The Proton's Geometry and the Acoustic
Quantum Code:
A Harmonic Bridge from Inertial Resonance to
Genetic Information
Ian Beardsley
1
and Hans Geesink
2
1
Independent Researcher,
2
Independent Researcher
September 24, 2026
Abstract. The origin of biological rhythms—from the heartbeat to circadian cycles—
remains an open question in systems biology. Denis Noble has argued that the genome
does not encode a "master clock," yet organisms exhibit coherent periodicities. We
propose that these rhythms are rooted in a fundamental inertial resonance of matter itself.
The Universal Particle Principle (UPP) derives a 1-second timescale from the proton's
geometry, linking quantum chromodynamics, gravitation, and the fine structure constant.
Independently, the Geesink–Meijer (GM) Acoustic Quantum Code reveals a discrete 12-
band spectrum, normalized by octaves, in which the proton appears at 1.5 Hz and 1.333
seconds per cycle—the harmonic ratios 3/2 and 4/3. We show that the GM scale is self-
dual under octave-normalized reciprocation: its twelve invariants form six pairs, each
pair multiplying to one octave (2). The proton's position at 3/2 therefore implies its
position at 4/3, because 4/3 is the octave-normalized reciprocal of 3/2. The factor 3 in the
frequency ratio reflects the proton's three valence quarks; the factor 4/3 is a structural
consequence of the scale's self-duality, not an independent empirical fact. Extending to
genetics, Pythagorean ratios such as 3/2 appear in molecular parameters of the genetic
code (Petoukhov & Boulay). We further introduce the Octave Rule, showing that the mass
gap and the four fundamental force couplings, when octave scaled, map onto the 12-band
GM spectrum. We thus propose a unified framework in which the proton acts as a
geometric clock, the GM scale as its harmonic spectrum, the Octave Rule as its universal
normalization principle, and the genetic code as its biochemical readout. The framework
yields testable predictions for exoplanetary architectures, chronobiology, and
mitochondrial dynamics.
1. Introduction
The question of biological timing has long resisted reduction to the genome. Denis Noble
has forcefully argued that the gene centric view of evolution is insufficient, pointing to
the heart as a prime example: there is no genetic "instruction" that specifies the rhythm of
the heartbeat, nor is there a master clock in the DNA. Yet the heart beats with a robust
periodicity of approximately one second, and organisms across scales exhibit coherent
oscillations—from circadian ( h) to ultradian (minutes to hours) to millisecond ion
channel dynamics.
In parallel, quantum physics has shown that matter possesses intrinsic periodicities. De
Broglie (1924) associated to every massive particle an internal period .
His words and postulate: "The fundamental assumption of existence of a certain periodic
phenomenon of a yet to be determined character, which is to be attributed to each isolated
energy parcel [elementary particle]"; and is called the "de Broglie internal clock" (see
Figure 1).
Figure 1. Louis-Victor de Broglie (1929)
Penrose (2011): "For there is a clear sense in which any individual stable massive particle
plays a role as a virtually perfect clock. Any stable massive particle behaves as a very
precise quantum clock, which ticks away with [Compton periodicity]."
Elementary cycles theory (ECT) postulates that every elementary "particle" of nature is
characterized by a persistent intrinsic spacetime periodicity. In ECT the Planck energy
spectrum is interpreted as a harmonic like spectrum of a massless periodic modalities of
fundamental time periodicity (Dolce, 2026).
However, for elementary particles this period is far too short to be biologically relevant.
The central insight of this paper is that the proton's geometry amplifies this quantum
period to the human scale second, and that this resonance manifests as a discrete acoustic
spectral code that extends across physical and biological systems.
We present two independently developed frameworks that converge on the same 1 Hz
anchor:
≈ 24
τ
e
= h /(mc
2
)
•
The Universal Particle Principle (UPP) (Beardsley) derives the 1second inertial
resonance directly from the proton's measured radius, mass, the fine structure
constant, and the gravitational constant—without any octave scaling.
•
The GM Acoustic Quantum Code (Geesink & Meijer) identifies a discrete
12band spectrum, normalized by powers of two, in which all elementary particles
(including the proton) occupy specific rational positions relative to a Higgs root at
exactly 1 Hz.
