Does a connection exist between the geometric vision of
a particular territory (geometric system) and the music it produces? Can music
be considered the sonorous expression of a territorial space? Does an
instrumental and functional relationship exist between Geometry and Music?
The leading idea of this brief paper is the hypothesis
that an intimate connection exists between making music and doing
1. Geometry in science and music.
From the Greek géa (earth) and metria
(measure), geometry is the method by which we measure the earth. It represents
the idealisation and study of the properties of physical
space and of the figures contained in it. The ideative process, a
characteristic at present attributed only to our own species, allows the
formation of ideas which are interpretative visions of the world.
No dominant ideas exist, because every human being and therefore every culture
is able to manage several visions simultaneously (Mercadante F., 2005). The term
geometry comes to us from the Greek via Latin. In the III-IV century B.C., the
Greek mathematician Euclid conceived it as an abstract science whose object is
space, considered as a togetherness of points and figures.
The new discipline (but not new practice
which was already present in ancient Egypt) emerges therefore as a study of
space. Actually useful for essentially practical purposes (such as measuring
land), with Thales (still earlier then Euclid) it encountered a fundamental
transformation. In fact, Thales introduced a new cognitive methodology, thanks
to which it is possible to imagine points, lines, planes and spaces. The
imaginative process results in considering these elements no longer as material
entities but on the contrary as abstract ideas observable only through the eyes
of the imagination. The modern neuro-sciences have identified in a particular
zone of the human brain a population of neurons which allows the mind to operate
inventively, that is to say “to imagine”. Some years ago Giacomo Rizzolatti
of the Parma University of Studies discovered some neurons which he defines as
“in the mirror”. Thanks to this discovery cognitivism attains the
confirmation of a solid neurological base. The neurons of the F5 area are
objects of great scientific
interest to many scholars of the neurosciences, because they are part of a
population of neurons which carry out important tasks connected with sensorial
and motor activity. During an experiment with macacos monkeys, Rizzolatti’s
team noted that the monkeys undergo a variation of electrical potential,
corresponding to the area F5, in the presence of motor activity being carried
out by other subjects present in their visual field. This population of neurons,
unknown until then, is called “in the mirror” precisely because it
represents in a mirrored fashion the motor activity of a subject in the brain of
another subject (Bertirotti A., 2004:17). In other words, the cells of the F5
zone are activated both when an animal carries out a specific action finalised
with respect to an object, as when it observes other individuals carry out the
same type of action. Obviously, these cells are present in Man who can therefore
manage to project himself into a fellow
creature, becoming an ingenuous psychologist thanks to a process of incarnate
Consequent to this definition tending towards
idealisation are the words (really quite difficult to understand unless
accompanied by a strong effort to think in the abstract) that Euclid pronounces
as follows: “a point is that which has no sides while the (straight)
line is a length without width” (Euclid 1996, Book 1).
By the term geometry today, we mean the discipline
which deals with the abstract form of matter as well as the science of
proportion (in this case we mustn’t forget the famous 47th
proposition of Euclid, motive of the jewel of the Ex-Venerable and defined by
the same Anderson, in the constitutions of 1723, as “surprising”) and
measure. If the object of geometry is the abstract form of matter, then geometry
is a first physical theory of reality. One thinks of the link between mass and
geometry in the frame of general relativity, which will be mentioned later.
Modern geometry has as its object all that is
measurable such as lines, surfaces, solids, etc. This science-method utilises
mathematics as the form, and numbers as the language. It is based on axioms
(abstract principles considered true without demonstration) and on the theorems
descending from them.
In Masonic language the term geometry is synonymous
with order and harmony. For example, it can be asserted that the great men of
literature possess their own particular geometry of exposition; that geometry is
present in musical and architectonic works, etc.
The ancient Greeks tell us that geometry is
“solidified music” (Geymonat L., 1970), meaning by this expressions that in
geometry we find an evident fixity of theoretical structure, together with a
rational explanation (the
mathematical root) of the musical phenomenon which is anything but motionless.
For their teachers (the Egyptians), sacred geometry and music were inextricably
connected inasmuch as geometric
laws govern the diatonic and mathematical intervals which form the notes in the
Western musical scale. Centuries later Goethe himself was to say that geometry
was “frozen music”.
2. Darwinian and Masonic evolutive harmony.
From the point of view that we are proposing, the idea
of Harmony is originally associable with the relationship our species has
established with Nature; and consequently with
its territory and its rhythms. Its territory, that is the earth,
is the primary expression of Nature and her will. It is possible to participate
in her will insofar as man’s energies permit. These energies are not usable in
a generalised way, simply because some aspects and phenomena of nature cannot
always be controlled by Man. A constant rationalisation of this relationship
with the forces of nature is necessary to resolve the resolvable. Harmony with
Nature thus takes on the form of Utopia i.e. Nowhere, or in other
words fulfilment that is possible but not guaranteed[ii].
