Harmonics and Resonance: Cosmic and Musical
Fixing the traps to treasure
Salviati: [They say…] “Drop a lead ball from the top of the mast of a boat at rest, noting the place where it hits, which is close to the foot of the mast; but if the same ball is dropped from the same place when the boat is moving, it will strike at that distance from the foot of the mast which the boat will have run during the time of fall…[BUT] anyone who… [actually performs that experiment] will find that the experiment shows exactly the opposite of what is written; … the stone always falls in the same place on the ship, whether the ship is standing still or moving …”
Galileo Galilei, trans. Stillman Drake, Dialogue Concerning the Two Chief World Systems (New York: The Modern Library, 2001), pp. 146, 168.
Galileo’s Ship Experiment stands as a cornerstone in physics.
Initially, proponents of Aristotle’s theory of natural motion, recording that all objects gravitate towards the earth’s center irrespective of their motion, clashed with Galileo’s findings. However, many contemporary scientists agree – following the scientific method, deeply rooted in Aristotelian philosophy – that the relativity that Galileo describes is a valid way of understanding relative motion. Galilean relativity elucidates that the laws of motion remain consistent across all inertial frames of reference. While much of the matter we know of in the universe conforms to established laws, there exists the prospect of unearthing new phenomena even within the post-Copernican framework. Giordano Bruno’s elucidation of inertia closely mirrors Galileo’s stance. He asserts that particles persist in straight-line motion at a constant velocity unless subjected to external forces. Although particles lack inertial reference frames themselves, they adhere to the principles of inertia within the frames of reference in which they’re observed, emphasizing a clear comprehension of inertia as a pivotal concept.
Galileo uses several examples to explore the relationship between relative positions of an object as it moves through space. His other examples involve a cannonball and a bullet. What governs the laws regarding the paths that they follow? Beyond the level of the material objects, the same questions apply. At the quantum level, how do particles decide where to go? What governs the laws regarding the paths they follow?
In a groundbreaking advancement in antimatter research, physicists at CERN have recently crystallized a boundary point by setting a record for traditional measurements, managing to store antimatter for 57 days a previously unachieved length of time. This has the potential to lead us to new pathways of exploration such as investigating potential interactions of matter and dark matter candidates, e.g. the axion. It could enable higher-precision measurements and offer new insights into the fundamental nature of matter and antimatter. This perspective has the potential to reveal the interdimensional nature of motion and relative positions.
But every journey – every movement – has to start somewhere.
As theorized, during the Big Bang, both matter and antimatter were created in equal amounts. However, this balance was disrupted, leading to the overgrowth of regular matter in our universe. Baryogenesis, a pivotal concept in physics, tells a story of the origin of baryons, exploring the imbalance of matter and antimatter. Furthermore, recent studies on antimatter’s response to gravity, particularly antihydrogen, deepen our understanding of these fundamental building blocks. Baryogenesis theories delve into the interaction of fundamental particles, bridging the gap between the Standard Model and the next generation of physics.
How can we make sense of the movement of particles? If we can make sense of motion through observing how matter behaves, might we learn something about antimatter? And what could our explorations of antimatter teach us about the movement of matter?
Matter – comprised of particles such as protons, electrons, and neutrons – manifests in our cosmic surroundings, forming galaxies, stars, and planets. Antimatter, on the other hand, consists of analogous particles but with opposite charges. This distinction culminates in annihilations upon contact, releasing energy in the form of light. The asymmetry arising from baryogenesis during the Big Bang contributes to the prevalence of regular matter in our cosmic reality. Recent studies, particularly involving antihydrogen, affirm antimatter’s response to gravity, offering insights into the intricate interplay of these fundamental building blocks within the concept-space of the thought experiments outlined here.
Things move. Things also resonate. When a system (like a bridge, a musical instrument, or even a wine glass) is set into motion by an external force, it starts vibrating. That vibration can emit sound waves.
Harmonics are inherent to a system. They’re like the different colors a prism reveals from refracting light. When you play a note on a piano, or guitar, you’re not just hearing the fundamental frequency. You’re also hearing its harmonics, which give richness and complexity to the sound. Musicians love harmonics because they make music interesting, pleasant, and palatable to the ear. They’re the secret ingredients in the recipe.