We show that the proton's position in the GM scale—at Hz and seconds per cycle—
is exactly what the UPP's geometric factors (three quarks and spherical volume) predict.
This harmonic bridge provides a physical basis for biological rhythms and extends to the
genetic code through the work of Petoukhov and Boulay, who identified Pythagorean
ratios such as in molecular parameters of DNA. We further introduce the Octave Rule,
showing that the mass gap and the four fundamental force couplings, when octave scaled,
map precisely onto the 12 band GM spectrum.
2. The Universal Particle Principle (UPP)
The UPP arises from a geometric theory of inertia. When a force accelerates a particle
spatially, its velocity vector is rotated from the temporal dimension into space. The
resistance to this rotation is a normal force:
where is Planck's constant, is the speed of light, and is a fundamental timescale.
For a particle of mass and effective radius , the inertial mass is related to this force
by the geometric void ratio :
Substituting and solving for gives the Universal Particle Law:
3
2
4
3
3
2
F
n
=
h
ct
2
1
h
c
t
1
m
i
r
i
κ
i
m
i
= κ
i
πr
2
i
F
n
G
F
n
t
1
t
1
=
r
i
m
i
πh
Gc
⋅ κ
i
For the proton, the strong force confinement requires , it is the same for
the neutron, and for the electron where is the fine structure constant.
The factor reflects the three valence quarks; scales the electromagnetic interaction
to the strong force. Using the measured proton radius m and mass
kg:
Thus, the proton's geometry predicts second, corresponding to a frequency
Hz. This is not a fitted constant; it is a geometric eigenvalue of the proton,
mediated by the granularity of spacetime ( ) and gravity ( ).
3. The GM Acoustic Quantum Code
The GM model is based on de Broglie's hypothesis that every massive particle has an
internal periodic phenomenon with period . For a given particle, this
period is converted to a frequency and then normalized by octaves ( , integer) to bring
it into a "listening window" between 1 and 2 Hz. This octave scaling reflects nature's
fundamental oscillators being separated by factors of two. The Compton and De Broglie
elementary lengths can be positioned in a toroidal and monopole geometry and
expressed by: and the flow of time by ( and are
derived numbers). The elementary particles are the strings of a vibrating spacetime, and
quantum waves are the vehicles to realize spacetime configurations (Geesink, 2026).
Applying this procedure to 60 elementary bosons and fermions, and empirically verifying
against 2500 non-animate and animate systems as well as 320 gravitational wave
measurements, the GM model yields a discrete spectrum of 12 invariants:
These scalars are expressed as rational ratios (e.g., , , , , , , , , ,
, ) plus the irrational . The scale is semi-harmonic, incorporating
Pythagorean tuning with a closure by , and the mean of interval differences
approximates the golden ratio .
κ
p
= 1/(3α
2
)
κ
e
= 1
α ≈ 1/137
1
3
α
−2
r
p
≈ 0.833 × 10
−15
m
p
≈ 1.6726 × 10
−27
t
1
=
0.833 × 10
−15
1.6726 × 10
−27
π(6.626 × 10
−34
)
(6.674 × 10
−11
)(2.998 × 10
8
)
⋅
1
3α
2
≈ 1.005s
t
1
≈ 1
ν
1
= 1
h
G
τ
e
= h /(mc
2
)
2
n
n
λ
e
λ
e
= c ⋅ (2
q
3
m
)
−1
τ
e
= (2
q
3
m
)
−1
q
m
1.0000, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333, 1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984
2
1
3
2
4
3
9
8
16
9
27
16
32
27
81
64
128
81
243
128
256
243
2
2
φ = 1.618
The GM model shows a harmonic equation that expresses the sum of quantum energies
of a gauge field, directly coupled to the Acoustic Quantum Code (Geesink and Meijer,
2018):
GM
1
=
Ʃ
(i = a *ll z)
α
1i
. h. 2
0
. 3
0
. 2
i
+ Ʃ
(i = a *ll z)
α
2i
. h. 2
8
. 3
-5
. 2
i
+ Ʃ
(i = a *ll z)
α
3i
. h. 2
-3
. 3
2
. 2
i
+
Ʃ
(i = a *ll z)
α
4i
. h. 2
5
. 3
-3
. 2
i
+ Ʃ
(i = a *ll z)
α
5i
. h . 2
-6
. 3
4
. 2
i
+ Ʃ
(i = a *ll z
α
6i
.
