.pdf version here
"Toroidal spin resonance, predicting the formants in a way consistent
with our perception and other known criteria, while at the same time naturally
consonant with the biological speech mechanism, appears to provide a realistic
working model in the emerging field of causal phonetics". - Excerpt
"Every vibration in this universe has colour and sound. Every vibration
also represents a particular idea, and hence each idea has a vibrational
sound and vibrational colour".
Shrii P.R. Sarkar
It's ancient wisdom: if you can name it, you can control it. Possessing
language means, having the conceptual power to consciously deal with your
perceptions, and therefore control reality. It distinguishes human mind
from animal mind, more fundamentally than intellect per sé.
Hence, language is an essential skill. It is a conceptual phenomenon,
connecting subjectivity with objectivity. However, in traditional Eastern
perception, language has a different and virtually opposite impact than
in the West.
Ideally, in the subjectively oriented Eastern mind, language is universal
and hence generically creative. If the science of the sacred sounds of
creation is properly developed and cultified in one form or another, this
may result in some objective effect. This use of language is referred
to as "incantation". Vice versa, if objective language is cultified,
this may lead to conceptual insights. This use of language is called "physical
Clearly, both uses of language render some form of control over reality,
albeit from fundamentally different angles. In one view, nature is the
result of divine incantation. In the other, personal insight results from
describing the laws of nature.
The beautiful and very elaborate science of phonetics, with its sub fields
of articulatory-, acoustic- and auditory phonetics, objectively analyses
how the sounds of human speech are created, composed and processed, but
does not hint at the universal quality and creative potential of sound.
These complementary aspects of language use are captured together in the
geometric origin of selective sound perception. This article will first
discuss some key aspects of phonetics, focusing mainly on the acoustic
composition of vowels. Then it will be shown how sympathetic vibrations
in a universal (meta-stable) medium accurately predict the positions of
the vowel's characteristic resonance peaks, or formants. Finally this
will be placed in the context of contemporary creation theory, including
microvita cosmology and wave matrix physics.
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The phonetics of vowels
The physical composition of vowels has been studied virtually since the
time it was possible to record sound, in the late 19th. century, and will
be summarized here only briefly. Vowels are expressed through two main
resonance peaks in a harmonically rich sound flow. In human speech, the
sound source is the vocal chords, the resonances are shaped in the vocal
tract of mouth, nasal cavity, tongue and lips.
The resonance peaks are called
formants (F1 and F2, resp.), and their ratio as well as absolute position
determine the vowel. Vowel generation has the rather striking characteristic
that the formant positions are independend of the pitch of the voice.
For example, the formants for the sound "a" (as in spa)
are roughly around 800 (F1) resp.1200 (F2) Hz., equally for a child's
or a man's voice. Consequently, high pitched singing (soprano) may impede
the pronunciation. Another consequence is that pitch transition of a song
is not easy - e.g. spoken words pitched up tend to suffer the infamous
"Donald Duck" effect. Modern pitch transition software can deal
with it properly. Below picture shows the formants in a normal vowel spectrum
and spectrograms (spectral time progression) of the vowels [i], [u] en
There are about 10 clearly distinct vowels commonly used in English and
/ or other Western languages. Slightly different sounds and / or pronunciations
exist but can generally be considered variations of these vowels, mostly
in local languages or dialects. The vowels are mapped in the IPA vowel
chart (International Phonetics Association), which rougly coincides with
the actual formant positioning.
Formant (resonance frequency)
positions are usually mapped in a logarithmic F1 vs. F2 graph. Below example
shows the formant graph with the vowel positions which will be used later
on. The gray area is where the formant ratio is 1 or less, which is physically
Below table lists the 10 main
vowels and their formants (Herz) with examples in different western languages.
Throughout this article, phonetic characters are shown as images, as the
phonetic font (TTF) may not be available in the fonts archive.
Analyzing the acoustic phonetics
A major hurdle in discovering a deeper physical reality behind phonetics,
in this case the vowels, is the fuzziness of the individually perceived
and/or generated positions in the formant graph. This can be due to cultural,
inter- and to some extend intra-individual differences. Different sources
list different formant positions. One study resulted in below vowel distribution
(note: scale and orientation of the graph are different!):
Despite their rather sketchy
positions, the allover distribution of the formants seems to be roughly
uniform within the allowed bandwidths, leaving equal and ample space for
all the formants on the logarithmic scale. The bandwidths are approximately
known: the lowest F1 should not be affected by high pitched voices, whereas
the highest F2 should still be in the range of sufficiently powerful harmonics
from the sound source.
