Geometry, Music and Healing

Geometry, Music and Healing

by Ani Williams

 

“Legend recounts how Orpheus was given a lyre by Apollo…by playing his lyre, Orpheus produced harmonies that joined all of nature together in peace and joy. Inspired by this Orphic tradition of music and science, Pythagoras of Samos conducted perhaps the world’s first physics experiment. By playing strings of different lengths, Pythagoras discovered that sound vibrations naturally occur in a sequence of whole tones or notes that repeat in a pattern of seven. Like the seven naturally occurring colors of the rainbow, the octave of seven tones”.
The Harmonic Lyre’ by Stephen Ian McIntosh

All of Creation is a singing matrix of frequencies, which can be experienced as color, sound, matter and states of consciousness. Through the research of Stanford University physicist William Tiller PhD, we find that all space, even a so-called vacuum is waiting to receive instruction from us…waiting for us to project our intention so that space or matter can have direction and take on specific qualities. What intentions are we sending to our world? I believe that this matrix of creation is waiting for the most harmonious vibrating chord to sound it into a perfect idealized form.

The discoveries of Japanese researcher Dr. Masaru Emoto have shown the glorious snowflake-like mandalas that form in water when a beautiful piece of music is played, or similarly, when a positive feeling or thought is projected into the water, such as appreciation and love. He has even conducted global ‘appreciation meditations’ with the goal of purifying some of Earth’s great rivers that we have polluted.

“High-speed photography of crystals formed in frozen water reveals changes in the water after specific, concentrated thoughts were directed toward it… Naturally, since water covers the largest portion of our planet, and comprises the largest percentage of our physical bodies, the impact of our thoughts and feelings will play a large part in the way our environments get created, both globally and personally.” (Dr. Masaru Emoto). Water treated with love or beautiful music reflected a molecular change and a harmonious geometry. The following image was photographed by Dr. Emoto after 500 people sent the feeling of love to the water:

people

 

This is a perfect example of what Swiss researcher Hans Jenny (1904-1972) discovered while projecting pure tones onto fine grains of matter or liquid and observed the forming of distinct geometric shapes. He termed this sound-matter connection Cymatics and his groundbreaking work has become a cornerstone of sound healing. The following quote is from the Hans Jenny website at www.cymaticsource.com:

“For 14 years he (Jenny) conducted experiments animating inert powders, pastes, and liquids into life-like, flowing forms, which mirrored patterns found throughout nature, art and architecture. What’s more, all of these patterns were created using simple sine wave vibrations (pure tones) within the audible range. So what you see is a physical representation of vibration, or how sound manifests into form through the medium of various materials.”

The pioneering research of Fabion Mamon in the 1970’s found that when they sounded a specific tuning fork tone onto a cancer cell, that cell would dissolve. Even allopathic medicine has adopted this same principle in new, non-invasive forms of surgery. Scientific American magazine reported one example of an effective method for removing kidney stones by identifying the frequency of the stone, and projecting the ‘reversed’ frequency to dissolve it.

This interrelationship of sound and matter is at the core of an exciting new wave of science, which is based on timeless principles well known to all ancient and indigenous cultures. Billy Yellow, a Navajo medicine man summed it all up with this wisdom: “Our task is to chant the world, chant the beauty. The world is a reflection of our chanting.” How are we each using sound to affect our state of being, the health of the earth and our children?

Ancient Seekers of Universal Harmony

Throughout the last few millenniums, dreamers, scientists, philosophers and seekers of the patterns of creation have studied the movements of the cosmos and the mirroring of these cycles and proportions on Earth. The ancient Chinese, Egyptian, Sumerian, Druid, and Mayan cultures including great thinkers and pioneers such as Plato, Pythagoras, Copernicus, and Kepler, all discovered the interconnectedness of the planetary cycles, sacred geometry, and musical scales long before modern science began to confirm these connections. The divine order of the movements of the cosmos and the sacred proportions found in ancient temple design, are the same principles found in music.