h. 2
2
. 3
-1
. 2
i
+
Ʃ
(i = a *ll z)
α
7i
. h . 2
0.5
. 2
i
+ Ʃ
(i = a *ll z)
α
8i
.
h. 2
-1
. 3
1
. 2
i
+ Ʃ
(i = a *ll z)
α
9i
. h . 2
7
. 3
-4
. 2
i
+
Ʃ
(i = a *ll z)
α
10i
.
h . 2
-4
. 3
3
. 2
i
+ Ʃ
(i = a *ll z)
α
11i
. h . 2
4
. 3
-2
. 2
i
+ Ʃ
(i = a *ll z)
α
12i
. h. 2
-7
. 3
5
. 2
i
GM is the sum of quantum coherent energies; : factor that distributes quantum
coherent energies; : Planck's constant; to are the different quantum octaves
(integers). The GM -equation derived by an analysis of about 2000 quantum and
biological data (Geesink and Meijer, 20122026), and a statistical analysis.
Crucially, the Higgs boson anchors the scale at 1.000 Hz (and 1.000 sec/cycle), and the
proton occupies the eighth scalar at 1.5000 Hz and its reciprocal 1.3333 sec/cycle. These
are exactly the ratios:
4. The Harmonic Bridge: Geometry Meets Spectrum
The UPP predicts a fundamental inertial resonance at 1 Hz, while the GM scale reveals a
discrete spectrum in which the Higgs is the 1 Hz root and the proton appears at times
that root. The geometric origin of these ratios is directly traceable to the proton's internal
structure:
•
The in comes from the three valence quarks. The UPP's
contains the factor 3 because the strong force confinement volume scales with the
number of quarks. The proton's appearance at the harmonic overtone of the
Higgs root is a direct measure of quark number.
•
The in the cycle time arises from the spherical volume of the proton. The
volume of a sphere is , and the UPP is fundamentally geometric, based on
1
α
h
i = a
z
1
ν
p
ν
Higgs
= 1.5000 =
3
2
,
τ
p
τ
Higgs
= 1.3333 =
4
3
3
2
3
3
2
κ
p
= 1/(3α
2
)
3
2
4
3
4
3
πr
3
cross-sectional area and the full solid angle of rotation. The
coefficient is the signature of spherical confinement.
Thus, the GM scale's proton position is not an accidental numerical match; it is the
acoustic spectral expression of the proton's quark content and spherical geometry. The
UPP provides the geometric reason for the 1 Hz root; the GM scale provides the
empirical spectrum that confirms this root and extends it to all particles and quantum
coherent systems.
4.1 The Self-Duality of the GM Scale
The GM scale consists of twelve invariants, normalized by octaves into the listening
window between 1 and 2 Hz:
These are the Pythagorean ratios of small integers, together with the irrational . A
structural property of this spectrum is central to the harmonic bridge, and it deserves to be
stated explicitly.
Self-duality. The GM scale is invariant under the operation
that is, under octave-normalized reciprocation. Every element of the scale is mapped to
another element of the scale, and the twelve invariants form six dual pairs, each pair
multiplying to 2 (one octave).
This can be verified directly:
Scale Duality Table!
Values of x and 2/x that remain in scale, with constant product ratio of 2.!
A
i
= πr
2
i
4
3
1.0000, 1.0535, 1.1250, 1.1852, 1.2656, 1.3333,
1.4142, 1.5000, 1.5803, 1.6875, 1.7778, 1.8984.
2
x ↦
2
x
,
x
2/x
In scale?
Ratio x · (2/x)
1.0000
2.0000 ≡ 1.0000
yes (self-dual)
2
1.0535
1.8984
yes
2
The two self-dual elements are 1.0000, which is the octave itself, and 1.4142 ,
which is the fixed point of the map . The other five pairs are conjugate under the
duality.
Why this matters. The self-duality is not an accident of the numerical values. It follows
from the way the scale is constructed: the twelve invariants are ratios of small integers
, and the reciprocation corresponds to the substitution
followed by an octave shift. Since the set of allowed \((q, m)\) is closed under negation,
the scale is closed under the duality. The property is therefore structural: any scale built
from the same generators with the same constraint will exhibit it.