The relationship Man-Nature is expressed in the west by
attitudes of power, both in small
everyday resolutive interventions and in large projects of dominion.
Nevertheless, there is a widespread belief that it is impossible to carry out
sufficient effective change to alter the course of the collective’s daily
existence. One of the possible cultural reactions to this belief is manifested
in a collective/individual tendency to social de-responsibility,
involving a passive attitude to the will of Nature. This takes the form of
“strong individualism” which in turn leads to a mystification of the
concept/attitude of solidarity.
In short, the concept of harmony with Nature is
often reduced to a kind of passive acceptance
of harmony itself, with the consequent incapacity to rationalise, or
rather to find an acceptable explanation for events. The collective’s
relationship to its own territorial space is in direct function with the extent
of its absolute necessity to establish such a relationship, and with the concept
of harmony with Nature as a collective economic/productive necessity.
From this point of view, it becomes evident that there can be at least two
contrasting attitudes toward the space of Nature that is the
At this point we need to understand
the role and function that the territory
has had in the development of the human species. The territory is an area which
presents well defined characteristics of the ecosystem and which must be
defended from entrance by other individuals of the same species. Conquering a
territory signifies being able to reproduce. Every animal finds both its vital
space and place of refuge in the territory. Furthermore, a better distribution
of the population is possible within a well defined territory, preventing
excessive ecological exploitation. Inside the territory there is a zone which
has no need of any particular defence, and indeed is also frequented by
individuals from neighbouring areas. This is defined as the familiar or home
range. Within this zone the individuals present in a given territory move
about to perform their own activities. Apart from the nomad species of animal,
nearly all animals carry out their daily activities in the territory and on the home range. In some special
circumstances they may possibly go beyond the home range and venture into
neighbouring territories. In this case the venture
space is defined as the area of exploration.
Animal behaviour, including that of Homo sapiens
sapiens, is visibly modified according to the zone occupied. In fact,
aggressiveness diminishes when passing from a territory considered one’s own
to an area of exploration. The nearer an individual approaches a territory that
has to be defended, greater is the aggressiveness shown him, while it is almost
completely absent if the individual approaches the boundary area. The final
element to remember is linked to the evolutionary function that the area of
exploration carries out. Inside this area reproduction exchanges among
individuals of different territories can take place. In this way inbreeding,
the mating among relations within the same territory (a harmful consequence of
territorialism), is reduced by the possibility of meeting outsiders in neutral
The mirror neurons to which we have briefly referred,
intervene in all spheres of human knowledge exactly because they constitute the
foundation of the imitative processes and because they induce the formation of
awareness of self. In fact, the moment one realises that one’s actions are
similar (because imitable) to those of other individuals, a sense of collective
belonging develops and one becomes aware of one’s own volition. For these
reasons the crossing over from the territory to the area of exploration
(via the home range), which our species continually does even in the
present state of evolution, is a complex cognitive phenomenon thanks to which we
conquer space, trying to harmonise it with what we previously occupied
and lived in.
To sum up, Man searches for spatial harmony
through the temporal management of his own actions which are mirrored
in those of others. This is an anthropological valuation of a purely Masonic
thought. It is a matter of the search for harmony expressed in Jacob’s ladder,
Mosaic Law and the Spiral Staircase. The ascent is always a spatial conquest,
both in the metaphorical sense and in the more typical profane territorial
sense. One also ascends horizontally i.e. elevating our similars and working in
the area of exploration (Cedrini R,
Masali M. Chiarelli B., 2005).
It seems clear that, notwithstanding the fact that
anthropological science is erroneously held to be absorbed in toto by the
Darwinian concept, the Masonic concept of earthly existence is especially linked
to the cognitive evolution of Man independently of the scientific contributions
of Charles Darwin[iii].
In the Origin of man (1979) Darwin wonders whether man, and all other species,
descends from some pre-existent form of life. Secondly, he wonders in what way
Man eventually evolved and, thirdly, what significance there is in the
differences we find among diverse human races. The main concept dominating
Darwin’s work is linked to the conviction that there is no solution of
continuity between biological evolution and social-cultural evolution. Moreover,
some behaviour traits attributed to man can also be traced (by careful analysis)
in other animal groups. However, the following
question then arises spontaneously: is the social human dimension also
subject to the same selective laws as biological evolution[iv]?
As a matter of fact, Darwin establishes that “in Man a change of direction
took place as the process of civilisation gradually progressed. The combined
course of progress (selected) of rationality and development (also selected) of
the social instinct; the correlated growth in sentiments of sympathy; the
emergence of moral sentiments in general; and the combination of behaviour and
institutions which characterise individual life and community organisation in a
civilised nation, enabled Darwin to observe that Natural selection at this
stage of evolution is no longer the principal force governing the formation of
human groups, but that it has relinquished its place in this role to good
behaviour. (Tort P. 1998:60). It is indeed “good behaviour” that opposes
the eliminatory effects of natural selection and inversely directs an apart of
social activity towards the protection and safeguarding of the weak of body and
spirit and assistance of the have-nots. Natural selection has thus selected social
instincts which in their turn have developed good behaviour and favoured
ethical tendencies as well as institutional and legal devices, both anti-selective
and anti-eliminatory (Tort P., ibidem:60). In this way natural selection
has selected itself because it has eliminated an antique form of selection
substituting it with a more suitable one. A reversive effect of evolution
is established in which competition tends more and more towards ethicity,
morality and altruism, together with the values of intelligence and behaviour.