Harmony isn’t just musical. It can be cosmic. After all, anything has the capacity to resonate. Anything has the capacity to emit frequencies that have harmonics. The story of how this happens may well unfold as a captivating story through our exploration of consciousness and its interaction with various dimensions. And stories are things to engage with, to tell, and retell, just as we can engage with harmonic vibrations, feel them, play them, and play with them. To simply think of this is to consider our privileged position; to consider the energy that occupies space. And if we consider the governing principle of mathematical harmony within the human mind or how the harmonic series might be linked to higher dimensions, everything can become a question of the risks and consequences of participating consciously in energetic patterns, in a cosmic dance of time, and space, a phenomenon that unfolds harmonically and has been quantified in number since antiquity. One only has to think of the division of time into eras, centuries, years, days, hours, and seconds to realize the truth of this. Harmony – whether in physics, acoustics, telecommunications, or living beings – encompasses a range of phenomena. It’s based on the natural harmonics in a resonating system. Often referred to by jargon such as overtones, partials, or upper partials, harmonics, which comprise all of the pitches in a harmonic series, harmonics contribute to the pleasance of sound. Think of an orchestra playing a radiant chord together. Why do they sound harmonious? The harmonic series, including the fundamental frequency, forms the basis of this phenomenon.
Imagine pushing someone on a swing at just the right time to make them go higher. A bridge may sway more dramatically, which can be both fascinating and potentially dangerous. It’s all about timing and matching frequencies because sometimes those sound waves can match the natural vibrational frequency of other objects. They resonate harmonically.
To consider baryogenesis in this context sparks reflections on the annihilation of mind and body, releasing emotion and energy as light.
In the Cabalistic tree of life, Tiferet is one of the central sefirot. It’s a center of light which can be both destructive and enlightening. It’s a core aspect of moral consciousness and emotion. Tiferet traditionally translates as ‘beauty.’ This is neither intellectual, nor material, but rather, moral. Think of these ideas as being akin to nuclei touching ‘Tiferet.’ Consider the rise of anti-particles in 1955, cosmic ray showers, and symmetry breaking, which hint at a ratio explaining the asymmetry favoring regular matter. Think of them as propelling generations into prophetic exploration in a harmonious universe, connecting with the covariant formulation of classical electromagnetism expressing laws invariantly.
In the pursuit of a new reality, a new evolutionary cycle of our state of being, it’s vital to acknowledge the dimension of consciousness and its intricate connection to the harmonics of the universe. As David Ramsay Hay, a Pythagorean numerologist, aptly puts it, “There appears to be implanted in the human mind a governing principle of harmony of a mathematical nature.” The three main tuning systems (Pythagorean, meantone, and equal temperament), and especially precise temperament tuning (PTT), help to realize harmony in musical compositions, echoing the belief that harmony is a universal language that’s immanent to space-time.
The problem is that when tuning an instrument, we face the paradox that if we go up in seven octaves, doubling the frequency at each octave, starting from a note that vibrates 100 times a second (100 Hz), we get to 12,800 Hz (100 Hz * 27). However, if we go up to the same note using the interval of a fifth which is based on a 3:2 ratio (twelve fifths is all we’ll need), even though we start at the same note, we get to 12,974.634 Hz (100 Hz * (3/2)12). The difference is small but highly significant. We call this the Pythagorean comma. The mystery at the core of any temperament lies with how one resolves the paradox of the Pythagorean comma, the approximation between the ideal and the real, the immaterial and the material; how one achieves a sense of harmonic balance in how the notes of a scale relate.
An intriguing discovery intertwines with mainstream metaphysics – with implications in polymathy studies – emerges that may set a limit with anti-matter as a measure. Approached along the lines of a chakra-based meditation framework, this may present an island of stability and a path to spiritual unfolding through harmonic correspondence. The correspondence between number and scale, alongside the remarkable insights and discoveries by Robert Edward Grant and Toni Mazzotti related to music and tuning, particularly the numbers 432 (33 x 24) as a base frequency to which all of the other notes in the tuning system relate, and 60 (42 x 5 x 3) as a means of dividing time (as in 432 Hz or 432 vibrations per second) contribute to this pursuit of harmony, both on the physical plane of the body and the metaphysical plane of the mind. The 24-stage experience becomes a noteworthy aspect in the navigation of the comprehensive gesture.