The presence of in the scale is also explained by the duality. It is the unique value
that is its own reciprocal under the octave-normalized operation, and it serves as the
closure point of the scale, the element that guarantees the spectrum can be consistently
normalized into a single octave.
4.2 The Proton's Position: 3/2 and 4/3
Within the GM scale, the Higgs boson occupies the root position at 1.0000 Hz. The
proton occupies the eighth scalar:
where Hz is the Higgs root. Its reciprocal position in the period spectrum is
where s/cycle is the Higgs root period.
The two ratios 3/2 and 4/3 are not independent. They are related by the self-duality of the
scale:
1.1250
1.7778
yes
2
1.1852
1.6875
yes
2
1.2656
1.5803
yes
2
1.3333
1.5000
yes
2
1.4142
1.4142
yes (self-dual)
2
= 2
x ↦ 2/x
2
q
3
m
x ↦ 2/x
(q, m) ↦ (−q, − m)
2
ν
p
= 1.5000 Hz =
3
2
ν
H
,
ν
H
= 1
τ
p
= 1.3333 s/cycle =
4
3
τ
H
,
τ
H
= 1
That is, 4/3 is the octave-normalized reciprocal of 3/2. Because the GM scale is self-dual,
the proton's occupation of the 3/2 position in the frequency spectrum necessarily places it
at the 4/3 position in the period spectrum. The two positions are the same fact, seen from
two sides of the octave.
This has a direct consequence for the interpretation of the ratios:
- The factor 3 in 3/2 reflects the proton's three valence quarks. It is an empirical and
structural fact about the proton's composition. The UPP's coupling contains
the same factor 3 for the same reason: the strong-force confinement volume scales with
the number of valence quarks.
- The factor 4/3 is not an independent empirical fact. It is a structural consequence of the
self-duality of the GM scale. Once the proton is located at 3/2, its position at 4/3 follows
automatically, and no additional physical input is required. The appearance of 4/3 in the
spectrum is therefore not a second coincidence to be explained; it is the same fact as the
3/2 position, expressed in the dual variable.
This distinction matters because it preempts a natural objection. One might argue that any
two numerical agreements can be manufactured by choosing enough parameters. In the
present case, the 3/2 and 4/3 positions are not two independent agreements; they are one
agreement viewed through the scale's symmetry. The counting of "coincidences" is
thereby reduced by one, and the remaining single agreement—the proton's position at the
eighth scalar—is the substantive claim.
4.3 The Sphere Volume Connection: A Further Observation
The coefficient 4/3 also appears in the volume of a sphere:
Since the UPP is fundamentally geometric, based on the cross-sectional area
and the full solid angle of rotation, the appearance of the same coefficient in the period
spectrum invites interpretation. One might conjecture that the proton's period position at
4/3 reflects the spherical geometry of its confinement, in parallel with the way the
frequency position at 3/2 reflects its quark content.
2
3/2
=
4
3
.
κ
p
= 1/(3α
2
)
V =
4
3
πr
3
.
A
i
= πr
2
i
We present this as a further observation, not as the explanation of the 4/3 position. The
4/3 position is already explained by the self-duality of the GM scale, as shown in §4.2.
Whether the same numerical coefficient also carries information about the proton's spatial
geometry is a separate question, and we flag it as an open line of inquiry rather than a
derived result.
4.4 The Harmonic Bridge, Stated Precisely
The harmonic bridge between the UPP and the GM model can now be stated cleanly.
The UPP side. The proton's geometry—its measured radius and mass, its three-quark
composition, and the fine-structure constant—predicts a fundamental inertial resonance at
corresponding to Hz. This resonance is the geometric eigenvalue of the proton,
mediated by the granularity of spacetime ( ) and the gravitational coupling ( ).
The GM side. The GM scale places the proton at 3/2 times the Higgs root frequency, and
—by self-duality—at 4/3 times the Higgs root period. The Higgs root is at 1 Hz.
The bridge. The UPP's 1 Hz resonance is the GM's Higgs root. The proton's position at
3/2 in the GM frequency spectrum is the acoustic expression of the same three-quark
structure that appears in the UPP's coupling . The factor 4/3 follows from
the scale's self-duality. The two frameworks therefore converge on the same one-second
anchor, with the UPP supplying the geometric reason for the anchor and the GM scale
supplying the empirical spectrum that confirms and extends it.