“According to Plato there are five mathematical sciences: (1) Arithmetic (2) Plane geometry, or the study of numerical proportions (3) 3 dimensional geometry, including the ‘Platonic Solids’ (4) Astronomy and (5) Music, which illustrates the harmonious composition of the universe.”
‘The Dimensions of Paradise’ by John Michell

Plato believed that the strongest of all life’s influences is music. In his treatise the Temaeus, Plato describes the numerical (vibrational–musical) creation of the physical universe and the soul, which animates it. He called his students to activate the ancient shrines and sacred temples of the earth with sacred song, employing ‘perpetual choirs’ in order to echo the harmonies of the Heavenly Choir.

Plato’s ‘Republic’ describes the cosmos as being held together by eight spinning ‘whorls’, like a giant spinning wheel with eight feminine weavers sounding the fabric of creation. Each of the whorls contained a planet, and on each planet was a siren singing her particular note, and emitting a specific color. “The diameters of the planets can be seen as corresponding to the strings of a lyre, in which case the note sung by a siren would be in accordance with the length of diameter of the planet she rode upon.” — John Michell ‘The Dimensions of Paradise’

 

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The German astronomer and mystic Johannes Kepler lived from 1571-1630 and was possessed his entire life with finding the cosmic proportions and musical harmonies, represented by the distances and orbits of the planets. His writings reveal that in addition to his lifetime of calculations and observations, he was deeply influenced by Egyptian hermetical science. His monumental work ‘Harmonice Mundi’, or Harmonies of the World, contained five books covering his life’s work on the correspondences between music, astrology, geometry and astronomy.

According to Stephen Hawking in his book ‘On The Shoulders Of Giants’, Kepler discovered how planets orbited and he paved the way for the later Isaac Newton to discover why. Kepler’s work focused on the five Platonic solids, their harmonic ratios, and how these shapes correlated with planetary orbits and sound frequencies. He found the musical tones of individual planets, and the musical scales of planetary movements. He was even able to determine that “…four kinds of voice are expressed in the planets: soprano, contralto, tenor, and bass.” (Stephen Hawking). Basically, Kepler had found the music of the cosmos, and that the same harmonic principles found in the stars, and life forms on earth are musical.

Perpetual Heavenly Choirs

“God hungers for songs.” — Marius Schneider

Between 1100-1300 AD hundreds of Gothic Cathedrals were constructed across Europe, inspired by the eastern Hermetic knowledge rediscovered by the mystical order of monk-knights, the Knights Templar. During the tenure and excavations of the Tempars at Solomon’s Temple in Jerusalem, they discovered the vaults of hidden artifacts and scrolls concerning the alchemical sciences of sacred geometry and architecture, sound, astronomy, and genetics. Ancient sacred relics are also said to have been in the Templar’s cache of discoveries there, including the Ark of the Covenant, the Holy Grail, and secrets pertaining to Mary Magdalene and a Holy Bloodline. (See: Article about Mary Magdalene. The building of the great Gothic cathedrals such as the ones at Chartres, Notre Dame in Paris, Salisbury, St.Denis, and Cluny was inspired by these transforming discoveries. These edifices were monuments to the rediscovery of ancient mysteries, a new elevated awareness, and were constructed using the principles of sacred geometry, harmonic acoustics for their transforming potential.

“The huge number of Gothic cathedrals that were erected, as graceful and sublime as if they were designed in heaven, have yet to be surpassed for their dignity and spiritual potency, almost a thousand years later.”
Dance of the Dragon’ by Paul Broadhurst and Hamish Miller
(The authors discovered many of these cathedrals are located on a major energy grid they call ‘The Apollo- St. Michael axis’, and stretches from Britain’s St. Michael’s Mount to Mt. Carmel)

The sacred architecture employed in these majestic structures reflected a new ‘alchemical light and specific acoustical properties’, according to ‘Dance of the Dragon’ authors, that was conducive to the constant rounds of perpetual choirs maintained by the monks. Interestingly, it is precisely at these millennium shifts, when perpetual chanting becomes a device of the collective creative intention. Sacred music and chant is always with us, but surges in its necessary popularity at these crucial turning points, as during the inception of Christianity in the first century AD, during the beginning of the first millennium and time of the Grail Romances, and now as we forge a new paradigm and write our ‘script’ for the next one thousand years.

