Dissertation Literature Review



The literature in this review covers various themes and the analysis is aimed at furthering our understanding of how the number system constructs the universe, organic matter and their simultaneous relations to music harmony. Exploring connections between Numbers, harmony and Organic Life from the micro to the macrocosms of the universe. Identifying how tuning methods have developed and changed from ancient Pythagorean discoveries and how harmonies give physical/ emotional connections to music, using some examples from 21st Century music and holistic therapeutic approaches. These topics can be studied through the following breakdown in categories to identify the importance of harmony in life and music.

  • Mathematical Construct of the Universe
  • Micro to the Macrocosm
  • Importance of Harmony (528hz)
  • Tuning Methods
  • Holistic practitioner and the 21st century musician

The five main texts in this review are,

  1. Quadrivium (2010) – Various Authors
  1. The World is Sound: Nada Brahma, Joachim-Ernst Berendt (1983)
  1. The Book of 528hz, Prosperity Key of love: Leonard G. Horrowitz (kindle fire edition)
  1. A Beginners Guide to Constructing the Universe: Michael S. Schneider
  1. The Golden Section Natures Greatest Secret: Scott Olsen (2006)


Mathematical Construct of the Universe

Centuries of scientific study show that in all efforts to explain the wonders of the universe, Numbers and Geometric Shapes have been the tools and language in which such sanctified questions can be addressed. The numerical system is that of a universal resonance beyond all cultures and language and the Images of the numbers that we humans relate to are only cultural representations of the same system.

By looking at the qualities of each number in these tests we can see a clear illustration of how tangible matter is formed and how harmony is created, playing vital role in matter being manifested.

Sacred Number is the first text within the book Quadrivium, it talks about the attributes and power of each number. The One is described as ‘a mysterious conundrum’ (Lundy, M., P12, 2010) to explain it would lead to misrepresentation. The One is referred to by many names such as; unity, The One and God, (Lundy, P12, 2005) it is beyond all apprehension, unexplainable because to try and explain it is to be separate from it.

‘’The One is the limit of all, first before the beginning and last after the end, alpha and omega… …the origin from which the universe emerges, the universe itself and the center to which it returns. It is point, seed and destination.’’

(Lundy, M., P12, 2010)

Lundy states that the one exists in all equally, without one there is nothing but on the other hand there is no-thing within it (Lundy, P12, 2005), it’s a unique number as it remains one when multiplied and divided by itself. The One is unique, the seed and Omni-present, a pure tone in regards to music. Educator and Writer, Michael S. Schneider, author of A Beginners Guide to Constructing the Universe, agrees with Lundy stating,

…Oneness, expressed as a point and a circle, the foundation for our geometric construction of the universe.”

(Schneider, M. S., chapter 1, 1995)

Two is then described as duality or the dyad; it represents the opposites having equal force. Authors Lundy, Schneider and Berendt are in agreement about the principles of number two.

‘’..positive and negative charge in electromagnetism, the in-and-out of our breathing.’’

(Lundy, M., P14, 2010)

The balance created in the two bind the two opposites to create a harmonious one. 

‘’…that essence being to bind many together into one, to equate plurality and unity.’’

(Schneider, M. S., chapter 2, 1995)

In musical terms the dyad is represented as the ratio 2:1 being the octave above or below any chosen note. It is said to be,

‘’…the most ‘’harmonious,’’ namely the octave, the proportion 1:2, which has always been used to signify the polarity of the world: yang and yin.’’

(Berendt, J., P61, 1983)

Three is the first-born number out of the parental properties 1 and 2. Unifying the duality, three brings balance and harmony to the equally opposing forces. Past, present and future, the saying ‘’hip, hip, hooray’’, and the abbreviation of the alphabet, ABC’s are all rhythmically sound, rolling off the tongue with ease giving a sense of unification or completeness however, a sort of cliff-hanger dissonance if pronounced in any other way. On a two-dimensional plane the triad is the first drawn surface and a stable structural polygon. (Lundy, P16, 2010) Demonstrated through the process of birth, life and death,

‘’The triad appears in nature, in principle and in form… …In music the ratios 3:2 and 3:1 define the intervals of the fifth and its octave, the most beautiful harmonies other than the octave itself and the key to ancient tunings.’’