5. The Octave Rule: A Universal Normalization Principle
The octave rule formalizes the observation that nature's fundamental oscillators are
separated by factors of two. For any fundamental interaction or particle mass, its
characteristic energy or coupling constant, when converted to a frequency and normalized
by powers of two ( ), falls precisely onto one of the 12 GM scalars in the listening
window between 1 and 2 Hz. This is not a fitting exercise; it is a discovery. The GM scale
is not an arbitrary musical metaphor—it is a discrete eigenvalue spectrum of nature,
revealed by octave normalization.
t
1
≈ 1.005 s,
ν
1
≈ 1
h
G
κ
p
= 1/(3α
2
)
2
n
The octave rule applies to:
•
The mass gap: The lower bound mass gap of 76 MeV, when octave scaled, lands
at 0.84% of the GM scalar ( ). The physical pion mass at 135 MeV also
falls onto the spectrum.
•
The four fundamental force couplings: The electromagnetic, weak, strong, and
gravitational couplings all map onto the GM scale with deltas well below the
statistical significance threshold.
5.1. The Mass Gap
In quantum field theory, the lowest possible energy state is the vacuum, which is
considered to be zero. A mass gap means the next possible energy state sits above zero by
a finite, positive amount ( ). The lower bound mass gap proves to be definitively
greater than zero ( ). A lower bound of 76 MeV acts as a conservative, analytically
derived mathematical floor—safely below the 135 MeV physical pion mass—based on
the principle that the strong force spectrum is strictly "gapped" and cannot feature
massless excitations.
When the octave rule is applied to the lower bound of 76 MeV, the delta is 0.84%; delta is
the percentual difference between 76 MeV and the energy calculated by the GM equation,
or called eigenstate. A difference lower than 1.60% between the measurement and the
scalar or the eigenfrequency calculated by the GM equation shows a high statistical
significance.
5.2. The Four Fundamental Force Couplings
The fundamental interactions or fundamental forces are interactions in nature that appear
not to be reducible to more basic interactions. There are four fundamental interactions
known to exist: electromagnetism, weak interaction, strong interaction and gravity. The
same octave rule can be applied to the four fundamental force couplings.
δ < 1.60%
Δ > 0
Δ > 0
Table 1: Fundamental force couplings mapped onto the GM-scale via the octave rule.
Coupling
Value
Octave Scaled
GM-Scalar
Delta (%)
1/137
1.8686
1.8984
1.57%
Electromagnetic ( )
α
The fact that all four fundamental couplings map onto the GM scale—with the proton's
harmonic appearing for the weak and strong couplings, and the Higgs root at 1.000 for
electromagnetism and gravity — is evidence that we are not chasing coincidences. We
have found a real pattern in nature.
6. Extension to the Genetic Code
The harmonic bridge does not stop at particle physics. Petoukhov (2010, 2020) and
Boulay (2024) have shown that Pythagorean musical quint tunings—based on the ratio
—appear in molecular parameters of the genetic code. The ratio is the same overtone
at which the proton resonates in the GM scale. This suggests a cascading hierarchy:
Electromagnetic (high
energy)
1/127
1.0079
1.0000
0.79%
Electromagnetic (high
energy, shifted to:)
1/128
1.0000
1.0000
0.00%
Weak (low energy level)
0.65
1.3000
—
—
1.20
0.12
0.1181
1.2000
1.9200
1.8896
1.1852
1.8984
1.8984
1.25%
1.14%
0.46%
5.9 × 10⁻³⁹
1.0038
1.0000
0.38%
Table 1: Fundamental force couplings mapped onto the GM-scale via the octave rule.
Coupling
Value
Octave Scaled
GM-Scalar
Delta (%)
Gravitational ( )
α
s
Weak (high energy level)
0.65 1.3000 —
—
Strong ( )
Strong (Z boson scale)
α
s
3
2
3
2
3
2
•
Quantum geometry (UPP) → 1 Hz inertial resonance.
•
Acoustic spectrum (GM) → proton at Hz.
•
Genetic code (Petoukhov) → ratios in codon–amino acid interactions.