Author John Michell has researched the tradition of ‘perpetual choirs’, in ancient Britain. According to Michell, these choirs were maintained in Britain in at least three sites: Glastonbury, Stonehenge and Llantwit Major in Wales, which together form the rim of a circle in the landscape, with the center at an old Druid site called Whiteleafed Oak. He found the distances between these sacred sites to be equal and corresponding to sunrise points and sacred proportions. Similarly, sacred sites in other cultures were also laid out in geometric relationship, and were maintained with sacred music and chant, which were synchronized with the seasons and cosmic cycles.

“Similarly, in Revelations, 24 elders stand before the throne of the Lamb, ‘every one of them having harps, and golden vials full of odours, which are the prayers of saints. And they sung a new song…’ The elders’ new song was their accompaniment to the appearance of the New Jerusalem and a new dispensation on earth.” — ‘The Dimensions of Paradise’ by John Michell

King David and his harp from a Medieval Bible c. 1170 AD

King David and his harp from a Medieval Bible c. 1170 AD

 

The Music of Atomic Shapes

Five basic three dimensional geometric forms are found to represent the five elements in creation: The tetrahedron–fire, the cube–earth, the octahedron–air, the dodecahedron–ether, and the icosahedron–water, as shown in order here:

solids

 

These five Platonic solids comprise the constantly changing dance of creation, the alchemical dance of the elements. “In bringing order to the universe the Creator gave geometric forms to the atoms….interacting with human senses to produce appearances and feelings.” John Michell

I was able to experience the ‘musical proportions’ of Platonic solids many years ago, when I was studying with Michael Heleus, who I consider to be a reincarnated Atlantean wizard. Heleus’ early pioneering research in music, mathematical proportions, astronomy and healing became one of my areas of study in sound healing during the early 1990’s. Heleus had discovered the musical proportions and corresponding tone scales of the each of the Platonic shapes, which included tuning his keyboard to specific frequencies to achieve the exact proportions.

During his presentations Michael would play the scales and geometries of each shape and the participants would meditate on the five different musical pieces, without his disclosing which geometric shape he was playing. After each piece, the listeners would describe which of the shapes they experienced. It was quite extraordinary, that every Platonic solid was directly perceived, felt, and ‘seen’ with the inner eye during each of the five musical meditations. This was my first experience of realizing the power of musical transmission and its potential to specifically re-order creation. This is exactly what the ancient mystics and scientists were telling us!

I was especially profoundly affected by the Dodecahedron, and while Heleus played the musical proportions, I felt as if I ‘became’ this geometric solid, and this shape and I became the Great Mother matrix of the universe. The dodecahedron can be seen to represent the order of the heavens and also the perfect shape of mediation between the infinite and the finite, the sphere and the cube.

The dodecahedron is comprised of twelve pentagonal (five-sided) faces, and represents the fifth sacred element, ether, or divine potentiality. Recently, quantum physics researchers in the US and France have said that based on measurements of cosmic waves left over from the ‘big bang’, it appears that the shape of the universe is a Dodecahedron. This is fascinating, considering there are five platonic solids and the corresponding five basic elements of life. The entire human race is joined in these same basic sacred proportions of the physical body as it is overlaid in a pentagram, with the arms and legs spread to make a five-pointed star, with the reproductive organs at the exact center. And there are five appendages from the human torso, five appendages on each leg and arm, five openings on the face, and five senses of physical perception.

If we can imagine the dodecahedral-pentagonal shape of the uni-verse (meaning one song), and see the human body pentagram geometry, we find in both a divine proportion and potential for harmonic perfection, inherent in physical embodiment and the harmony of the spheres. We embody the geometry of the cosmos! And we find that the Golden Mean proportions of the cosmos and our body temples are closely aligned with the harmony of the musical ‘fifth’, or stated another way, the universe and humanity are geometries singing!

“One of the properties of the pentagram is that the lines bisect each other according to the Golden Section …the ideal human proportions lie in the canon defined by the Golden Section or PHI.” Nicholas Mann’s ‘Sedona Sacred Earth’.

 

PHI Ratio and the Musical Fifth

In the book ‘The Power of Limits’, architect Gyorgy Doczi surveys the similarity between the sacred geometry proportions in ancient temple construction of the Golden Mean ratio (1.618) and the interval of the fifth in music (1.667). The fifth is the interval found in most sacred music and has a powerful harmonizing effect on the human energy system. The fifth is the first harmonic sounded by a plucked string and gives the note its depth and beauty. This music–geometry connection is well stated in the poet-mystic Goethe’s phrase that ‘sacred architecture (or human body proportion!) is frozen music.’