PTT’s integration of Western and Eastern musical scales directly relates to the mystery of the Pythagorean comma, along with the interplay between the frequencies, tones, chakras, colors, sound textures, and timing.
Personally, when engaging with it, I experienced self-assurance, a light-spell while walking around, access to greater realms of knowledge and fulfillment. Suddenly, a broadening of the ground to be covered takes place, guided by an auspicious blueprint for the hours of the day, onto the dimensions of flux and transformed to principles of light, frequency, and color.
The PTT scale at 432 Hz remains a constant, allowing adjustments for acoustic or virtual instruments. Instruments with frets or individual strings per note can modify pitch and temperament, while non-tempered instruments can adjust intonation in real time. Virtual instruments are also considered in this exploration of musical harmony.
The basic harmonic relationships (1:2 octave, 2:3 fifth, 3:4 fourth) allow us to calibrate others, a process that demands more flexibility. You start with a pitch like A at 432 Hz. going up or down an octave involves doubling or halving the frequency, respectively, for Pythagorean Tuning. Other notes in the scale are derived by multiplying the starting frequency by the ratio of the note in the scale. A perfect fifth is a musical interval that corresponds to a pair of pitches with a frequency ratio of 3:2. Let’s break it down with Toni Mazzotti:
“In this discovery, 528,099 Hz appears as the C* note, being the seventh quarter of tone above that of Tom Padrao. That is, in 24-PTT, the Standard A4 Tone remains at 432,081 Hz.”
And Robert E. Grant noted the different ratios used to tune intervals of a third, in relation to a lower note which symbolizes a unit of 1:
“In this approach, the MINOR (3rd) interval FALLS (from 1.2 to 1.19) and the MAJOR (3rd) interval LIFTS (increasing from 1.25 to 1.26).”
In a separate domain, Mazzotti goes on to say,
“The sound experience needed to emphasize the 24 sound stages, so I developed a base tone, at the same time static in its fundamental frequency, but also very organic through multiple oscillations, creating a kind of sound massage and maintaining interest in each 2:30-minute song. Above this basic tone, I play and meticulously adjusted several sound textures that emphasize the characteristics of each chakra. Keeping the 24 tones subdivided between the 7 basic Chakras, exactly as proposed.”
The result of these two researchers coming together is a 432 Hz 12-note Scale experience, another 432 Hz 24-note Scale, and a 528 Hz 12-note Scale. Musical meditations based on these scales can be found free on the internet, as can Robert E. Grant’s paper, Toni Mazzotti’s website which contains detailed information on his project as well as on his YouTube channel.
Their revelations draw parallels to the sacred geometry forming pentagrams and hexagrams across spheres, creating a chaosmic dance observed from multiple planetary bodies simultaneously, which writers from Kepler, Martineau to Hartmut Warm have written about very eloquently.
This principle, based on 12-note tuning commonly associated with Pythagoras, traces its origins back to the Chinese Sanfen Sunyi Method, predating Pythagoras by millennia.
“In Chinese mythology, Ling Lun is said to have created bamboo flutes which made the sounds of many birds, including the mythical phoenix.” (Wikipedia)
This method involves placing perfect fifths within a wider interval to create a scale, in such a way that more harmonics become visible, exemplified in the mythology of Ling Lun’s creation of bamboo flutes for the Chinese court. The process involves dividing the length of a flute by three, adding or subtracting the result to obtain fifths above or below the original tone. By nesting these fifths, the Chinese scholars achieved intervals close to the fundamental tone harmonically. This tradition eventually led to the development of equal temperament by prince and polymath Zhu Zaiyu in 1584, marking a significant milestone in tuning history. Integrating these historical insights into the discourse on Precise Temperament Tuning enriches our understanding of its global roots and evolution over time.
