Harmonic Theory:
A long time ago, Pythagoras, the Greek mathematician; you know, the one who is famous for giving us the equation for figuring out the sides of a triangle (a²+b²=c²);
discovered what is known as the harmonic series. Pythagoras- his theories, theorums, philosophies, and equations- were all based on his observations of the natural world.
Pythagoras, like Plato, believed in what Plato called “The Music of the Spheres”.
Although referring to the planets in its phrasing, the philosophy of “The Music of the Spheres” extended to all relations in nature; within and without.
Within this philosophy, natural objects; like planets and stars on the macro scale, and trees and rocks on the micro scale; both influenced and interacted with each other. In fact, the scaler dimensions of this philosophy can be extended to the most macro (entire galaxies) and most micro (atoms, quarks, etc..). All things and groupings of things influence and interact with each other.
For Pythagoras, this was represented in what the Greeks defined as harmonia (basically translated as balanced and interconnected). Pythagoras postulated that all things, macro and micro, are in harmonic relationship with each other.
In order to test this theory, Pythagoras performed a number of experiments with resonant objects of differing length. It is thought that Pythagoras worked with strings of varying length, yet it is completely possible that he also worked with sticks, rocks, and resonant containers as well.
Pythagoras observed that objects shared harmonic qualities of tonal vibration when cut in half or doubled. We know this harmony to be an octave. In observing this 2 to 1 octave relationship across differing media, Pythagoras continued to experiment by making adjustments to the respective lengths. He took the length of a string halved twice (observing two octaves and equaling 1/4 in length) and added this to one halved section. This creates, of course, 3/4 the length of the total string. When compared against each other; the whole length against the 3/4 length; we hear what is known as a perfect fourth in harmony.
Pythagoras continued these experiments and observations (halving and combining) until he was able to complete the entire chain of what is known as the harmonic series.
Pythagoras observed the pattern of relationships and deduced mathematical representations that allowed him to continue the pattern even when halving was no longer possible.
Pythagoras observed the harmonic chain of frequencies within the harmonic series to have tonal relationships and order that today we call an arpeggio, or 1st, 3rd, 5th, 7th, 9th, 11th, 13th.
Pythagoras continued the math examining octave 2:1 relationshiops and finally reduced the frequency relationships down to one full octave. This is what ultimately led to the solfeggio system, or “do re me fa so la te do”, that is most common today. This chain of frequencies is also known as the major scale.
Pythagoras and Plato believed that certain harmonies- the 4th, the 5th, and the octave- were more dominant and special than other harmonies. Due to these special qualities, the 4th, the 5th, and the octave were supposedly considered to be more healing and divine.
The specific quality that 4ths, 5ths, and octaves share is known as consonance. Pythagoras observed that certain harmonies (the 4th, the 5th, and octave) vibrated more symmetrically and mathematically even; while other harmonies within the harmonic series vibrated more erratically and uneven. These erratic harmonies are known to have a quality which called dissonance.
So, harmony is composed of both consonance and dissonance. Each individual resonant object or string contains all the frequencies within the harmonic series. In fact, everything is composed of frequencies that conform to the harmonic series relationships, and so, all things share qualities of dissonance and consonance.
Sympathetic Vibration/Resonance:
Sympathetic vibration is a natural harmonic phenomenon and tendency that occurs automatically as material objects, substances, energies and wave forms come into contact with other wave forms having similar harmonic frequency qualities. It is also known as sympathetic resonance.
During sympathetic vibration/resonance, independent vibrational actions co-occur in sympathetic response to each other.
Due to the overtone relations within the harmonic series that exists in nature and the universe overall, like frequencies vibrate with like frequencies according to the harmonic principles which Pyrhagoras illuminated.
Basic examples for understanding:
- Tuning forks- When one tuning fork is struck and held near another fork of the same frequency, the unstruck fork will vibrate.
- Piano strings- Shouting or singing near a set of undamped piano strings can cause the strings to vibrate.
- Body cavities and organs- Low frequency sounds and infrasonic vibrations can cause body cavities and organs to vibrate.
- Bass notes- Bass notes from music can travel through walls and ceilings because most construction materials have low resonance frequencies.
- Cymatics- Exposing water and other substances like sand to vibrational frequency shifts the organizational patterns of the substance. Quite literally, the substance sympathetically configures itself into geometric patterns that represents the frequency wave-form in a visual expression of sympathetic resonance occurrence.