“Since its discovery by Pythagoras, the fifth has come to be universally recognized for its beauty…the fifth is an archetypal expression of harmony that demonstrates the ‘fitting together’ of microcosm and macrocosm in an inseparable whole. The fifth is a beautiful sound because it demonstrates how the universe works.” – ‘The Harmonic Lyre’ Stephen Ian McIntosh

All of creation expresses itself through number and number is frequency, manifest as color, sound and form, and even as emotion and states of consciousness. The effects of harmonious design based on sacred proportions can be experienced first hand when one enters an ancient temple in Egypt or a Gothic cathedral, such as Chartres. The effect can be immediately sensed as harmonious, powerful and centering, and being inside a space designed with sacred proportions helps us to access other dimensions of consciousness.

“The most common proportions found in ancient Egyptian temple architecture correspond to the most harmonious intervals found in music: the octaves, fifths, fourths, thirds and sixths. In the temple of Horus at Edfu, the dimensions of one chamber’s measurements of width to height equaled 2:3, which defines an interval of a fifth in music.” — ‘Rediscovering Music in the Architecture of Egyptian Temples’ by Antoine Seronde.

This expansion and transformation experienced by being inside a sacred space, can also be reached directly through listening to sacred music, or ‘aural geometry’. Most divinely inspired music, such as Gregorian chant, some ‘new age’ music, and the music of indigenous cultures, features the musical interval of the fifth. An easy way to understand a musical ‘fifth’, would be to use the white keys of a piano, and play middle C and counting C as the first note, play the fifth key up, which is G.

“… the Egyptians utilized musical scales analogous to our own. The positions of the harpists’ hands on the strings clearly indicate ratios such as the fourth, fifth and octave, revealing an unquestionable knowledge of the laws governing musical harmony.” – Lucy Lamy, Egyptian Mysteries (Thames and Hudson 1981)

The basic chords of most western music are made of a combination of a fundamental tone, a fifth with a third, or in the case of a C chord, the notes C-E-G, the first, third and fifth notes. However, when we leave out the third (E), the chord sounds distinctly ancient or sacred. I can remember that when I first began teaching myself to play the harp, I tended to play mostly in fifths, just because I liked the sound and the feeling effect of being centered and expanded when playing them. At that time I was not consciously aware of the harmonious principles at work. During those early days of my ‘harping’, I had a music colleague who played in symphony orchestras, who commented: ‘didn’t I play anything other than temple music?’

The Circle of Fifths and Chakras

The circle of fifths is a musical sequence in which we can find the harmonic progression of musical scales and also the harmonic relationship of the human energy system. Each human energy center, or chakra, is a spinning wheel or mandala of geometries, sound and color. The musical tones and colors traditionally associated with the chakras are: C (root) red, G (throat) turquoise, D (belly) orange, A (brow) indigo, E (solar plexus) yellow, B (crown) magenta, and F# (heart) green.

Beginning this harmonic cycle at the root or first chakra with the tone of C, we progress in the sequence of fifths, and end at the heart chakra and a tone of F#. Many have wondered why the heart chakra would be represented by the tone F#, rather than F, and the circle of fifths answers that question.

This interweaving of the charkas is more complex than the traditional linear progression and it is interesting to note the connections between these ‘chakra harmonics’. For instance, in energy and sound healing, there is a strong correspondence between issues in the root chakra–sexuality, survival and money and the throat chakra–our expression, speaking our truth. Working with the fifth harmonic of the root chakra and the throat chakra of authentic communication, these survival issues can heal. The harmonic relationship of the other chakras invites further explorations.

To the find all the notes in the western chromatic twelve-tone scale, we continue creating musical fifths beyond the first seven tones of the chakras. If we begin at the note ‘C’ and sound each consecutive fifth, we have all twelve tones, and arrive at the thirteenth tone, ‘C’ on a higher octave: C–G–D–A–E–B–F#–C#–G#–D#–A#–F–C. In the circle of fifths we can see how a musical scale is geometry!

