Geometry, Philosophy, and Tone

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Complete Tonal Integration

Sacred Sonics' geometric tuning systems tap into the natural geometries of nature, chemistry, acoustics, and energy. To create healing tones and music that are most compatible with the manifestation of healing and wellness. Each playable on standard equipment.

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Instant Tonal Mastery

Experimenting with any of our tuning systems is as easy as loading a MTS file into your compatible keyboard or VST. Each tuning standard is designed to a twelve-tone octave and provide a wide assortment of harmonicly colorful tone palettes for composition of healing music.

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Downloadable Assets

Don't care to take the time building the tuning system files from scratch? We've got you covered. Our downloads area provides .TUN and .MTS files for every tuning system within the Sacred Sonics library. Purchase licenses for single or multi-packaged systems for fast download

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Supporting Concepts for Geometric Tuning and Theory

Putting History and Research to Work... In Theory

Now we will continue our exploration of ancient contributions to the Sacred Sonics systems by exploring some specific aspects of the ancient Aegean cultures of Greece and Macedonia. And , while much of the preceeding articles' content has focused on historical connections and associations; The Ancient Aegean cultures, especially Greek culture, is literally where we gain some traction with the theoretical concepts that bring Sacred Sonics to life.

To be clear, this writer believes, in no uncertain terms that; much of what is valuable and/or useful to modern society has its origins in the various earlier societies. Writings of Plato and Solon traveling and studying in Egypt for years is a clear indicator that the knowledge, which was passed to us from the Greek and Macedonian cultures, was in fact, passed on to them from the Egyptians who in-turn, preserved much more that was passed from the Sumerian and Babylonian stores of knowledge and technology.

The passing down of esoteric knowledge from prior civilizations logically explains the sudden and voluminous revelations associated with the Greek civilization. The phenomenon also provides likely scenarios for both the spread of that knowledge, once held as sacred and secret within the ruling and priestly classes, as well as the erosion of much of the high knowledge apparent in the accomplishments of those earlier civilizations. This gradual trickling dissipation of knowledge is exactly why the Greek society is so incredibly important to us today. It was the Greeks, in western civilization, and the Persians of eastern civilization, who strove to recover and preserve the vast stores of knowledge held by earlier cultures. If it were not for these two entities, the greater portion of human knowledge would likely have been lost forever. The preservation along with literacy programs among the middle stratae of these societies, resulted in a kind of renaisseance of knowledge as citizens who would have been wholly uneducated in any but their specifically designated professions, were encouraged and enabled in the broadenening of their horizons with a wider educational foundation.

For millennia, higher knowledge was not generally available to the more common people. It was the Greeks, and to a lesser extent, the Persians who made this once restricted or sacred knowledge more widely available. Thus ensuring that much of it would survive the coming struggles and oppressions resulting from future empire. This prescient attitude proved fortuitous for the human race, as the coming Roman Empire was to be decidely less ecumenical in its politics and policies as well as foreshadowing the coming 'Dark Age' of human civilization.



Part IV

Supporting Concepts From

Ancient Greece & Macedonia

A Re-Discovery of Ancient Knowledge

Now, let us consider the civilizations of the Greek and Macedonian era. In no particular order, the first master that we will briefly consider, is Pythagoras. (somewhat whimsically pictured above)

Pythagoras of Samos is best known for a mathematical theorem that bears his name to this day. An understanding of the Pythagorean Theorem is not directly pertinent to our discussion of Sacred Sonics and alternate tuning systems. However, it is very useful to understand that the Egyptians and Sumerians clearly understood the relationships within triangles – based upon the obvious architectural evidence. Also worth noting, for our purposes is the fact that Pythagoras himself, was the modern originator of sonic or acoustic research.

When you stop to think about it; It seems beyond farcical to suggest that full-toned musical structures were non-existent prior to the Greek civilization. Yet, that is what many music educators and professionals seem to expect us to assume. Archeologists have uncovered ancient clay tablets in Mesopotamian digs, that represent what one could consider to be the sheet music of the era. Musical notation, complete with mathematically determined, interval harmonies and lyrics, exist as far back as we are currently capable of exploring.