Sympathetic vibration occurs when a passive object responds to external vibrations that have a harmonic relationship. The effect is most noticeable when the two objects are tuned in unison, an octave, 4th, or 5th apart, yet all shared harmonic intervals along the harmonic series do resonate sympathetically. The more consonant harmonies are more easily observed and have greater resonant effect.
Sympathetic vibration can be used in musical instruments to produce desirable and undesirable effects, yet sympathetic resonance also has many inherent applications as well as potential applications within extra-musical domains such as physiology and health, biology and environment, physics and energetics, and even imagination and psychology. It may be important for humanistic capacities such as empathy and compassion with respect to relationships, as it allows us to feel what others are feeling.
Concept of the Fundamental:
The fundamental is the primary frequency all other frequencies orient sympathetic vibrational relations from. In the solfeggio system- DO RE ME FA SO LA TE DO, DO is the fundamental. When DO is struck, all the remaining frequencies within the solfeggio system vibrate sympathetically. Although other frequency notes share sympathetic resonance qualities within the scale, DO is the most dominant and gives emphasis to the other harmonic relations and patterns for what is called the key.
All resonant frequencies, regardless of dimensional range or field scale, resonate sympathetically with the relative fundamental. This relationship in particular has many applications that will be discussed throughout the teachings presented
Entrainment:
Entrainment is like sympathetic vibration if the frequency was greatly slowed down. Whereas sympathetic vibration or resonance concerns frequencies, entrainment is concerned with rhythm or beat, and, ultimately, rhythmic beat is a synonym for frequency in a way since rhythmic beat concerns a definite pulse within a specific period of time.
Whereas frequency is wave cycles per second or Hz, rhythmic beat cycles are calculated according to beats or pulses per minute.
Entrainment is the process of synchronizing or aligning systems. It can occur in many contexts including biology, engineering, neurophysiology, and psychology.
Entrainment is defined by a temporal locking process in which one system’s motion or signal frequency entrains the frequency of another system. In basic terms- as a rhythmic pulse or pattern is repeated within one domain or system, the rhythmic nature of another domain or system will begin to mirror the pulse. This is entrainment.
Imagine a large group of individuals randomly playing drums in a circle while one large base drum in the center maintains the same moderate steady pulse. Eventually, all drummers will align with this central pulse; not necessarily playing exactly the same pattern, yet in sync rhythmically.
The application on a musical level is obvious, yet this principle of entrainment applies to extra-musical contexts as well.
General Practical applications of entrainment within-
The Body:
Within the body there are many rhythmic cycles that occur daily, seasonally, and through the various stages of life.
Circadian rhythms refer to biological variations or rhythm that occur within a cycle of approximately 24 hours. The circadian clock of the body is based upon the approximate 24 hour light and dark cycle of the day.
Organ regeneration, chemical and hormone activity, nasal dominance, tissue regeneration, and circulation are all processes that follow circadian rhythmicity within the body. Research has shown that regular exposure to light and dark entrains the circadian rhythms of the body.
Depending on location, the regularity of the light and dark cycle varies, as well as within different seasons. Although seasonal shift can be considered natural, things like artificial light and illuminated screen technologies can throw off circadian rhythmicity and result in imbalanced health.
Mental:
Mental states and activity as well can be affected by circadian rhythmicity due to the inherent connections with neuro-endocrine chemicals and hormones such as melatonin, dopamine, and serotonin, yet brain activity has also been shown to be entrained to more than just circadian rhythms.
Overall, when exposed to specific rhythmic patterning, various layers, areas, and hemispheres of the brain have been shown to be entrained. This entrainment has been shown to alter mental states of perception with regards to attention and focus.
Some rhythmic exposure entrains the brain in such a way that more acute and pinpoint attention results, whereas, other rhythmic tempos and patterns entrain the brain to produce states of perception that are more expansive, meta-conscious, and global.
Emotions:
With respect to emotions, entrainment has been shown to both produce and alter states of perceptual feeling. If excitement and anxiousness is perceived, a slow calm regular rhythm can entrain the emotion into calmness.
The opposite is also true- a quicker rhythmic pulse can produce excitement and related emotional qualities.