Circle of Fifths (E to A) from ‘The Harmonic Lyre’ by Stephen Ian McIntosh

Circle of Fifths (E to A) from ‘The Harmonic Lyre’ by Stephen Ian McIntosh

 

Fibonacci Ratios and Musical Intervals

Leonardo de Pisa (circa 1180-1240 AD), better known as Fibonacci, discovered the uniformity of ancient harmonic wisdom. He realized that the natural branching, flowering, and spiraling forms in nature follow the same uniform laws found in musical scales.

He found this harmonic in nature is equal to a number sequence of 1–1–2–3–5–8–13–21–34–55–89–144 and so on, found by adding each number to the previous one to get the next number.

The Fibonacci series relates to all of the musical intervals, which comprise beautiful chords. The following table shows some Fibonacci ratio musical chords using the fundamental tone ‘A’:

 Note A A D F E C E C# F# C# D F
 Interval root octave 4th aug. 5th 5th minor 3rd 5th 3rd 6th 3rd 4th aug. 4th
 Fibonacci Ratio 1/1 2/1 2/3 2/5 3/2 3/5 3/8 5/2 5/3 5/8 8/3 8/5

 

The Fibonacci ratios were also utilized in sacred temple architecture, including the towering Gothic Cathedrals. Guillaume Dufay (c. 1400-1474) from the Netherlands composed music for the dedication of Florence’s cathedral of Santa Maria del Fiore in 1436. His musical piece was based on the Fibonacci series of tones, which corresponded to the dimensions of the cathedral’s dome. These ‘musical temples’ were part of the medieval renaissance of sacred geometry, Hermetic mysteries and the flowering of art and music.

The Geometry of Sound Healing

“The sky and its stars make music in you.”
Denderah Temple wall inscription, Egypt

The healing potential of the magical fifth and the natural harmonics of our beautiful earth hold a powerful key for bringing us back to a state of well being. Songaia (song of the earth) Sound Medicine was founded in 1992, a system of sound therapy based upon ancient knowledge of the harmonious arrangement of heaven and earth. The ancients understood that if we live harmony with the heavenly and earthly cycles, and use those harmonic principles in our physical environment, we can be whole, healthy and truly connected. Just spending time in nature puts us back in touch with the primordial harmonies that heal.

The basic purpose of Songaia Sound is to reintroduce the harmonic fields found in nature into our lives using a musical formula in twelve sound recordings. The twelve musical meditations are based on the twelve tones of the chromatic music scale, and incorporate the pure healing harmonics of harp, Australian didjeridu, voice overtones, and Tibetan bowls, all instruments used by ancient cultures in healing. Each of these twelve tones correlate with specific physical conditions, organs of the body, emotional states, and even vitamins and minerals.

The Songaia Sound Wheel illustrated below, shows sound, color and zodiacal associations. According to the findings of Johannes Kepler, Pythagoras, and many ancient cultures, the planetary frequency patterns are mirrored in life on earth, in music, geometry, and in our bodies. This was called ’musica speculativa’, or music as a mirror of the cosmos, by many researchers in Kepler’s era of the 16th century. (In the GONG project, modern science has been monitoring the tone emissions from the sun, and observing those effects on earth.)

One of the most exciting aspects of our work at Songaia Sound is in observing thousands of clients demonstrating the truth stated on the Egyptian temple wall at Denderah: “The sky and its stars do make music in you.” The pattern of sounds emitted from the planets at the time of birth, based on the positions of those planets, is mirrored in the human energy system. This pattern is like a blueprint of influences and tendencies, and each one of us has this unique ‘song-print’. The amazing thing about an individual ‘song-print’ is that the same planetary sound pattern is detected in the frequency pattern of the speaking voice. (Voice frequency patterns are also mirrored in each person’s ability to hear specific frequencies. Dr. Alfred Tomatis, a French ear and eye specialist, developed the Tomatis Method, with diagnostic and therapy centers around the world.)