These criteria concern the absolute positions of the F1 and F2 formants,
however without explicity relating them to one another (i.e. within a
vowel). The latter, defined as the formant ratio F2 / F1, will be shown
to be of pivotal importance for a geometric analysis, whereas at the same
time it should be mentioned that the formant ratio alone does not uniquely
identify all vowels. In other words, different vowels can have the same
formant ratio but with different absolute formant positions.
The combination of the individually perceived formant positions, the criteria
for their absolute positions and the ratio within each vowel will be used
as the phonetic basis and reference to develop a consistent geometric
(wave matrix) model for a true physics of vowel expression. In addition
to the existing sub-fields of phonetics and within the light of the universal
meaning of language, this new field could be referred to as causal
Symmetry-operations and topology of the activated universal medium
The medium which contains or embodies the whole of classical physics plus
all expressions which are commonly considered "anomalous" (in
fact, life and all its unique characteristics), is referred to as the
universal medium. Association of the universal medium with "consciousness"
may not in all circumstances be inadequate, but is better avoided.
The priomordial state of the universal medium, rather than considering
it "active" or "inactive", is described as the phase
of "homomorphic evolution", that is, there is no net causation
and hence no actual creation. The phase of awakened causal factors is
referred to as "auto-genesis". The universal medium itself remains
the ultimate material cause. However the mechanism of causation is not
one of actual control, i.e. it is not a linear projection, but it consists
in the form of a dynamic balance of facilitating and attractive forces,
called causal factors. This constitutes the triangular receptacle of the
universal medium in the phase of auto-genesis, also referred to as the
Causal Matrix. In the phase of homomorphic evolution, the causal factors
If the triangular figures of the universal medium in the phase of auto-genesis
are taken in the form of waves (i.e. causal waves), the creating entity
is referred to as a wave matrix. Conceptually, each individual
wave is contained in the triangular receptacle of causal factors, whereas
vice versa, causal factors are expressed through wave coherence (interdigitation
and nesting). Thus, there is an intimate mutuality between the Causal
Matrix and the wave matrix. As the intermediate stage to subsequent stages
of expression, the wave matrix could be considered the secondary stage
of the Causal Matrix, whereas the receptacle of causal factors constitutes
the primary stage.
In physics terms, the activity of the Causal Matrix, resp. wave matrix
is called symmetry operations and essentially describes the phase of auto-genesis
or generic causation.
Creation however would still remain rather theoretical without the emerging
of individual mind (in practice, biological mind with senso-motoric faculties
and a central nervous system). This will not be discussed in detail here,
however the impact of individual mind, that is, individual perception
and conception is critical to understand the geometric origin of phonology,
or causal phonetics.
The essence of individual mind lies not in any physical separation or
even distinction from the universal medium (resp. Universal Mind). It
rather consists in the individual and collective idee-fixe that the objective
world, including our biological body represents the ultimate reality.
This is in fact our normal state of mind, philosophically referred to
as "maya" or "samsara", or similar ideas. For clarity
sake, "spiritual liberation" means that the mind realises subjectivity
as the greater reality, and is thus freed from all physical bondages.
However the true state (salvation) is that neither objectivity or subjectivity
is the ultimate truth, but the universal medium itself which has nothing
to do with any conceptual or perceptive effects.
Hence, the transformation of the universal medium into the medium of the
individual mind is clearly not one of subjectivity into objectivity, but
one from universality into subjectivity-plus-objectivity. Whether
or not this is considered a psychological event, it definitely has a physical
effect. Clearly at this stage, psychology and physics go hand in hand,
leading to the tangible universe as we know it. In terms of contemporary
computer games, this does not create virtual reality alone - it verily
has a built-in physics-engine. In this condition, the Causal Matrix is
totally hidden from our view and as a result we have become immersed in
the mental and emotional imagery of everyday life. It is a state of inversed
causation, with its own consistent reason and logic.