(Lundy, M., P16, 2010)

Schneider’s book identifies the same findings by stating,

‘’A triangle is a statement about relationships and balance. As the centers of the two circles repel and pull at each other, a reconciling t

hird point occurs naturally above the place where the circles cross and agree.’’

(Schneider, M. S., chapter 3, 1995)

Four becomes the first tangible manifestation in numbered geometry as the two-pairs make the first 3rd dimensional shape. The four-faced tetrahedron is just as fundamental as the sphere and triangle for the construct of all matter (Lundy, P18, 2005).

‘’Four is the first-born thing, the first product of pro-creation, two-twos. …the basis of three dimensional space…

…All everyday matter is appropriately made of just four particles: protons, neutrons, electrons, and electron neutrinos.’’

(Lundy, M., P18, 2010)

 Used often in figure of speech such as

“a square meal, of square living, being fair and square.’’

(Schneider, M. S., chapter 3, 1995)

 We associate the structure of reliable strength to this shape subconsciously (Schneider. chapter 3, 1995). Schneider also relates to this by calling it ‘the mother substance’ referring to the four elements as Air, fire, water and Earth as the symbolic tetrad for the natural earth (Schneider, chapter 4, 1995).

‘’Solid ground, terra firma, is the supreme symbol for substance, mass, volume, strength and stability’’

(Schneider, M. S., chapter 4, 1995)

Schneider and Lundy share similar views about the number Five. Claiming it to have a magical quality and directly linking it to life itself many times. The torso owns five extensions, we own five senses, and more obviously five fingers and toes. The straight edged outlining shape of most leaves are mainly pentagon, there are 5 petals on many flowers including the daisy (Schneider, Chapter 5, 1995). Country flags or company brandings also frequently use the five-pointed star as a psychological icon brandishing Excellence or Energetic Power. (Schneider, Chapter 5, 1995) Venus is the goddess of love, orbiting around earth leaving a five-pointed star in the geometric orbit path and in music the pentatonic scale is the most universal harmony created in intervals of fifths.

‘’The Renaissance demand for intervals involving the number five, like the major third, which uses the ratio 5:4, produced the modern scale.’’

(Lundy, M., P18, 2010)

 Comparing the perspectives, Schneider and Lundy’s comments about different dimensions of space, and space within space lean toward the argument that numbers, or the counting system really is integral to development of tangible matter. The geometry becomes more intricate with more sides or faces as the system grows. Take the number 12 for instance, 12 houses the 1, the monad. The 2, Duality, the 3, first born number, the 4, tangible shape and the 6. It is the first abundant number with all of the sub-sets adding up to more than the starting number. The western chromatic scale is simultaneously mapped out using 12 steps. Each note placed a semi-tone apart, the scale is measured that of equal temperament.

‘’12 enjoys the third dimension and is the number of edges of both the cube and octahedron. The icosahedron has 12 vertices, and its dual; the dodecahedron (literally ‘twelve facer’) has 12 faces of regular pentagons. Twelve spheres fit perfectly around one to define a cub octahedron.’’

(Lundy, M., p.34, 2010)

From the discussions about numbers we can see that integral to the development of tangible matter is a step-by-step process that inherits more qualities each time, having undergone a transformation in space-time. Reaching beyond all cultures and language the number system is encoded into everything we know from the micro sub-atomic levels to the macrocosmic constructions of the universe, numbers make shapes, which are the fundamental building blocks of life.

