable civilization, a harmonic framework must be reintroduced into our schools, our science and our society. Continued avoidance of harmonic principles resulting from long gone theological associations is no longer warranted and has indeed become a clear impediment to progress. The sooner this is recognized and rectified; the sooner science can begin fixing the really big problems that will ensure mankind’s survival.