For scientific reasons we may or may not appreciate the concept of "individual
mind", as it can seem a bit distractive. Either way this will not
affect the physical reality of the transforming universal medium, which
can physically (as well as psychologically) be described as the phase
of "inside-out-ness". It should be understood that this does
not mean "inside versus outside our body", as with not too much
introspection we will find that the body equally belongs to the outside
world, and even does our brain. Instead, it means, inside versus outside
our true selves, that is, the deepest creative and witnessing state of
our being. And this is of course, the Causal Matrix itself.
The individual mind's polarisation of the universal medium into objective
versus subjective regimes, is physically modelled as a torus. Clearly
it is not the "mind" itself which constitutes that state, as
"mind' is nothing but a name for the endless stream of associative
imagery. It we define "physical reality" as that which is thus
created by, or in the individual mind (while anything else is called "abstract")
we can say that the torus represents the only sustainable, and therefore
primordial physical shape in the original, that is, undifferentiated universal
Summarizing, the Causal Matrix
constitutes the total body of symmetry operations of the universal medium,
wheras the torus models the universal topology of the universal medium
being turned "inside-out". The generic "subjective"
and "objective" principles, being utterly conceptual, belong
to the Causal Matrix, and neither to the transformed medium, nor to the
mind. The physical binding between the causal symmetry operations and
the torus is therefore considered to be based on charge flow, rather than
on wave discipline directly.
When Neo sees the Matrix he has completely freed himself
limitations of the illusionary world - from the movie "The Matrix"
Analyzing the topology and spin of the torus
The torus forms the topological shape of the universal medium turning
inside-out. Hence it is not bound to any actual physical size. Its shape,
rather its inner aspect ratio's may not be of immediate importance to
its dual spin principle, however there is a compelling geometric clue
that a purely circular model, with zero hole diameter is ideal. This model
will be used.
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the animations, click here
In pure physics terms, the
torus could be identified as an electro-gravitational hydrodynamic vortex,
whereas it is suggested that coherent electro-gravity is but another term
for expressed consciousness. Another term is a hydrodynamic charge domain.
In that capacity, the torus constitutes the ultimate physical shape or
The combined rotational and toroidal spin, creating a vortex in the centre,
is visualized by means of a single representative charge path. Now, the
physical state (not: shape) of the E-G-hydrodynamic torus is determined
by the absolute spins as well as the spin ratio, defined as rotational
spin / toroidal spin. In physics terms, it could point at a certain balanced
or imbalanced electro-gravitational effect, however the relevance for
phonetics can be extracted from the pure principle.
The toroidal vortex can be considered kinetically balanced in the following
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Integer spin ratio's (1, 2, 3, ..)
Geometrically balanced inbetween two adjacent integer spin ratio's:
Adhering to a bandwidth within
reasonable spin numbers, most of them are only theoretical. Practical
spin ratios lie in the range of 1.5 to around 10. Yet higher ratio's are
not effectively different. Lower than "1" ratio's imply a toroidal
spin number higher than the rotational spin, which is unlikely to create
a stable vortex. Considering a balanced situation, that is, either a closed
charge path or the geometric average of two closed paths, the following
spin ratio's would be relevant:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
1.41, 2.45, 3.46, 4.47, 5.48, 6.48, 7.48, 8.49, 9.49
This sequence constitutes resonant spin ratio's of a self-sustaining toroidal
vortex. The challenge of "causal phonetics" is to correlate
acoustic phonetics, that is, the formant positions of distinct vowels,
with toroidal spin physics, in other words, sustainable spin ratio's in
a universal medium.
Causal phonetics - vowels giving a spin to the universe
As mentioned in the introduction, the science of phonetics objectively
analyses how the sounds of human speech are created, composed and processed,
but does not hint at the universal nature and creative potential of sound.
With the discussion of respectively the physiological principle of speech
generation, and the emerging of a toroidal principle in a universal medium
we have stumbled upon a striking similarity: both principles describe
the emerging of a stable dual resonance or -oscillator in a harmonically
Biological speech or toroidal spin: either way, a stable
dual resonator in a harmonically rich medium
In acoustic phonetics, allthough
the formants, that is, the individual resonance peaks for each distinct
vowel are known, there is no clue about a non-trivial physical correlation
between the two, that is, their ratio. Such correlation was found in the
case of the essentially same principle of toroidal spin physics, resulting
in a sequence of resonant spin ratio's.