Micro to the Macrocosm


A Beginners Guide to Constructing the Universe has outlined what some have reviewed as suppressed or forgotten but sanctified information (Schneider,1995). Educator and writer Michael Schneider argues that having always existed simultaneously with the patterns of nature,

‘’Geometry is the bridge between the one and the many’’

(Schneider, M. S., chapter 1, 1995)

Whether counted in notched bones, rope knots, pottery markings, (Schneider, 1995) a tally system or roman numerals they are all simply means to communicate the same process of development of space in time. Every shape, pattern and network of patterns that we see in the beauty of natures creations, are replicated in the structure of numbers.

‘’By studying the recurring harmonious patterns inherent in mathematics, music, and nature, ancient mathematical philosophers recognized that consistent correspondences occur throughout the universe’’

(Schneider, M. S., 1995)

 Maria Lundy correlates with Schneider in her book titled Sacred Geometry by giving example to the One, as the single point on a piece of paper, the oneness, the infinite wholeness. Two, being the duality or horizontal line away from the central point and then Three, being the plane joining the one and two, thus creating a 2D shape or plane of existence. If 2D shape is rotated, it takes on a 3rd dimension thus becoming the architectural blueprint to the platonic shapes.

‘’Sacred Geometry charts the unfolding of number in space and differs from mundane geometry in the sense that it moves, concepts and products are regarded as having symbolic value and meaning.’’

(Lundy, M., P63, 2010)


 The Golden Ratio, also known as the geometry of everything is a sequence of numbers are concluded from adding the previous two together for example,

0+1=1, 1+1=2, 1+2=3, 3+2=5, 3+5=8 and so on.

These harmonious intervals duplicate just under double the size difference, 1.61803398875 to be precise.

Professor of Philosophy & Comparative Religion at the College of Central Florida, Scott Olsen decodes the geometric mysteries in his book the golden Section, Natures Greatest Secret running parallel to the views of Schneider, Lundy and Brahma about the Fibonacci code.

‘’Nature widely expresses the golden section through a very simple series of whole numbers. The astounding Fibonacci number series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377…is both additive, as each number is the sum of the previous two, and multiplicative, as each number approximates the previous number multiplied by the golden section. ‘’

(Olsen. S., The golden section nature’s greatest secret, P10, 2006)

Most plants replicate the harmonic fifth interval by spreading their leaves exactly half or a third of the distance away from the first leaf to ensure enough surface area feeds from the sunlight. The golden ratio is found in all living things.

‘’Fibonacci numbers occur in the family trees of bees, stock market patterns, hurricane clouds, and self-organizing DNA nucleotides… … A turtle has 13 horn plates on its shell, 5 centered and 8 on the edges, 5 paw pins, and 34 backbone segments.’’

(Olsen. S., The golden section nature’s greatest secret, P10, 2006)

The institute for the Science of Harmonics in Vienna studied the dimensions and proportions of the female to the male human body. In conclusions they reported that,

“in women, the minor proportions, minor thirds and 6th’s, are dominant, whereas in males it is the corresponding major intervals.’’

(Berendt, J., P83, 1983)

Olsen concurs by saying,

‘’The structure of both rhythm and harmony is based upon ratio.’’

(Olsen. S., P10, 2006)

 He goes on to say that musical harmony is a means to lift the soul out of the realm of mere opinion, allowing it to pass through intelligible realms of knowledge structured on mathematical reasoning. (Olsen. S., P38, 2006)

In relation to the research study of this literature, it is clear to see that the harmonious intervals of the golden ratio are apparent in all living things from plants to humans, As we grow and develop these harmonious intervals should we not live in harmony with the natural order of creation?