It appears evident that every form of biological sociologism attributed to
Darwin is absolutely contrary to the theory of natural selection itself, and
that his ideas have instead been distorted and instrumentalised.
Equally evident is the Masonic functionality of the
Darwinian doctrine: the constant formation of a Masonic identity is linked to
the evolutionary principle which pushes men towards selecting the
highest degree of both social and biological harmony. In the present writer’s
opinion, the metaphor which best explains the socio-existential action of the
Mason is the Mobius Strip, whose torsion manifests didactically both the revolutionary
continuum and the idea of the infinite.
3. Ernest Ansermet and music.
Music has both a globalising and globocentric role (A.
Bertirotti 2005). Music leads to transcendency. Ernest Ansermet, in the first
page of his essay, Les fundaments de la
musique dans la conscience humane, begins by setting “auditory awareness” into the frame of an auditory Horizon. He then
goes on to describe the appearance of music in the action of sounds, through which the auditory image is transformed
into musical image[v].
This passage to imaginative behaviour is made possible
because affective activity (neuronal population of the limbic system) is linked
to that of hearing, thus giving sounds and image which has conscious meaning for
Man. Mans musical consciousness produces a precise emotion to the musical image formed by sounds that reflect a
singular existential course. On the one hand, auditory awareness, understood as
a particle of the species’ existence, identifies the sound; on the other, the
sounds heard circumscribes the existential course of consciousness. In this way
a close relationship is established between the sounds heard and real life,
because the former are inserted into human existence and set themselves up as
milestones of experience. The dichotomy between the outside world and the
intimate human one, between the abstract and real life, is resolved in man’s
consciousness. The moment he hears the sounds, a dual action takes place,
neuronal and cognitive. Both a simply two ways in which this unique structure,
the perception of the mind, is lived as an event of consciousness. Music
resembles God because it says things that are infinitely diverse, in affective
situations that are infinitely variable, and through human subjects that express
there own infinite needs through concrete every day ones. For this reason its
creative activity can be endless. But it can only be endless in its tonal and
These in synthesis are the guidelines to Ansermet’s
thoughts on music. Music originates in human affectivity, in those emotional
depths of the individual that are impossible to explain fully in words, and
which are expressed by utilising what Ansermet describes as the only means
possible i.e. Western tonal and rhythmic language. (In this perhaps resides the
philosopher’s limits). A further element underlined by Ansermet is Man’s
desire to be in the likeness of God. Ansermet is profoundly religious and the
whole of his philosophical thinking expresses this conviction more or less
clearly. He also maintains that the dialectic medium which links Man to
transcendency is the tonal system, precisely because it is so rooted in human
nature that no other ways of expression can exist beyond it.
The concept of creativity is inserted into a
philosophical-individual dimension and linked to wider concepts such as: talent,
ingeniousness, inspiration, imagination, form and style, etc. These terms, even
if they denote apparently quite distinct spheres, are in fact very often
inter-connected. In creativity – according to Ansermet – resides the purest
musical talent of the composer, even if his personality is manifested in the
personal style, original form and affective pattern, all translatable into human
sentiment. In the first dimension which Ansermet defines as pure
reflection, the composer finds himself
in direct contact with the musical image and with his own imaginative
powers. For the author, pure reflection is almost a conditional reflex. The
Great Architect of the Universe (defined as the Creator by Ansermet) comes into
direct contact with the musical image and He Himself
- as the impulsive consciousness of self – is implicated in the act of
expression. In pure reflection of the
imaginative act, the composer places his faith in intuition only. This input towards transcendency, part of the psychic dimension, is
integrated, transcended and perfected by another dimension: the second
reflection, i.e. the dimension of thought or abstraction. This dual route
– first reflection/second reflection – is important, since the Grate
Architect of the Universe is continually found in equilibrium between the two
poles of spiritual affectivity and absolute values. Both contribute to forming a
work of art.
From this point of view, creativity expresses the
musician in his entirety, his emotional life included. The work of art
transfigures and transcends what is performed, and contains a whole world and
way of being in the world. The musician, though starting out from his individual
dimension, moves away from his real and contingent mental situation to enter a
world of spiritual affectivity and of absolute values.
Music (as a creative-cognitive activity) becomes a human
expression of universal architectonic transcendency, and therefore propounds a
metaphysical cognition, even though rooted in the neuronal map of our brain.