Therefore, Pythagoras could not have possibly originated musical structure or invented the tonic intervals, as at least 3000 years of musical civilization preceded his ‘discoveries’ of tonics and intervals. Additionally, pre-dating the Classical Greek period, no fewer than a dozen examples of stringed instruments exist, which would necessarily require a systematic method of tuning, as well as requiring some type of common root-relative method of coordination, in order to play accompanied. These instruments are illustrated on various Babylonian, Semitic, and Egyptian works of art and serve as evidence for the above assertions. Based on these extant examples and logic; The best that this writer can manage is to credit Pythagoras with certain RE-discoveries and possibly some few enhancements of harmonic value. These ‘advances’ were almost certainly due to the more than twenty years he spent studying the esoteric arts in Egypt (according to Diogenes and Isokrates) as well as an additional period of more than a decade in Babylonia.

What Pythagoras did accomplish for us, was to elucidate a system of harmony that is still pertinent to us today. As previously mentioned, none of his original notes or writings have survived the ravages of time and conflict. What little we think we know about Pythagoras was passed on to us by contemporary philosophers, writers and those of later periods who preserved copies of his work, or elucidated their own concepts upon the foundations of Pythagorean works, known at that time.

One anecdotal story regarding his work on tone and pentatonic harmony is described in the trope that “Music was born in the forge”, and is related as follows: As the story goes, on a non-specific day, our hero was walking along near a metal working facility. We will call it a ‘forge’ as your writer is not energetic enough to look up the proper Greek terminology. In any event, the sounds of various hammers striking metal anvils suggested regular harmony to Pythagoras. So he paused to investigate.

To jump to the end of the story, Pythagoras, who was primarily a mathematician, discovered an interval relationship between the tones produced by each hammer strike, and the weights of the various anvils in use at the forge, which were also weighted in somewhat regular intervals.

Our hero apparently noted that an 'anvil' of half the weight as another, produced a tone that was a full octave above that of the heavier anvil. This mathematical relationship of 2:1 between metallic mass and tone, of course could not be ignored. So, his mind went to work establishing the foundations that underpin the mathematics of intervallic harmony, in use to this very day. With no more than this basic foundation, we can easily derive, with whole number divisors, what is called the ‘pentatonic’ (5-tone) scale that is somewhat erroneously associated with one of the many ‘modal scales’ of music today. The creation of the full twelve-tone octave requires a bit more than that which has been attributed exclusively to Pythagoras.

Thus, with the telling of this story, we reveal the first contribution of the Greek period to our Sacred Sonics system of tone. Without the circuitous preservation of Pythagoras’ work on intervals, we would be wholly-unable to build even the most rudimentary musical tone system.

One of the most famous quotes, attributed to Pythagoras, indicates a belief in an almost spiritual connection between the planetary motion, geometry, and the strings of musical instruments. This connection is an integral construct within the theory of ‘Sacred Sonics’ as it provides what may well be the most ancient expression of the core belief that underpins the entire theory. In the attributed words of Pythagoras: “There is geometry in the humming of the strings. There is music in the spacing of the spheres.”

Indeed, Pythagoras and his contemporaries hypothesized that the “…spacing of the spheres” was a heavenly expression of a specific type of harmony – A 'musica universales' that could be calculated based upon nature, and expressed through the proper frequencies and harmonies. The intended result was a tonal structure, which could be utilized for the uplifting and betterment of all humankind. The name given to these harmonies is called, “The Music of the Spheres”. The recording of these observations comes down to us, primarily through the works of Ovid, Philolaus, and other philosophers.

Plato: Legendary Greek mathematician and philosopher

Plato: Legendary Greek mathematician, philosopher as well as prolific author and teacher

Our next Greek master is another triple-threat genius. The great mathematician, philosopher, prolific author and teacher, Plato was reportedly born, sometime around 423 BCE in Athens and, like Pythagoras, lived well into his seventies. Some authoritative sources even say that Plato was approaching 80 years of age upon his passing.

Imagine if you will, that nearly 2500 years of history have passed by. Now, imagine that people around the world still quote you, respect your accomplishments, and continue to honor your teachings. This is the position that the legacy of Plato holds in world history. I say 'world' history, because unlike many of the great minds of western civilization, Plato's work is arguably, the most recognized across many cultural boundaries. His work is studied in colleges and universities around the world. And his name is virtually synonymous with a love of knowledge (philosophy). More than any name from antiquity, 'Plato', for many, is the first name to come to mind when ancient philosophy or esoteric knowledge is the topic of discussion. Modern language even honors his teachings of love without desire or sensual attachment - put forth in the text, 'Symposium', by applying his name to the concept. (e.g., Platonic love)

It would be difficult, if not impossible to over-estimate the contributions of Plato and his contemporaries to modern ways of thought and civilization.