Importance Of Harmony


Dr. Leonard G. Horrowitz is a master of public health working in the Research

Facility at Harvard University. At the for-front of the re-emerging ‘knowledge of the ancients’ and advantages of vibrational harmony, his book 528, The prosperity of Love compiles intense studies on the subjects matters; energy, frequency and vibration. We can measure frequencies of energy and matter giving us further insight to the benefits of harmonious vibrations on organic matter. Although referencing his work from previously relevant sources like Platonic and Pythagorean beliefs, Horrowitz is often concurring with Schneider and Lundy’s ideas about the constructs of the universe, explaining in detail how the alphanumeric system is totally responsible for the creation of cymatics, which is the study of ‘sound on matter’. He explains how Peter Petterson’s extensive studies of cymatics are,

“ the primordial musical-mathematics of existence and sustenance.’’

(Horrowitz, L. P24, 2011)

‘’…creative connection between sound vibrations and physical reality. His work laid the foundation for scientifically comprehending creationism…

(Horrowitz, L. P24, 2011)

Horrowitz also identifies that human DNA and Chlorophyll resonates at 528hz, with this being said, in relation to the earlier mentioned studies of the golden ratio relating to the the male/ female body proportions in Vienna, (Brahma, P83, 1983) are we beginning to see a structured symphony of life emerging within harmonic intervals of organic growth through frequency and vibrational manifestation? Schneider’s book agrees by saying,

‘’Look at the forms your most familiar with, like plants, a flower, pineapple, or pinecone, and practice seeing them as not as ‘’things’’ that simply pop in into view but as the result of gradual process of manifestation.’’

(Schneider, M. S., 1995)

Understanding that organic growth is a gradual process Brahma states:

‘’There is nothing harmonic in germs, seeds, or sprouts. The plant has first to develop before its harmonic beauty reveals itself to our eyes, in the leaf shapes and in the blossoms. The growing process of a plant from germ to fruition is a constant reminder that harmony is a goal to be reached.’’

(Berendt, J., P122, 1983)

Vital for organic growth, chlorophyll is responsible for carrying the charged energy electrons from the sunlight into your bloodstream, and is also responsible for sun energy being absorbed through leaves to plants. If we take a closer look at the molecular structure of chlorophyll compared to the hemoglobin (oxygen carrying molecule) in your blood we see the geometry is almost identical.


Referring to it as the superconductor and optimum energy transducer this spiritual transformation of energy exists universally, eternally and hydro-sonically vibrating reality into existence through electron resonance.

‘’You are a digital bio-holographic, precipitation, crystallization, miraculous manifestation coming out of water!’’

(Horrowitz, L., P24, 2011)

Referred to as the ‘Frequency of Love’ Horrowitz discusses how we can map out the frequencies of feelings and emotions to seven points of the chakra in the human body. Love is a harmonious 528hz e-motion. E being the electrical impulse sent through the nervous system in motion vibrating harmoniously with another source or stimulant.

‘’Based on substantial evidence compiled in this book, that warm fuzzy feeling you have in your heart when you are in love – the vibration of heart-felt adoration is 528. It is a key, a musical note like no other, fundamental to creation.’’

(Horrowitz, L., Preface XVII, 2011)

 He proves there were 9 original core tones of the universe known as the solfeggio tones. Horrowitz discusses that 528hz is the central triad frequency of these original solfeggio tones and is the harmony of love.


Berendt appears to relate to Horrowitz harmony theory by identifying in various cultures the Great Tone:

“Hsüeh-tou Ch’ung-hsien, a chinese Zen Master of the tenth century, once said: ……The Great Tone is the tone that goes beyond all usual imagination.”

(Berendt, J., P171, 1983) 

“The great tone is the tone of being or, as the Indians put it, the tone of the self, of the Atma. The Great Tone is Nada Brahma, the tone from which God made the world, which continues to sound at the bottom of creation, and which sounds through everything.’’

(Berendt, J., P171, 1983)

“In Latin the term meaning “to sound through something” is personare. Thus, at the basis of the concept of the person (the concept of that which really makes a human being an unmistakable, singular per-sonality) stands a concept of sound: “through the tone.” If nothing sounds through from the bottom of the being, a human being is human biologically, at best, but is not a per-son, because he does not live through the son (the tone, the sound). He does not live the sound which is the world.”