4. Geometry and Music.
The relationship existing between geometry and music
has remained essentially the same as conceived it Pythagoras in his time. He
observed in fact that the hammer blows of the blacksmith at work are sometimes
consonant and sometimes dissonant, tried to find out the reason. He weighed the
hammers that produced the sounds, and at once noticed that the sound produced
depends on the weight of the hammers. From there it was a short step to the
stretched nerve strings of the ox and to stringed instruments in general, such
as the lira. Pythagoras discovered that the same rule applied: if one string is
twice the length of another, the two produce sounds at an interval of one octave[vi].
When on the other hand one string is one and a half times as long as the other,
they produce sounds at an interval on one fifth.
It was thus that Pythagoras discovered the musical
intervals. In the temperate tonal System (fig. 1) each note or degree is signed with Roman numeral: I II III IV V VI VII VIII.
The temperate tonal System with relative degrees
The first note of any scale is called tonic precisely
because it defines the tonality. In this System, the tonic note is the most
important of the scale (unlike the dodecaphonic System). Immediately, after the
tonic in importance comes the dominant, because it carries out a fundamental and
central role from the aspect of harmony and melody. Then come the sub-dominant
that carries out a slightly inferior role to the dominant.
The leading note is the VII degree of the scale in the tonal
System and has the extremely important role of leading the melody and harmony to
Pythagoras numbers the whole universe and it is
difficult to move away form such a brilliant and portentous product of the mind.
For years Geometry and music began to speak to each other only through the
harmonic intervals or, at best, through the play of symmetry and movement of
J.S. Bach or the Flemish counterpoints. More recently, the amazing fractals are
5. Living system and music.
“Consciousness is a process,
not an object”
(Edelman G.M., Più
grande del cielo).
Diverse animal species manifest complex co-operative
behaviour. Glow-worms that light up in synchrony, crickets that sing in harmony.
Animal behaviour from which a definite scheme seems to emerge of
The interpretation of living structures as open systems
(exchanging matter and energy) and of the work Ilya Prigogine on the Theory
of dissipative structure, the co-existence of structure (the scheme of
living being) with change, enable us to see organisms as living system that
operate far from the point of equilibrium (death) by means of myriads of
irreversible processes, the chemical reaction of life[viii].
A living organism is structurally linked to its habitat, in the sense that it continually
carries out structural changes (adaptation, learning) in reply to interaction
with the environment. Ontogenesis outlines the history of change every living
structure through the process of the Piaget theory: assimilation, adaptation and
equilibrium. Analogously, the structure of the living organism determines its
From this point of view, communication is not intend as
an exchange of information, but only as behaviour
co-ordination between living organism in a reciprocal structural
combination. This kind of mutual interaction applies to the simplest organ as
well as to more complex ones.
Humberto Maturana, Chilean scholar of neuroscience, was
struck by one clear example of behaviour
organization, a non-human case of communication that he found in the song of
the African parrot during courtship and the formation of the pair. The two
parrots are enable to see each other through the thick forest and to the ear it
seems that only one bird is singing. But in fact both partners are singing one
melody in unison, and the melody is unique to each pair of birds. The song is a
duet in which each bird begins a refrains of each pair. And naturally the melody
is a not passed on the offspring (Capra, 1996).
Still on the same theme of behaviour co-ordination, a
group of Ditch biologists has discovered that titlarks (Parus Major) sing a
higher frequency in town in order to overcome the noise of traffic and attract a
mate. Probably the first case reported of a wild bird modifying its mating call
to adapt to an ecosystem altereted by the human species. Other bird species lack
this singing flexibility and could lose the opportunity to mate in extremely
noise conditions, victims of the changes introduced by urbanisation. It emerges
from this research that birds living in very noisy area choose to sing at a
higher frequency noise of cars, aeroplanes and factories (unlike those living in
quieter streets). This would explain why some species survive without difficulty
in the large cities of Europe compared to sparrows, for example, which are less
able to modify their singing.
Duncan Watts was able to observe on hot summer evenings
that when crickets populating the countryside emit sound by rubbing their wings
together, they do so in amazing unison. Since the intellectual capacities of
crickets are not particularly well developed, now does each insect known in
advance when they emit a sound and when to stop? Similar phenomena have been
observed in glow-warms that emit light in synchrony by means of the sinoatrial
node, the natural pacemaker that
regulates the heart beat.
We are once again in the presence of an organisational
tendency in nature. When a crickets sings it induces the crickets nearby to emit
sound a little earlier than they would otherwise have done if they had not heard
the signing. If this process is repeated with other neighbouring insects, in the
end they will all sing in harmony[ix].
What kind of geometrical diagram can best explain the
interaction between these insects? Just as in a stadium we hear the voices of
those nearest to us more loudly than those furthest away, so it is possible that
the principal harmonic interaction takes place amongst crickets nearest to each
other. All the same, to explain the speed with which the harmony speeds we also
need to consider a small number of casual links amongst crickets further away.:
some crickets sing more loudly so as to be heard by others more distant. In this
way we obtain the small world network
illustrated in Fig. 2 in which a few casual connections also enable elements
further away to connect quickly.