A universal denomination of the vowels of human language might therefore
be formulated as a combination of the criteria for toroidal spin resonance
physics, with those for vowels known in phonetics. The latter included,
recapitulating, the perceived rough formant positions, the permissible
bandwidth and the formants' optimized distribution. Adding to the latter
the resonant spin ratio's of toroidal physics might accurately predict
the formant positions for all distinct vowels.
An important additional requirement is that (near) higher harmonics of
steady or dynamic spin ratio's are not permitted, as they could induce
harmonic cross-over jeopardizing the distinctiveness of the vowels. To
quickly determine "near" higher harmonics, the dynamic spin
ratio's are effectively treated as (integer + ½). This eliminates
all integer ratio's above 2, plus all multiples of 1.5. At last, ratio's
<=1 are not allowed as F2 <= F1 is acoustically trivial and physically
unlikely. With these additional criteria, the list of applicable spin
ratio's reduces to the following:
1.41, 2.45, 3.46, 5.48, 6.48, 8.49, 9.49
The remaining permissible spin-ratio's can now directly be identified
in the logarithmic F1-F2 graph:
Now, determining the absolute positions formants of the key vowels
on this map requires the combined skills of using documented values, as
fuzzy as they may be, plus actual hearing the results. For the latter,
the freely available phonetic software "Praat" ("Talk")
of the University of Amsterdam proved a fantastic help. Among a wealth
of other phonetic analysis and synthesis options, it provides the same
formant graph on which you can literally "draw" sounds, which
will then be played in real time. The possibility to slide from one vowel
to another makes it more easy and accurate to assess the result. This
combined process resulted the following formant schedule for a very substantial
part based on toroidal spin physics:
With the formant positions deliberately corresponding to the preferred
spin ratio's, the proof of the pudding is to check the allover distribution:
Discussion and conclusion
From the final result, the fairly equal distribution of the formant positions
based on the proposed literary, physics and perceptive criteria, it appears
that the approach is far from trivial. In fact, considering the available
formant bandwidth, the positioning of the formants could hardly have been
any different or any better and nature seems to have keen in utilising
the given space to the maximum. Admittedly the personally perceived vowels
locations are necessarily a bit fuzzy, however this was severely constrained
by the permissible ratio's, while the resulting distribution appears to
substantiate a fairly consistent choise.
Especially favouring the toroidal spin resonance argument is the fact
that the relatively widely spaced lower ratio's (1.41 to 2.45) are fully
utilized, while those who would not likely contribute to a nice distribution
(4, 4.47, 5) were anyway not allowed by the harmonic criteria. All by
all it seems a unique and very consistent niche where nature has allocated
our phonetic space.
The map could be optimized a bit and especially the vowel "i"
seems quite out of league, but it was left original to preserve the authenticity
of the process. As a matter of fact, a more or less ideal position of
the "i" formants (F1=280, F2=2200) was choosen by the makers
of "Praat". Clearly there are interpersonal differences and
simply taste. Finally, the (optimized) set as a whole could theoretically
be fine-tuned along the ratio's.
The presented evidence and proposed principle by itself clearly do not
constitute solid physics proof. However, as discussed in the introduction,
this new kind of physics includes "subjectivity" - not meaning
personal interpretation, but as a universal, generic creational factor
- verily the realm of pure idea. "Evidence based" thus gets
a novel and more expanded meaning, beyond the traditional quest for objective
proof. In this new line of thought, the principle of language can be understood
as a universal means of expression, rather than a merely descriptive principle.
Toroidal spin resonance, predicting the formants in a way consistent
with our perception and other known criteria, while at the same time naturally
consonant with the biological speech mechanism, appears to provide a realistic
working model in the emerging field of causal phonetics.
Practical applications of the proposed physics principle of vowel creation
could lie in the field of phonetics itself, for example speech synthesis
and developing a universal vowel standard. A much wider field of application
could be in emerging intuitional sciences, especially creational physics
which could generate an entirely new understanding of, and eventual control
over physical effects which today are considered "anomalous".