The basic harmonic relationships (1:2 octave, 2:3 fifth, 3:4 fourth) remain the foundation from which other relationships with greater flexibility can be constructed. Chinese music is committed to a pentatonic scale (presented in the use of the black keys on the piano), giving six notes including the octave. Greeks and Persians usually performed with two sets of tetrachords, exemplified by intervals like C to F and G to C. These, combined, give eight notes to the octave. Persians, including Turkish music, subdivided the octave into 53 intervals (54 notes including the octave), a topic explored in detail by Wenham-Prosser. Beyond this, Middle Eastern and Carnatic Indian music incorporate microtones, further expanding the spectrum of musical expression.
Toni Mazzotti’s reflections on the 24-PTT unveil a formidable integration of two healing scales, once considered irreconcilable, in a single musical scale. This discovery, rooted in the Middle East, reflects a cultural consciousness of quarter tones flowing to the West. Its mathematical unification of previously conflicting healing scales in a harmonious form invites us to consider the effect on our hearts, souls, and spirits.
Grant and Mazzotti are on a simultaneous mission to “integrate innovation, mathematics, artistic design & entrepreneurship into balanced creations intended to benefit all.” This endeavor, demonstrating as it does the principle of oneness, where each element can coalesce to form a harmonious whole, thereby enriching the musical landscape and fostering cultural understanding could be very good for unifying disparate elements of existence.
Talking of unifying disparate elements of existence, I’m reminded of Quentin Meillassoux’s idea of subtraction as a process that takes us on a detour through a simultaneously material and virtual past, a process that may summate the Absolute in some way. The subtraction model examines the living being in relation to its process of becoming. Extended beyond its end, it sees the solidification and reduction of natural substances as a subtraction through the rhythm and duration of the rarefied vibrations of its material existence, along with its underlying principles, matter, and memory. These principles encompass four elements: firstly, the transmission of matter to the body, then the necessity for the body to choose from an infinite array of images, followed by the emotional and cognitive aspects of the mind adhering to natural laws, and finally, their interaction with memory both insofar as it rushes from the future toward the present and also from the present toward the past. A non-material past gives rise to folding and the dynamic flow, exemplified by the timeline of music’s impact on an audience split into two periods: before and after the fixing of ‘scientific pitch’ (or Verdi’s ‘A’ of 256 Hz).
In essence, experiments of this kind represent a virtual rarefaction, each in itself now immanent to the body of work relating to the development of consciousness. Briefly put, there is a reduction of matter occurring in the transition from material to immaterial past events. The formula thus becomes monism equals pluralism, fostering a correspondence of disconnection when events interact with diverse matter. In summary, through the subtractive model, it could be possible for us to discern a body in its continual process of reconstitution.
Gathering these detours from the immaterial past leads to the richness of this navigation, and therefore the issue of the arche-fossil, which states that “the problem of the arche-fossil points to the ontological question of the coming into being of givenness as such, the factality [factualité] – the transcendental structure – of the “there is,” and the very possibility of thinking the absolute.” (Meillassoux, 2008.10.12).
If this is the case, then we must overcome the obstacles hindering our transition to a less dense state, which may involve challenges related to perception, thereby in pure terms, shaping order, and depleting material richness. This connects to the frameworks of understanding recorded before the advent of the Internet and how we may better treat the concept of a material artifact. Our perception of the past influences involuntary restrictions, leading to the degradation of matter. The unfolding process of the body involves exploring different temporalities, such as the resonance in the SHAPE disciplines (the Social Sciences, Humanities, and the Arts for People and the Economy), a concept being explored by many people, me included.
Following the thread of becoming further and further back in our imagination could have us reach a point at which, undoing the binds of memory, we reach a state of possibility, of unknowing – a quantum state of indeterminacy where we become baryon-like, the path we take as yet undetermined. It could have us regarding the quantum state as encoding information pertaining to potential measurement outcomes, rather than as a definitive representation of a system’s objective state. This perspective aligns with the notion of perceiving musical harmony as a delicate equilibrium between consonance and dissonance, focusing on the consequences of measurements or observations.
Another approach might well involve devising tangible models of reality that challenge prevailing assumptions about the quantum state. This parallels the exploration of various tuning systems in music and their compatibility with our understanding of harmony.
In this state, “One path or many?” could become a perennial question of consciousness.