On the right, the small world network
quite likely that the function of this kind of arrangement is to ensure greater
cohesion un the group, and as such guarantee greater control over the territory
and frighten away eventual predators.
6. Anthropology and music.
“And what do you say about
the message which says we
should look for the truth?
It makes us forget that life
without mystery is arid
and that certain things – for
example our friends – should
be loved more than happens
(Feyrabend P., Dialogue
The evolution of Homo
Sapiens Sapiens is shaped above all by continuous and constant adaptation to
the spatial-temporal. This
characteristic, which is truly cognitive ability, enables us to colonise
(anthropomorphis) the entire planet, including areas with difficult climates
(poles and equator). In fact, every environment in which Man is present is
witness to the immense flexibility and enterprise that distinguishes our
participation in the ecosystem.
On the long course of evolution (which is still not
complete), every migration has carried us towards newer and pleasanter regions.
That course, however, has also necessitated adapting to changes in the time
zones in order to get used to different rhythms in the day. Here too Man has met
with complete success, revealing his second great gift of flexibility, that of
Studies have revealed the existence of special internal
biological rhythms lasting roughly 24 hours. The rhythms called circadian
(from the Latin circa, about, and dies, day) are present in most living organisms, from unicellular to
more complex ones like Man. These regulate numerous vital functions (from
photosynthesis to cellular division, from the blossoming of the flower to
baby’s sleep). The circadian rhythms are not the effect of an external
phenomenon (such as day alternating with night or the ebb and flow of the
tides), but of internal biochemical mechanism. What is surprising is that the
human biological clock has 25 hours and not 24, and that a complex biological
mechanism called dragging provides for
bringing it into alignment with day alternating with night. This discovery
(1972) was made by the French speleologist Michel Siffre who spent 7 mouths of
solitude in a grotto in Texas. At the end of the experiment he found that his
organism was synchronised to 25 hours. The circadian rhythms in the behaviour,
psychology and biochemistry of mammals are controlled by the central internal
clock of a brain structure known as the superchiasmatic nucleus (SCN). The clock
is synchronised to the environmental cycles of light and darkness. It is well
known thanks to everyday experience that a number of days are needed to adapt to
a new time zone. Nevertheless, the details are not yet altogether clear how this
adaptation takes place. In a paper published in the magazine Current
Biology, a group of researches led by Johanna H. Meijer of the Dutch
University of Leiden, reported their discovery that this process does not
necessarily involve the gradual adaptation and synchronisation of the neurons
comprising the central circadian clock. The authors studied the behaviour of
specimens exposed to a 6-hour delay in the normal cycle of alternating light and
darkness (a change covering the transition of the time zone from the eastern
Unites States to western Europe). Thanks to electrophysiological analyses of
cells constituting the central circadian clock, the scientists made a surprising
discovery: a part of the cerebral mechanism (represented by a dorsal group of
cells) shows oscillations of activity corresponding to a slow regulation of the
clock to changes in rhythms, while another part (represented by a ventral group
of cells) shows a distinct scheme of activity that corresponds to a much faster
regulation. It is probable that all this due to the effects to the
neuro-transmitter GABA which, the researchers found, stimulates the dorsal SCN
and inhibits the neurons of the ventral SCN. Since GABA transmits information to
the two part of the SCN, these differences could in fact have a complex
influence on the way in which the two groups of cells adapt to the change of
light (Albus H., Vansteensel M.J., Michel S., Block G.D., Meijer J.H.,
A highly evolved animal, therefore, creates geometry
around itself of both a simple and complex nature. Hunting (in its social and
co-operative organisation) the perimeter of villages in which it is organized,
its very movements in search of new areas to exploit and know are expression of
this important and refined existential
In observing its own territory, both the inhabited area
and the one to be domesticated, mental geometrization
(also defined today as mental maps, or
conceptuals) is the basis of complex
and fundamental evolutive behaviour. The mental maps allow us to codify and
decode everything that reaches our brain, through the senses. Every event
typical of daily human life, every reaction and observation, depends on these
maps. They are veritable windows on the world which often we confuse with true
reality. In fact, mental maps always are untrustworthy in greater or lesser
measure. An absolute reality simply does not exist exactly because reality
is absolute for each individual, and is the architectonic result of one’s own
mental maps, or rather those which reveal themselves and continue to reveal
themselves as useful strategy in personal adaptation. The communication of
several maps takes place in the cultural system, thanks to which diverse and
personal ideas are compared to each other[x].
The retina absorbs less than a trillionth of a quantity of electromagnetic
energy reaching it. It is consequently impossible to see-constructs the world as
it actually is or could be, since each individual automatically excludes a part,
even before the whole is elaborated by the primary visual cortex.