Written records of the Classical Greek period are somewhat better preserved than those from Pythagoras’ earlier period. This is likely due to the existing works being directly preserved by the activities of the Great Alexandria Library (c. 285-245 BCE) which boasted the ancient world’s most prolific knowledge sharing, duplication, and distribution operations. It is due to this fortunate timing and the popularity of Plato's works, that entire copies of his manuscripts are still available to us today. Even so, there remains a not-insignificant reliance upon contemporary writers, copies, and later texts referencing Plato’s work, in addition to the scarce original manuscript socked away in some museum.

Plato, who lived during the Greek civilization's ‘classical’ period, is primarily known for his more reflective philosophical work such as the ‘Allegory of the Cave’, still taught in many humanities-based curriculums. Many high school and college students may not be aware of his work in fields such as geometry, cosmology, or music. It is especially easy to miss his work on three-dimensional geometric constructs due to the overriding authoritative, mathematical texts of Euclid and Aristotle as well as further elucidating Pythagoras’ work on three-dimensional solids.

It is his work on these three-dimensional geometries that directly links Plato to our theoretical tonal systems. His development and discovery of the five ‘Platonic Solids’ could well be considered “harmony in geometric form”. The five solids were said to represent the five states of matter (Air, Water, Fire, Earth, and Aether). In Sacred Sonics, we have drawn upon the work represented by Plato’s five ‘sacred’ solids to extract from them a harmonic code of sorts, which along with other ‘sacred geometries found in the ancient world, guide us to tones and harmonies that are designed to be uplifting, healing, and generally beneficial to humanity.

All five Platonic solids can be nested to for a single conctruct

Plato is credited with the discovery that five 'perfect' 3-D solids nest together to form a single compound structure. Johannes Kepler and Tycho Brahe also used this as a rudimentary cosmological model over fifteen centuries later.

It is Plato's work on these three-dimensional geometries that directly links him to our theoretical tonal systems. His development and discovery of the five ‘Platonic Solids’ could well be considered “harmony in geometric form”. The five solids were said to represent the five states of matter (Air, Water, Fire, Earth, and Aether). In Sacred Sonics, we have drawn upon the work represented by Plato’s five ‘sacred’ solids to extract from them a harmonic code of sorts, which along with other ‘sacred geometries found in the ancient world, guide us to tones and harmonies that are designed to be uplifting, healing, and generally beneficial to humanity. To be completely fair, Pythagoras worked with these same three-dimensional constructs. But, it was Plato who discovered that five of these geometries are special constructs, each formed from a different, single polygon type. He further discovered that the five 'Platonic Solids', in proper proportion, contain or nest within each other to form a single construct that incorporates all of the five Platonic solids, and geometrically represents the theoretical structure of the whole universe. Of note, is the fact that Johannes Kepler and Tycho Brahe both utilized this same nested structure as a basic model of the cosmos some fifteen centuries later. (Nested Platonic Solids - Image credit : CosmicCore.Org)

Plato, like Pythagoras and Philolaus before him, also believed that properly constructed tone and frequency were important for healing human ills. Plato, however seemed to be primarily interested in treating or ‘soothing’ the ‘humors’ of the human mental states, rather than focusing on physical maladies. This period may represent the very first division point between holistic and allopathic approaches to health and wellness.

While Pythagoras lived much of his productive years as a political exile, in Crotone, the more politic Plato took up the mantle of his mentor, Socrates, and managed to carefully and successfully navigate the hazards between politics and higher knowledge. One must assume that the forced execution-by-suicide of his mentor Socrates, served as sufficient motivation for a more moderate approach than his mentor seemed capable. Plato’s school, founded in Athens became the model upon which future ‘Lyceum’ were operated. Like his predecessor, Pythagoras, Plato’s school provided a wide variety of intellectual pursuits of which music therapy was but a small part. However, the concept and practice of healing tones in music has never been far from the mainstream as even today, music therapy is a mainstay in mental health and spiritual practices.