(Berendt, J., P171, 1983)

Horrowitz also talks about how John Lennon’s,

‘’…research probably indicated that diatonic scale tunings produced more “ecstatic listening,” as he sought superior, more spiritual, resonance with longer sustains.”

(Horrowitz. L., P36, 2011)

Is it possible John Lennon had an understanding of the meta-physics of music given the anti-war and peace loving nature of his work? Horrowitz discusses how tuning methods have changed over time and by using John Lennon’s, Paul McCartney and Elvis Presley’s sound works as examples, he expresses the impact different tuning methods have had on the music industry in the past. It was common knowledge that the piano that recorded Imagine was tuned to the Solfeggio harmony of 528hz (A-432hz).

“…Christopher Louis… An avid investigator of the solfeggio frequencies… posted on youtube comparisons of 528hz and some Lennon and McCartney classics, including Imagine, Hey Jude, Let it be… concluded, McCartney “has been tuning himself and his band to 528 since at least 1999”.”

(Horrowitz. L., P37, 2011)

 Horrowitz gives us great insight to the importance of 528hz harmony and Ancient Solfeggio Tunings. Although the standard tuning may have been imposed and institutionalized, Cymatics are a visual representation for all to see the geometric harmony in the original Solfeggio note of A, as compared to the ‘standard’ 440hz tuning. Should all musicians be tuned the original Solfeggio Frequencies?


 Tuning Methods

 There are varying but similar views between Ashton, Berendt and Horrowitz on the subject of tuning methods. Taking the more holistic approach Berendt disserts the ear to be an accurate mathematical measuring device, similar in that to Olsen’s views about the eyes, the ear is also

“a gateway to the soul”

(Berendt, J., P136, 1983)

…Including that,

“Most musicians have discovered that a highly trained ear can beat the tuning fork,”

(Berendt, J., P136, 1983)

The underground health reporter published some familiar views with Berendt online. Conversations with Dr. Mitchell Gaynor, Director of medical oncology in New York reveal how the medical industry is only recently beginning to seriously consider the ancient knowledge of harmonic vibrations. Recent scientific studies show,

“Sound can actually change our immune system,” explains Dr. Gaynor. “Our Interluken-1 level, which is an index of our immune system, goes up between 12 ½ and 15% after Gregorian chanting or listening to certain forms of music. And after listening to this music for 20 minutes, our immunoglobin levels in our blood are significantly increased.”

(Read more: http://undergroundhealthreporter.com/tibetan-singing-bowls-sound-healing/#ixzz3YVd2iuDr)


 Since the Pythagorean days of tuning it is known that space was divided by ratio and frequencies assigned to them. The study of whole tone ratio’s such as the harmonic fifth were considered ‘perfect’ however the ancients already knew there as a slight imperfection in that after every 53 ‘perfect fifths’, the difference in ratio or space is 1.013643, commonly known as the Pythagorean comma,

“Is this why a near miss is so often more beautiful than perfection?”

(Ashton, A., P226, 2010)

 Berendt appears to agree with the Pythagorean Comma by stating,

 “Harmonic correspondences are correspondences in two senses: they are quantitative, since they can be computed, and qualitative since they can be heard. Yet the fact that a differentiation exists between “qualities” and “quantitative” implies that “deviations” must exist.

(Berendt, J., P86, 1983)

528 the prosperity of love talks about how elite banking families have played part in the changing of tuning methods and investments into Sonic Warfare studies are responsible for ‘standard tuning’.

“The monopolization of the music industry by banking families representing the illuminati, features this imposed 440hz frequency that is “herding” populations into greater aggression, psychosocial agitation, and emotional stress.”