Click on above vowel
chart to see the corresponding toroidal
spin resonances of all vowels as 3D-interactive animation
note #1: brief survey of wave matrix physics and cosmology
At the primary causal level, wave matrix physics or generally the Causal
Matrix consitutes a full-fledged creational paradigm. However, as discussed
before, without the individual mind there can not be any question of practical
manifestation. The creational stages anticipating the biological mind,
rather than saying those stages are merely theoretical, they are highly
conceptual. Nevertheless, these initial, conceptual stages in cosmology
include not only the subjective, but both the subjective and the objective
portions of the material world, in seed form.
In particular, and especially in the light of above discussion, the
interaction between the Causal Matrix, in the form of the wave matrix,
and toroidal spin physics should be studied. This is sure to provide
a much needed link between contemporary physics (quantum / particle physics
and general relativity) and the symmetry operations of the wave matrix.
Moreover, it holds the promise to unify physics itself in the first
place. This very specific stage could slightly philosophically be
referred to as "Universal Mind", and constitutes the intermediate
phase inbetween the biological mind and the earliest causal stages.
As hinted before, the interaction between the wave matrix and toroidal
spin physics is one of charge exchange, rather than one of wave discipline
directly. The activating mechanism of the Causal Matrix is articulated
in the form of coherence patterns among causal waves, serving as an engine
or "pump" for scalar energy. The term "scalar" at
this stage may equally be interpreted as the Maxwell potential of electro-magnetic
waves, or in a more abstract style, as the qualitative aspects of EM-
or causal waves. The term "scalar waves" is slighly misleading,
i.e. all transversal waves have a scalar potential.
2D artists' impression of wave matrix coherence, plus or minus scalar
The integral system of wave matrix physics plus toroidal spin physics
may be illustrated as follows:
Integral wave-matrix - torus cosmological system. The
spin ratio controls, or
is controlled by scalar energy released and resorbed by symmetry operations.
This means that the torus,
emerging as a stable oscillator in the universal medium is identical
with, and physically constitutes the 3-D embodiment of the non-commutative
circulation of scalar potential among the coherence poles of the causal
wave matrix. The question arises then, whether this identifies the individual
mind, or more accurately, the impact of individual mind on the universal
medium? Indeed it does, noting that the existence of toroidal "inside-outness"
in the purely universal phase is entirely theoretical. In a more general
sense, in fact every stage in the cosmological paradigm can only be defined
in terms of the consecutive order.
The toroidal resonance
entity in the universal medium, direcly captured by the 7 tetrahedral symmetry
arrows of the causal wave matrix - geometric control over the tilting angle?
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settings and how to control the animations, click here
The somehow limited scope of the individual mind results from it's starting
point, which is the gradual, coherent assimilation of scalar potential,
which takes the material form of the biological body with its evolving
glandular, senso-motoric and central nervous faculties.
The non-commutative flow maintained among the internal faculties of the
wave matrix exists in two complementary forms. That is firstly, the potential
emanating from infinite scalar synergy is "microvita"
[P.R. Sarkar 1]. Secondly, the potential emanating from the
infinite scalar connectedness is energy. Microvita + energy = life.
Disambiguation: Golden Mean wave physics is properly associated with,
and in a way facilitates scalar synergy, but is not identical to it. Golden
Mean wave physics is textbook physics. Scalar synergy should be described
in its own physics and mathematical regime. See e.g. the work on potential
vortices by prof. Konstantin Meyl 2 (http://www.meyl.eu).
The wave matrix - torus interaction however shows a special and amazing
feat, discovered before by the author, which in fact does imply some sort
of geometric interdigitation. If a spin-ratio 2 torus topology is visualized
through 7 distinct charge paths, those 7 paths are each exclusively
and accurately indexed by one of the 7 spin angles (4 vertex, 3 side pairs)
of the tetrahedron. The meaning of it, mathematically or in physics,
is still barely understood.
note #2: The geometric origin of selective color perception
In ancient Vedic tradition, as well as in contemporary spiritual philosophy,
the Universe is considered to be made of "sound and light".