Available Light & Sacred Sonics

The Home of Geometric Tone

The Mathematical Genius of Euclid

The Mathematical Genius of Euclid

One of the most mysterious of our Greek masters is Euclid. It is widely believed that ‘Euclid’ is not the man’s actual name but, is instead nothing more than an Anglicized version of, possibly of Euklees, Eukles (or similar). The tragedy here is that; no one knows for sure. And, we likely never will. On one hand, the word ‘euclid’ is said to mean “a copy of the same” and is sometimes synonymous with the word ‘geometry’. (Source: Wikipedia) Despite the widely held belief that Euclid lived after Plato and before Aristotle, placing him somewhere within the third century BCE, nothing is really known of the entity that put together incredible works such as ‘Elements’, a massive work of over 1200 pages (In the English translation) that pulls together an amazing array of mathematical and geometric knowledge into a single volume. Euclid is also credited with other monolithic works such as ‘Optics’ and ‘Data’. What this means to us today is unclear. But scholars have somewhat collectively stipulated to the principle that Euclid was indeed a real person, and that his works, especially in the field of geometry, are essential to the foundations of mathematics and of civilization.

This writer’s personal theory, should anyone care, is that some great team of scholars in the Alexandria Library complex, sometime during the reign of Ptolemy I, got together and pulled together all of this information from various sources, and compiled a single collection under the name ‘euclid’, which as mentioned above, could mean ‘copy of the same’. This wouldn’t be the first or last time a compendium of assorted works from various sources was placed in a single volume and given a simple, descriptive term as a descriptive title. And to me, it makes a lot of sense that this may be the case. But, to date, no one has stepped up to agree with me. So, there’s that.

The prevailing opinion seems to be that Euclid was an actual person. And there does exist some fairly decent evidence of this. But If this is true, the sheer genius of that one person absolutely beggars belief. The systematic collection of works that we call Euclidean geometry that are exhaustively outlined within the thirteen volumes of the work titled ‘Elements’, is a prime example of a level of mathematical and theoretical mastery that is difficult to believe could have originated from a single individual working alone, in Alexandria… in the third century BCE, among so many masters from around the ancient world. Nevertheless, we shall proceed as if the common consensus is indeed the case, and that Euclid is the name of a person and the originator of these massive volumes of knowledge.

Among the expositions of Euclidean geometry are the 360º in the radius of a circle and the formulae for calculating internal and external angles of polygons as well as the angles of intersection between any two line segments within an irregular polygon. These two applications are the primary contributions of Euclidean geometry to the theory of Sacred Sonics.

By analyzing each of regular polygons using Euclidean formulae, we are able to derive that polygon’s ‘resonance’ frequency from the sum of its internal angles. Available Light is NOT the first to utilize this method or to employ the resonance theory of geometry. However, our application of the frequencies obtained is applied to a wholly unique system in order to build entire tonal systems for any musical application.

All of this, thanks to Euclid, whoever that may have been.

Delphi, on the slopes of Mount Parnassus, was the site of Apollo's main temple complex and the home to the 'Oracle' and the Omphalos stone

Delphi, on the slopes of Mount Parnassus, was the site of Apollo's main temple complex and the home to the 'Oracle of Delphi' and the Omphalos stone; used by the Oracle to reveal the will of the gods.

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Philolaus of Croton

Philolaus of Croton, a student of Pythagorus, built upon his teacher's work and reportedly gave us the twelve-tone octave

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Musicians painted on papyrus

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What is Geometric Sound?

Honoring Nature and History To Affect Healing and Wellness

1

Natural

Geometric sound is not a unique concept within the musical realm. From the very beginning, great minds such as Pythagorus, Philalaos and many others have advocated for sounds that complement nature and the human-compatible frequencies

2

Verifiable

The nature of each tone in our geometric tonal systems can be reverse engineered using simple mathematics and geometry that have existed from time immemorial. One can trace the tone back to its roots in Pythagorean, Platonic, and Euclidean disciplines.

3

Balanced

Depending on your choice of tuning system, the practitioner will immediately notice differing but naturally harmonic tonal balance allowing for an extremely wide range of tonal palettes and emotional colors to work from.

4

Modern Equipment

Technology is a musician's friend - to a certain limit. The wide range of tools available in the modern market are still capable of working outside the confines of standardized tuning. Geometric tuning systems are designed for this world.

5

No Dogma

The world of Sacred Sonics is for everyone. The systems are flexible enough to allow modification into non-geometric and microtonal tuning systems. It's all about nature and choice. Now, we can actually have BOTH.

6

Well Documented

The long story of Sacred sonics, geometric tuning, as well as the full library of tuning tables are fully documented in the book, 'Sacred Sonics' - available in paperback or ebook formats at the more popular book outlets.