It is possible therefore that a given geometric
system, characterised by mental maps, has led to a consequent codification
of expression (hendecasyllables, sonatas, various communicative styles, music)
and produced precise anthropological results, as well as enlightening roots. In other words, the telemetrical apparatus of Man
(constituted by the synergic action of sight and hearing) is closely linked to
the walking mobility of our species. When an individual
moves from one place to another, he creates the time for covering the
distance by the adverbs before and after. These
two adverbs are really tow sounds
which acquire a linguistic significance only when our species ascribes a precise
semantic value to them. The terms before
and after do not refer to real objects
present in nature, nor to living subjects or organism. They describe a temporal
process that occurs in a geometric space. This exact space is that of the walking
movement. In this way, the sound of the morpheme before and after become
expressions of an existential segment
which is geometric, because inserted
in the space-territory where it was born and developed.
Pankepp (Altenmuller, 14:42-53) maintains that music
was born from the cries of a few who, moving away from the group for hunting or
other necessary purposes, kept in touch with the others by signalling their
position in the territory (Révész G., 1983). The “Call Theory” shows
exactly how much these cries can depend on the perception of space, and so on
the geometric interpretation that one
has of one’s own territory. We are dealing with a truly geometric system which
each individual shares and that matures and consolidated within the social group
the individual belongs to. The sound, in the form of a cry (call and recall), becomes
a signal of individual specification in space (territory) and time (day). On
this subject, we recall the presence of a symbolic isomorphism between the
spatial temporal dimension of making music and geometry and that represented by
musical notation. The musical score, when not referring to a monodic instrument,
extends along the two Cartesian axes of space (vertically, from low to high,
i.e. harmony or sonorous density) and time (horizontally of melody i.e. of the
chronological sequence of a linear series of sounds).
The present author maintains that the sonorous
measure of this geometric spatial-temporal system is music. It takes shape
therefore as a geometric perception of territory, of its particular vital
organisation, and is meant to be a mirror of its culture through the formation
of semantic sounds, .i.e. the verbal language.
The geometry that every culture creates is the formal
expression in signs a particular of ecobiological system of life, because it is
functional to survival in that particular ecosystem. In revealed and formalised
geometry, every individual reflects his own territorial identity, an evident
necessity of onto-filogenesis[xi].
While on this subject it is useful to remember the
revealing contribution of Karl Abel (the German glottologist) given in 1884 on
the opposite meanings of primordial words
(Abel K., 1884). He sustains that “in the Egyptian language, the only relic of
a primitive world, we find a considerable number of words with two meanings, one
indicating the exact opposite of the other. Try to imagine, if one can manage to
visualize anything so obviously absurd, that the German word for strong
signifies not only strong but also weak.
That the substantive light is used in
Berlin to indicate both light and darkness.
In face of this and several other similar cases of antithetical meaning there
can be no doubt that at least in one language a large number of words signified
one thing and its opposite contemporaneously” (Abel K., ibidem:4-7-).
Certainly this linguistic tendency is not yet a matter of chance, particularly
considering the number of examples cited by the glottologist. Furthermore,
“Egypt was not at all a country of the absurd. On the contrary, it was one of
the first places where human reason was developed. They posses a pure and highly
dignified morality and had formulated a great part of the 10 commandments at
time in which people to whom we attribute civilisation today were still in the
habit of sacrificing human victims to gods thirsty for blood. Of all the
eccentricities of Egyptian lexicon, perhaps the most extraordinary, apart from
the word that contain in themselves their opposite meaning, is the inclusion of
other compound words in which two terms of opposite meaning are united in a
combination in which only one of the two terms has meaning. There therefore
exists in this extraordinary language non only words that mean strong
as well as weak, command as well as obey,
but also compound words like old-young,
far-near, join-divide, outside-inside,
words which although they join extreme opposites, intend the sense of only one
of the two words young in the first
case, near in the second, join
in the third, and inside in the
fourth. Initially, therefore, conceptual contradictions were united in these
combined words not in order to create a third concept, as sometime occurs in
Chinese, but simply to convey with these composite words the meaning that one of
the two contradictory words would have indicated on its own” (Abel K.,
ibidem:15). The question however is relatively simple, since our concepts are
formed by comparison, i.e. through the relationship that an individual
establishes between numerous aspects of nature. On our planet all things are
relative, especially with respect to the place-time position in which the
individual finds himself. “Since every concept is in some way the twin of its
opposite? (…) Seeing that bit was not possible to conceive the concept of
strength if not bi opposition to weakness, the word that signified strong
a simultaneous reminder of weak, and
only in this way could its existential meaning be reached. This word defined in
fact neither strong nor weak, but rather the relationship between tow concepts and their
difference, which created a likeness in both (…). In fact Man could not
acquire his simplest and most ancient concept except by comparing them with
their opposites, and has only learned gradually to separate the two parts of the
antithesis and to think of one without consciously measuring it against the
other” (Abel K., ibidem:18).