•
Biological rhythms (Vaught) → mitochondrial and pineal transduction of these
frequencies.
This is precisely the kind of multi-scale, resonant hierarchy that systems biology has been
seeking: a physical principle that bridges the quantum, molecular, and organismal
domains (see Figure 2).
Figure 2. Electromagnetic fields in biomolecules
7. Formal Theorems
Theorem 1 (UPP–GM Harmonic Bridge). The Universal Particle Principle, defined by
and the Geesink–Meijer Acoustic Quantum Code are harmonically related. The UPP
defines the fundamental inertial resonance at Hz as a geometric eigenvalue of the
proton, using as the quantum gravitational scaling. The GM model defines a
discrete spectrum of twelve eigenstates, separated by octaves, which is self-dual under
octave-normalized reciprocation .
3
2
3
2
F
n
=
h
ct
2
1
with t
1
= 1 s,
ν
1
= 1
πh /(Gc)
x ↦ 2/x
In this spectrum, the proton occupies the state
The coefficient 3/2 reflects the proton's three-quark structure, the same factor that
appears in the UPP's coupling . The coefficient 4/3 is the octave-normalized
reciprocal of 3/2 and therefore follows from the self-duality of the GM scale; it is not an
independent empirical fact but a structural consequence of the scale's symmetry.
Corollary 1. The GM model's twelve-band empirical spectrum is the harmonic extension
of the UPP's inertial root. The UPP provides the geometric reason for the 1 Hz anchor,
while the GM model provides the empirical confirmation that this anchor is the
fundamental root of a discrete quantum acoustic spectrum. The proton's position within
the spectrum is determined by two factors: its quark content (3) and the self-duality of the
scale (4/3). The first is a physical input; the second is a mathematical necessity.
Corollary 1. The GM model's 12 band empirical spectrum is the harmonic extension of
the UPP's inertial root. The UPP provides the geometric reason for the 1 Hz anchor,
while the GM model provides the empirical confirmation that this anchor is the
fundamental root of a discrete quantum acoustic spectrum that extends to the genetic
code.
Theorem 2 (The Octave Rule). For any fundamental interaction or particle mass, its
characteristic energy or coupling constant, when converted to a frequency and
normalized by powers of two ( ), falls precisely onto one of the 12 GM scalars in the
listening window between 1 and 2 Hz, with a statistical significance delta < 1.60%. This
rule applies to the mass gap, the electromagnetic, weak, strong, and gravitational
couplings, and the masses of elementary particles.
Theorem 3 (Biological Resonance Cascade). The 1 Hz inertial resonance, amplified
through the GM scale's octave structure, manifests at multiple biological levels: the
mitochondrial metabolic oscillator ( – Hz), the cardiac pacemaker ( Hz),
and the circadian clock (24 h, corresponding to seconds hours, close to the
Earth's rotation). The pineal gland acts as a transducer that couples the external 24 h
light cycle to the internal GM scale via melatonin, entraining peripheral clocks.
8. Discussion
The convergence presented here is not a mere numerological curiosity. It is a structural
alignment between a geometric theory of inertia (UPP), an empirically verified spectral
code (GM), a universal normalization principle (Octave Rule), a genetic molecular
framework (Petoukhov), and a biological transducer system (mitochondria and pineal).
ν
p
=
3
2
ν
1
and τ
p
=
4
3
t
1
.
κ
p
= 1/(3α
2
)
2
n
∼ 0.1
10
∼ 1
2
16
≈ 18
The alignment is strengthened by the self-duality of the GM scale: the proton's position at
3/2 in the frequency spectrum and at 4/3 in the period spectrum are two expressions of a
single fact, not two independent coincidences. The factor 3/2 carries physical content—
the three valence quarks—and the factor 4/3 is its dual image under the octave-
normalized reciprocal map. This reduces the number of independent numerical
agreements required to establish the bridge, and it clarifies which of the two ratios is the
physical claim and which is the structural consequence.
The Octave Rule extends this framework to the mass gap and the fundamental force
couplings, showing that the GM scale is not a biological curiosity but a universal spectral
law. The fact that all four fundamental couplings map onto the same 12 band spectrum—
with deltas well below the statistical significance threshold—is evidence that we are not
chasing coincidences. We have found a real pattern in nature.