Especially in the case of sound in any classical sense, we cannot take
that too literally. Rather, this deep intuitional statement should be
understood in terms of the respective underlying principles, that is verily,
the generic causal structure of sound and light, rather than its objective
form. The causal structure of sound, insofar the vowels are concerned,
is the subject of this article. Similarly, the causal structure of light
was discovered earlier by the same author, demonstrating how wave matrix
physics accurately predicts the wavelengths of the primary colours, as
well as that of the retinal peak sensitivity.
wave matrix plus toroidal mechanism can thus indeed be explained as "made
of sound and light", modelled as follows:
as the vowel formants found were all based on balanced dual spin
configurations, this would imply there is no net perceptible creation
yet. Adding consonants might add some juice to the genesis machine and
actually get things started. This is exactly the traditional Vedic interpretation:
most (not all) Sanskrit sounds of creation are combined consonants and
vowels, e.g.: Ka, Kha, Ga, Gha, Una, Ca, Cha, Ja, Jha, Ina, Ta,
vibration in this universe has colour and sound. Every vibration also
represents a particular idea, and hence each idea has a vibrational sound
and vibrational colour. Many vibrational waves are too long or too short
to be perceived by human beings - we cannot hear their sound or see their
colour - but they do exist. We can speak of them as causal matrices in
the realm of vibrational colour; and consider them as the biija mantras
[acoustic roots] of the ideas with which they are concerned" - P.R.
Additional note #3: having
fun with "Praat"
The elaborate open source research tool "Praat - doing phonetics
by computer" was developed by the Phonetic Sciences group of the
University of Amsterdam (Paul Boersma, David Weenink). For this article
one of the many modules intensively used is the graphical vowel editor.
Open the vowel editor as follows:
In the Vowel Editor,
point at an F1-F2 combination or draw any line or curve through the F1-F2
space and it will synthesize and play the sound immediately. Below example
shows how to draw "you"..!
can be downloaded from http://www.fon.hum.uva.nl/praat/.
Additional note #4: wave matrix physics in heart and brain electrophysiology
Biology's skill of attracting and organising scalar flux, and therefore
its ability to be alife, can be measured at those places where the mind
is most directly associated with the body. That is, the heart and brain.
The highly conceptual, causal fluctuations of the wave matrix can obviously
not be measured directly. The central nervous system (CNS) which practically
evolves a microcosmic ("inside-out"..!) replica of the macrocosm,
if for nothing else than for survival, obviously does that in the electromagnetic
regime. In order to escape from endless cognitive regression, we should
not forget that also the body and brain are but emerging mental constructs.
That means, that the individual mind is rooted in universal principles,
in the way described above, and not in the physical body.
Thus it seems that the biological materials of heart and brain are the
only places in the universe where the symmetry operations of the causal
wave matrix can be measured directly.
Practical application lies in the field of psycho-physiological diagnosis
and training using the specially developed applications CardioGem and
NeuroGem. Being a very early application of wave matrix physics, having
hardly any classical context and reference, otherwise progressive therapists
sometimes have a hard time fully embracing the principles. Unless they
possess well developed intuitional skills and do not suffer too much academic-
or peer-pressure, there is the risk of old, restrictive thinking patterns.
With an openminded and somewhat playful approach, amazing experiences
and results can easily be achieved.
The psycho-physiological reality of wave matrix physics is easily demonstrated
with below real-life samples from the CardioGem and NeuroGem, each showing
low- resp. high coherence. More details and psychological interpretation
are available from the website
Wave matrix physics at work in psycho-physiology.
Two geometric spectrograms from the NeuroGem, brain coherence diagnosis
and training. Each track shows peaks indicating geometric recursiveness
in the EEG spectrum. Typically these peaks are located around Golden Mean
and Octave ratio's. The left recording (L + R hemisphere) shows little
coherence, the right recording shows very high coherence as a result of
biofeedback. Both recordings same person. During high coherence the test
person reported a feeling of trancendence and strongly increased mental
clarity, which lasted a few days.
Two tacho (red) and ICC (Internal Cardiac Coherence,
blue) history plots and ICC-histograms from the CardioGem, heartcoherence
diagnosis and training. The first person is an adolescent with typically
lower ICC. The second person, a mid-aged healthy subject shows good HRV
(Heart Rate Variability) and ICC. The CardioGem provides an final assessment
of combined EGC and HRV coherence.
- P.R. Sarkar, Microvita
in a Nutshell (Microvita and cosmology), Ananda Marga Publications,
- Prof. Dr. Ing. Konstantin
Meyl, Scalar Waves
- P.R. Sarkar, Discourses
on Tantra Volume 1, The acoustic roots of the Indo-Aryan alphabet, Ananda
Marga Publications, Calcutta
rights reserved, Triguna Media, 2010