“The body is held together by sound–the presence of disease indicates that some sounds have gone out of tune.” — Dr. Deepak Chopra

‘Songaia Sound Wheel’ © Ani Williams

‘Songaia Sound Wheel’ © Ani Williams

 

Each of us is a living symphony of frequencies…some of our notes singing in harmony, and some singing ‘off key’. Because of stress, trauma, and negative mental and emotional patterns, the instruments of our symphony need tuning up. Some notes in our body-mind symphony have become so stressed that they are missing, which makes it more difficult for our orchestra, or whole energy system to play. These missing tones can be identified by listening to the notes in our speaking voice with a digital tuner. (These frequency patterns are also mirrored in the individual’s planetary tone frequencies.) By knowing the frequency of something, we can alter or change it, and when the missing frequencies are played back, we can return to wholeness, health and harmony. (See Voice Spectrum Analysis)

Playing the full spectrum of tones of our living symphony, and especially audibly sounding these tones (called toning), has been found to have the following effects:

  • Releases ‘feel good’ endorphins and supports healthy immune system function
  • Nourishes and feeds the physical and emotional bodies, harmonizing the system
  • Assists in releasing limiting belief systems, stress and general dis-ease
  • Alters brain state, inducing alpha-theta states associated with healing
  • Synchronizes mind-heart-body rhythms and a sense of being centered and balanced
  • Expands creativity, vision, and clarity, opening a gateway for soul freedom

In our modern high-tech digital world, we have lost much of these healing harmonies in our daily lives. Hours spent at computers, on cell phones, traveling in cars and planes at high speeds, and living in structures that are most likely not designed with sacred architectural principles, we are removed from the natural harmonic environments that heal. In the ideal whole and healthy state, our bodies and minds are ‘singing’ with the harmonic ‘fifths’ and Fibonacci ratios of the stars and with all of the natural world.

“We are the stars which sing–we sing with your light.”
Algonquian traditional song

The Musical Geometry of Crop Circles

Gerald Hawkins, astronomer at the Smithsonian Astrophysical Observatory, author of ‘Stonehenge Decoded’ and crop circle researcher, has found that the proportional dimensions of the extraordinarily complex geometries of the crop circles are also in direct correspondence with musical intervals of the white keys of a piano. Does this indicate a musical intention from the ‘circle makers’? Given the divine harmonics within these amazing formations, they appear to be mandalas for awakening, or visual ‘alarm clocks’ with a language calling us to return to the essential harmony of creation before we destroy our beloved planet. They call us to return to the healing potential within divine proportions and sacred music, as in the writer Dostoyevsky’s prophecy that ‘beauty will save the world’. Most creation myths maintain that the world grows by way of song and music, and ’God hungers for songs’. (Marius Schneider)

After visiting many of these amazing crop circles in Britain over the last decade, I have found the energetic intensity and consciousness expanding effects to be immediate and potent, even greater than those experienced in ancient temples. Perhaps, that is because these ‘geometric temples’ are freshly constructed, and hence still alive and active in their energetic effects. Upon entering a formation, I have often heard the sound currents like a ringing in the air, and have seen increased light particles within and above the formation. In others, it has felt as if my very cells were being realigned and harmonized with a higher design or template. It is quite exciting that crop circles are now forming not just in England, but more frequently in the US and Canada, and Europe, including Poland.

While discussing the mathematics and geometry of crop circles with Michael Glickman in 2000, he said that the language of the circles appears to intentionally increase in complexity in a progression that correlates with expanding knowledge and consciousness. And these progressions of geometry often mirror the current planetary alignments and eclipses, a mirroring of the cosmos on the earth.

Regarding the claims that many of these phenomena are ‘hoaxes’, I would like to see someone work out the mathematical precision required to manifest one of these forms in the short time that lapses between a farmer seeing his field of growing grain and looking again, sometimes only minutes later, to see a huge design imprinted in the field. Often these formations are accompanied by observations of unusual lights and sounds.

The following crop circle images are from the 2003 season. The 13-pointed star geometry of the top image appeared at West Stowell, near Huish in Wiltshire, England. It was first reported on July 20th, and the photo was taken by Nick Nicholson.

The second formation shown here is the fantastic pentagram within the rays and pentagon, which appeared on June 29 at Sharpenhoe, near Barton Le Chay, Bedfordshire, England. The photograph was taken by Russell Stanard.

weststowell

Barton

 

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text and photos
©Ani Williams January 2004