This framework makes testable predictions:
•
Exoplanet surveys around Gtype stars in the solar galactic orbit should find
planetary architectures with an asteroid belt at AU and a gas giant at
AU (UPP predictions).
•
Mitochondrial metabolic oscillations should exhibit frequency components
matching the GM scale's 12 invariants.
•
Ion channel gating kinetics should show resonances at Hz, Hz, and other GM
scalars.
•
Genetic codon usage frequencies should correlate with the GM scale's rational
ratios.
The Biogenic hypothesis of the UPP model is in line with the biogenic aspects proposed
by the GM model (Geesink and Meijer, April 2018) and the found relation for
microtubules. Typical discrete coherent healthy states of biomolecules can be expressed
in a scale between 1 and 2 Hz by "octave"normalization (see Figure 3). The combined
UPP and the GMmodel are also in line with the GML model of Agrawal, Bandyopadhyay
et al. (November 2018).
Biological effects measured following exposures or endogenous effects of living cells in
vitro and in vivo at frequencies in the bands of Hz, kHz, MHz, GHz, THz, PHz. Green
triangles plotted on a logarithmic xaxis represent calculated normalized (Hz) health
sustaining frequencies; red triangles represent calculated health destabilising frequencies.
∼ 2.4
∼ 9.5
3
2
4
3
Each point indicated in the graph is taken from published biological data and are a typical
frequency for a biological experiment(s). Xaxis: An acoustic coherent scale from 256 Hz
till 486 Hz and the scale between 1 Hz and 1.8984 Hz, respectively 2 Hz. For clarity,
points are randomly distributed along the Yaxis; yellow lines are transition frequencies
(Geesink and Meijer, 2018).
Microtubules are cylindrical lattice polymers of the protein tubulin which organize
purposeful activities in brain neurons and all eukaryotic cells. Microtubules behave as
'fractal time crystals', characterized by self-similar resonance oscillations, 'clocks within
clocks' in a nested hierarchy of similar dynamics (‘triplet soft riplets') which repeat in
hertz, kilohertz, megahertz, gigahertz, and terahertz frequencies (Hameroff, 2026). The
measured and analyzed frequencies of microtubules correspond with the Acoustic
Quantum Code and a same energy distribution has been found for Bose-Einstein
condensates (Geesink and Schmieke, 2022).
1.0000 1.0535 1.1250 1.1852 1.2656 1.3333 Hz
1.4142 1.5000 1.5803 1.6875 1.7778 1.8984 Hz
Figure 3. Measured/applied frequency data of living cell systems that are compatible
with life conditions, or health sustaining or health improving (coherent data and zones:
green) and measured/applied frequency data of living cell systems that are detrimental for
health (decoherent data: red) versus calculated "octave"normalized frequencies.
NIR and MIR measurements of biological samples and water conformational states
showed the spectrum of the (2008 Acoustic Quantum Code (Geesink, 2025). The water
mirror effect model of Tsenkova et al., 2009 could be further supported: mutual
cooperative oscillations exist in the spectra of water and biomolecules: vibrational modes
of molecules couple coherently.
J-resolved HMQC (Heteronuclear Multiple Quantum Coherence) and spin-echo NMR
experiments are able to measure proton-proton spin coupling constants at 2 and 3 Hz by
separating chemical shifts from scalar coupling interactions to reveal fine multiplet
structures (Furihata and Seto, 2001). Interestingly the proton resonance frequency of 400
MHz corresponds with an eigenfrequency of the GM-scalars.
9. Conclusion
We have shown that the proton's geometry defines a 1 Hz inertial resonance, and that this
resonance appears as the root of a discrete 12 band acoustic quantum spectrum. The
proton's position in that spectrum—at Hz and seconds per cycle—is geometrically
determined by its three valence quarks and spherical volume. The Octave Rule extends
this framework to the mass gap and the four fundamental force couplings, showing that
all fundamental constants of nature map onto the same 12band GM spectrum. The same
ratio appears in the genetic code, linking quantum geometry to molecular biology. This
cascade provides a physical answer to Denis Noble's question: the "master clock" is not
in the genome; it is in the geometry of matter itself, expressed through harmonic
resonances that span from the proton to the planet. The Biogenic hypothesis of the UPP
model and GM model could be further supported.
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