Whether we uphold Aristotle’s scientific method or embrace Galilean relativity; whether we use the musical scale in a way we see as binding the quantum, the human, and the cosmos or whether we tune in a different way, any of these experiments represents a distinct quantum state within the space of conceptual understanding, based on each observer’s frame of reference. But these planes are all connected by what some may see as the immanence of the Body of Christ, that others may see as the Body of Work, and that yet others may see as the continuous unfolding of the universe as a musical work.
Just as in quantum mechanics, where particles can exist in superposition states until observed, the theories of harmony coexist in a superposition of possibilities until tested and observed and “collapsed into solid matter.” I imagine these thought experiments reflecting the multifaceted nature of understanding (e)motion, and reality as a fact which is bypassed in cosmic memory. According to Galileo’s argument, “The cause of all these correspondences of effects is the fact that the ship’s motion is common to all the things contained in it, and to the air also.” In other words, something independent of subjectivity is taking place and bound to the rotation of the earth in space-time. The universal scale: atom, tree [I’m smudging, ship], cosmos is already calibrated by many mathematical, geometric, and harmonic connections which have led to the clearest-sounding musical compositions and physical instruments. How else would we construct musical instruments that have the power to touch our hearts, souls, and spirits when played?
As you navigate this mythic spiral creation myth, how might you, the hero of your own story, harmonize the tangible physicality of your existence with the intangible metaphysical essence that animates you, despite their apparent opposition?
As our cosmic symphony reaches its crescendo, picture a metaphorical dinner party aboard a ship navigating celestial waters. This vessel, embodying the harmonious dance of particles and energies, sails through the vastness of the cosmic sea. At this ethereal gathering, the guests are not individuals but rather vibrations, particles, and energies [electromagnetism and the Higgs field] donned in the attire of light and sound. Keep in mind that this story suggests a heightened awareness of the harmonious dance of particles and energies which might imply a greater discernibility of both position and momentum than generally achieved.
In this metaphorical soirée, Galileo’s Ship Experiment takes center stage. The ship, a symbol of our cosmic reality, moves steadily through the interdimensional waves of existence. Objects on its deck, representing the cosmic entities, follow the laws of motion and relative positions. They, too, engage in a dance, unaffected by the ship’s uniform motion.
Baryogenesis, the birth of cosmic matter, is akin to the rhythmic sway of the ship, marking the ebb and flow of existence. The imbalance between matter and antimatter echoes in the undulating movement, creating a cosmic choreography on the ship’s deck.
As the ship progresses, harmonies of light and sound fill the metaphysical air. The harmonics, supplying overtones and undertones, paint an image manifested with vibrant hues. The ship’s journey becomes a celestial melody, resonating from its deck to the cosmic horizon of the zero-point.
Enter harmonics and precise temperament tuning, the nucleus of this cosmic vessel. Like the guiding force in Galileo’s experiment, it influences the ship’s course, directing the harmonious interplay of vibrations. The 24-PTT scale ensures that each particle, each manifestation of an energy source aligns perfectly, contributing to the grand symphony of the universe.
In this metaphorical journey, where the ship encounters geotrauma (a disturbance in the harmony of the cosmic waves), the ship’s deck (representing the nucleus of precise temperament tuning) navigates these disturbances with grace. It becomes a beacon of resilience, guiding the ship through the undulating currents of cosmic existence.
As the ship sails toward the cosmic horizon, the interplay of light and sound becomes a metaphor for the cosmic rhythmic motion. The vibrations, orchestrated by precise temperament tuning, mirror the resilience of the ship amidst geotrauma. Each cosmic entity, a participant in this celestial gathering, contributes to the harmonious narrative carved into the cosmic domain.
In this cosmic party aboard the ship of existence, Galileo’s Ship Experiment unfolds as a metaphor for the rhythmic dance of cosmic entities. Shift up a level, and the ship becomes a vessel of harmonies, guided by the nucleus of precise temperament tuning. As it sails through the cosmic sea, encountering geotrauma and cosmic disturbances, the harmonious interplay of light and sound manifests, resonating toward the cosmic horizon.
The overall goal of this project is the activation of cosmogonic eros and the transformation of consciousness to create a more modern and liberated world. It aims to free individuals from attachment to the brain and guide them towards the heart, the two core spaces of the cosmos. When visualized on an oscilloscope, this dance would appear as waves that synchronize at regular intervals, showing the harmony of their movements through space.
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