This occurrence has been demonstrated time and time again in movies, marketing, shopping malls, and gyms.
The Senses:
Rhythmic entrainment can both excite and sedate sensory activity. Certain rhythmic pulses can entrain the body in such a way that the eyes focus more acutely and the ears listen more intently. The nose can smell with heightened discernment and the tongue can taste more refined.
As well, rhythmic patterning can entrain the senses to broaden perspective in scope and take in more information and detail. The skin can feel from greater proximity, the eyes can perceive expanded ranges of color and light, the ears can attend to broader expanses, the nose can smell at greater distance, and the tongue can taste more informed.
The senses become entrained to both the world within and the world outside.
Nature:
All of nature is rhythmic–
- the day and night,
- the seasons,
- the spinning Earth,
- the orbit around the sun,
- the galactic cycles beyond our solar system.
- Migration patterns of animals in response to seasonal rhythm.
- Plant behavior with respect to fluctuations of the sun’s light.
- Mycological communication and networking in response to temperature change, moisture levels, and chemical variability in soil.
Rhythmically responsive…
All of nature is rhythmically responsive, and all of nature both entrains and can be entrained.
We are nature too…
Dream and Imagination:
As stated, the senses become entrained to both the world within and the world outside. The interior world or worlds include all internal levels and ranges of perception such as internal feeling, inner sensing, and overall objective observation of happenings in the body.
This perception of inner activity and sensational occurrence includes physical, sensory, and nerve stimulations, and this form of perception also includes the ability to imagine into or envision the interiority of the body, its organs, areas, and parts. Taken together, this total interior range of perceptual activity is what neuroscience has named interoception.
The inner worlds of perception are not limited to pure interoception, though…
Dream and imagination within all the possible forms- daydreaming, reminiscing, projecting, night dreaming, and fantasizing– are also a part of inner perception and interoception both relatively and reflexively.
All memory is imagination, and much of what is held in the psychology and even body memory is largely based on imagination. Therefore, much of identity, personality, and the conception of one’s own life is based on imagination and the function of imagining that is active within memory.
Research has shown that the physical body responds and can be changed by visions held in the mind. There is a harmonic relationship between mental state and body.
Repetitive envisioning imprints and entrains the body condition, as well as the psychology and emotional character. This envisioning includes all the senses of imagining, not just vision.
Combining imagination exercises with definite rhythmic routines or beats entrain the harmomic connection even further.
Rhythmic beat entrainment has been shown to expand imaginative states for deep healing and insight. In fact, this is an ancient methodology that is believed to give access to deep inner knowledge of nature.
There seems to be an intrinsic connection between interoception, imagination, intuition, instinct, and nature.
Imagination, Nature, and Intuition:
Most ancients cultures and belief systems through history forward into depth psychology and other areas of modern philosophy and conception have proposed that dream and imagination are a part of nature. Meaning; the inner imaginings that take part throughout the day, in memory, and in sleeping are direct counterparts to the nature that is alive in the world and existence through time.
There is a resonance between imagination and the outer nature of the world…
Sensing, feeling, and perceiving on the interoceptive level are channels of reception for this sympathetic resonance with nature.
These channels go both ways- they can both receive and transmit…
Research has shown in a multitude of ways that interaction with nature- forests, hands in soil, observing bodies of water, etc..- sympathetically entrains the biorhythms and activities of the body. And both older and newer emerging research validates the proposition that nature responds sympathetically to human attention and presence as well- plant growth, microbial activity in soil, water constitution, animal activity, forest health, movement of water in the atmosphere, etc…
We sympathetically resonate with nature and nature’s systems, and the imagination is harmonic with this resonance.
Attuning with inner and outer nature allows the intuition to be in relationship as a guide of what exists betwixt and between, as well as within and without. Harmonically attuned intuition in resonant relationship with nature is a strong and reliable guide for health and living.
Intuition can be entrained through rhythmically and ritually connecting with imagination and nature.
The related pages, blog posts, podcasts, and videos on this site expand these ideas into a further working curriculum of study and practice.
Beyond the teachings on this site, the accompanying book, and offered courses, a few other websites, books, and curricula develop these ideas and practices further into a total paradigm.
To dive in deeper, visit:
https://reharmonizinghealthwiththedreamtime.com
and…
https://anahata-nada-yoga.com