In communicative writing is antithetical lemmas (such
as strong-weak) had to be included in
some way to respect the intention of the writer. To deal with the problem the primitive
Egyptians added determinative images
to the writing. “When the word ken
is meant to signify strong, the image
of the straight, armed man is placed after the sound written alphabetically;
when the same word is meant to signify weak,
the letters represented the sound are followed by the image of the crouched,
indolent person” (Abel K., ibidem:18). In the spoken language quite probably
gestures took the role that the images express on the papyrus.
The stylized geometry written besides the word
indicates its true meaning in the context in which it stands. In order to
stimulate the formation of the idea of strength
in individual I must be able to associate it with the action that expresses it. Every action is sign-design in space.
Every action is a geometry which is codified in the syntax of the language so
that it is more easily administer to and understood by the whole of humanity.
In this way, music becomes a key to reading and an
expression of geometry. In fact, both time and space reside in music because
they are its constituent elements, obviously subject to the perception of these
two categories that the people who develop them posses (Bertirotti A., 2003;
Bertirotti A., 2004).
For example, the measurement of space can be in the
oral tradition by means of the time employed to traverse a given space while
producing sounds. The sounds therefore become a musical expression ante
litteram of the given space inside which the same sounds move and are
reproduced. In this way, both time (understood Aristotelian accession of measure
of movement according to before and after) and movement become components of
sonorous space (Aristotle, Physics).
The measurement of a space can therefore be expressed by the sounds that Man
attributes to the movements in the course he covers, inside the space itself.
There can be many examples, of play in this behaviour. Take, for example, the
games linked to the reproduction of songs that mark the time in which one must
carry out particular actions.
In addiction, music offers the possibility of
quantifying space (simply by passing from a single melody to a polyphonic one we
sense intuitively a growing fullness of volume). As a further example, think of
the noise of the heard of buffalo which different from the noise of the single
animal and immediately coveys the intuitive knowledge of the numbers
of element involved, and therefore of the space that they occupy.
7. Geometry, sound and action.
“The hands are the soul of man.
They are our character.
Educating a hand means
teaching it how to be
(Merini A., The
A child crawling on all fours in a straight line is
already constructing a rudimentary form of geometry. The first fortress he
builds with material to hand to defend himself from childish fears is also
geometry. The games he creates on his on with the help of building blocks (or
clay etc. for children thousands of years ago) express the child’s
consciousness of the space around him and of the relationship resulting from it.
Actions of this kind are important for forming a sense
of personal identity which is the result of an endless process of
ontogenetic, exactly because every individual experiments with daily life as an imperfect
approximation to himself. No human being who has the fortune to live (not to survive) to the end of his days can claim
that he has achieved a sense of knowing who he really is. There always is some
difference between what we are or what we believe we are and what we would like
to become. If this were not so, no individual would have projects in his mind
for living. From this point of view, the sense of personal identity is not a state
so much as a continual process of architectonic construction of what we would like to
be. It is a process which develops during the time of one’s existence,
during the history of evolution of Man, and within the space of one’s own
Within the bounds of spatial perception, the very
presence of sound and of its interpretation plays a significant role. The
lateral changes in the source of sound are in fact more easily perceived that
the vertical changes. It would therefore be easier for a child to understand the
concept of segment or the straight line in general when this is represented by horizontal lines rather than vertical
ones. The sound of this representation would reconcile a profound spatial interpretation in the
brain and a fundamental medium. For these reasons, a
knowledge of the Set square and of the Masonic compass demands a high level of abstraction from the neuronal point of view which young
evolutive ages cannot attain. The
symbols,(particulariy masonic ones) and their comprehension
require not only the initiation and conclusion of neuronal myelination, but also
the connected and refined action of
neuronal maps in the frontal, prefrontal and
to the subject of sound perception in the spatial ambit, the position of the
ears helps us to localise the source of sound just has the frontal position of the eyes enables us to evaluate distance. The direction or provenance of a
sound is identified thanks to the sensibility
of the scolopidian cells and to the difference in time of the latency of activation between the two
sides (Giulio L.F., 1991).
The decodition of sound
does not take place exclusively on one definite, precise side
of the brain, it has been shown that the difference in auditive elaboration of sound already originates in
the ear. “From birth – explains Yvonne Siranger of the University of California at Los Angeles – the ear is structured
to distinguish between different types of sound and to
transmit them to the optimal side of the brain for elaboration.
The different treatment of
sound on the part of the two sides of the brain is well known.