(Horrowitz. L., P85, 2011)

Introduced and institutionalized to the western world in 1930’s and naming it cult control over the music industry ‘standard’ 440hz is interestingly opposing the nature of John Lennon’s works particularly the track Imagine that was recorded on a white piano being tuned to the original Solfeggio Tuning, A at 432hz. For the purposes of changing key easily the western chromatic scale has proven to be integral however the amount of intervals does not change when changing tuning.

Only the frequency or pitch of the sound is changed in turn having massive affect on the physical properties of matter. Therefore; it is true to understand that shifting instrumental tuning up from the original Solfeggio Frequencies, being note A at 432hz to the ‘standard’ A at 440hz, not only vibrates in dissonance to natural harmony but also causes physical distortions on molecular level, this is also proven visually through cymatics studies.

“…he was alarmed at his discovery that bioenergetics research in acoustic science funded by the Rockefeller Foundation focused on producing the social impacts of emotional arousal and even mass hysteria.”

(Horrowitz. L., P95, 2011)

 Holistic practitioner and the 21st century musician

Horrowitz explains that popular music and tuning methods were experimented with, resulting with the mid 1950’s seeing the first case of music “mass hysteria” during an Elvis Presley concert. The musicians playing for the king of pop were all playing in the newly ‘standardized tuning’ as opposed to a more relaxed crowd he previously played to using the original Solfeggio frequencies.

“These revelations best account for the mass hysteria demonstrated by audiences responding to “rock-n-rollers”, initially Elvis Presley and the “British Invaders” The Beatles. It was recently revealed that The Beatles were barred from playing in Israel following an investigation that promoted the education ministry to conclude The Beatles performances caused: Hysteria and Disorder… “There is no musical or artistic experience here, but a sensual display that arouses feelings of aggression replete with sexual stimuli.””

(Horrowitz. L., P96, 2011)


 Considered ancient healing knowledge, Buddhist monks for centuries have made singing bowls that are singing the same resonance as the 7-chakra points earlier mentioned in Horrowitz feelings and e-motions studies.


The literature in this review has shown similar and different themes throughout. Some books within the Quadrivium series, The Golden Ratio and The worlds is sound: Nada Braham have strong correlating findings of the importance of numbers and geometry in relation to harmony in life and music. The book 528 gives an in-depth look at the solfeggio frequencies and the importance of harmony and its effects on biological matter.

The objective of this review was to determine correlating themes between literature in order to establish the importance of harmony in life and music, accomplished by identifying a list of themes to research. From the literature reviewed it is clear that this subject is vast and complex. In order to research further in this particular subject area other possible literature to review could be;

  • Sonic Warfare By Steve Goodman
  • Music and the Making of Modern Science by Peter Pesic (which looks at music from ancient Greece to how it has shaped modern day science.)

Researching additional literature would enable further themes to be explained such as

  • Sound as weaponry
  • Music development of science through history


  1. LUNDY, M et al. (2010). Quadrivium: Number, Geometry, Music, Heaven. Glastonbury, UK: Wooden Books.
  2. SCHNEIDER, M. S. (1995) A beginner’s guide to constructing the universe: the mathematical archetypes of nature, art, and science. New York, NY: HarperCollins Publishers.
  3. BERENDT, J. (1983), The World is Sound: Nada Brahma. Vermont, USA: Destiny
  4. OLSEN, S. (2006), The Golden Section Natures Greatest Secret, Glastonbury, UK: Wooden Books.
  5. HOROWITZ, L.G., (2011), The Book of 528: Prosperity Key of LOVE, USA: Tetrahedron Publishing Group.
  6. http://undergroundhealthreporter.com/tibetan-singing-bowls-sound-healing/#ixzz3YVd2iuDr)


  1. GOODMAN, S. (2010), SONIC WARFARE Sound, Affect, and the Ecology of Fear. USA: Massachusetts Institute of Technology.
  2. PESIC, P. (2014), Music and the Making of Modern Science. USA: Massachusetts Institute of Technology.

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