The left side dominates the decipherment of language and of other signals of rapid change, while
side deals with elaborating the tonality of music”.
studying the tiny cells of the internal ear which pact as vibration amplifiers,
Sininger and Barbara Cone-Wesson of the University of Arizona discovered ~in a
sample of 3000 new-born baby) that the left ear provides greater amplification
of musical sounds while the right aniplifies more loudly the spoken language (Sininger I., Cone-Wesson B., 2004). This
asymmetry between the two sides turns out to be fundamental adapting to the
universe of sound, consenting to its better scansion.
own geometric vision of the world can
be defined, interpreted and explained by the expression vital geometric system. From this thesis it follows that Masonry
configures a cognitive process as a form
of visual-auditory architecture of the world.
geometry was sufficient, to a Limited degree, for a vision of the
pre-relativistic world. Einstein’s theory and his Weltanschauung
a new geometry: a non-euclidian geometry even more suitable for explaining
reality compared to the traditional method. This variation can also be considered as a radical change in the vital geometric system. Einstein
sustains in fact that space is not
linear but on the contrary curved, due to the multitude of celestial bodies. The presence of the Sun has the effect of
deforming the surrounding space, and time muovement of the planets round the
sun takes place along the “natural lines”
(the geodetics) of space, which of
course have also undergone this curvature. In other words, space becomes curved,
and in this curved space the shortest
distance between two points, which previously one imagined to be a straight line, is
deformed into a curve.
geometry of action.
In the history of western
philosophical thought one often comes across diatribes about how much the body
influences the psyche and vice-versa. According to a
cognitive-connexional prospective (to which the writer makes reference) the
question put in these terms constitutes a false problem (Siegel D., 2002). The
development of human thinking, always configured as thought,
comes through action. Even in remote times, Man began to explore his
environment. He moved, acted and projected new actions. These always were
penetrative, i.e. linked to the necessity of moving to achieve the objectives
and aims to be found in his ecosystem. This matter has already been dealt with
in the question on the home range.
actions directed to the outside, one then passes on to the formation
of awareness of the actions themselves[xii].
Man learns to understand that in order to plan
a course of action he must imagine himself moving, both in space and time (Rizzolatti
G., 1998). This is extremely refined form
of cognition can usefully be expressed in a code
that formalises it exactly. This code is
called language, whether it be
numerical, verbal or geometrical.
For us masons it is called ritual. Movement
(therefore action) becomes the
prerequisite of verbalisation, of numeration and of geometrical music. A really true system of spatial –temporal
codification begins to take shape based on existential geometry, in which every form of movement constitutes cognition of the action. For this reason, theory cannot exist without practice,
which precedes the former, ab origine. Clearly, both act as reciprocal carriers at the present
stage of our evolution:
the actions stimulate the formation of conceptual maps (it is no coincidence
that they are defined as maps) and these in turn stimulate the actions, both
present and future.
7.2 The geometry of sounds.
Listening to sound often induces the evocation of
images. A high frequency sound can evoke (with a formal symbol) a shape
with few details, visualized as a texture
with smooth internal transitions.
A bright, acute and highly articulated sound, on the
contrary, will evoke a shape rich with indented and well outlined details.
In the same way, well defined sonorous articulation can be born from images, contexts, habitat, or from the unconscious visualization of them in relation to the geometry
attributed to them or invented for them.
But what motives can there be for inventing a
Herodotus and Aristotle did not believe that the
birth of geometry (and of mathematics in general) was possible in any age before
the ancient Egyptian civilization.
Aristotle assumed that its origins should be looked for in
the well-to-do priestly class present in Egypt, who used it for ritual
ceremonies. Herodotus dates geometry back to the particular necessity the Egyptians had to
restore territorial boundaries after the periodic flooding of the Nile. The fact that
the Egyptians surveyors were also known as “layers of
cords” might mean that they used them both for relaying the territorial boundaries, and for tracing the plans
for religious buildings[xiii].
Neolithic Man reveals its own peculiar interest for spatial relationship, probably
propaedeutic to the birth of geometry far from the rock face, even though it could have simply
been aesthetic pleasure for its own sake that give origin to the pictographic
exertions of our ancestors. Further evidence derived from India also induces us
to think that the
need to construct buildings and
measure land played a part in
the origin of geometry. Arabesque
appears later, probably originating in the taboo
placed by the Islamic religion on depicting
the realistic (in terms of human or animal figures with the purpose of avoiding
ill-omened idolatry). This prohibition induced artists and decorators to direct their
creative imagination toward a characteristic abstract dimension.
attention to geometry, and sensibility to the different kinds of geometry, comes about through the basic
urge to resolve practical problems – like the position of horses
and of men during a hunt or a battle – or
through social coercion.
We also observe that a parallel can be drawn between
the dimensional development of
geometry and the anthropological
of music. Geometry of a linear
dimension that exists on a straight line can be compared to the first indistinct
repetitive sounds made almost accidentally by Man. The extension to the plane,
to two dimensions, can be compared to the emergence of the stratification of
space, and of the classification and arrangement of sounds, this time
differentiated. The passage to three dimensions, space in its stricter sense
(codificable in forms of superposed
lines, just like the future pentagram), gives origin to move
complex scores, inside which can be
identified the precise it is musical tasks assigned to them. As already mentioned,
it is the manifold variety of timbre that creates the sensation of increased
Music is linked not only to
the geometric-spatial dimension, but also to expressig the perception of time,
obviously through the duration which
is one of the four fundamental parameters of sound.
tradition, the Jubilee year (shenat
yobel: Leviticus 25, 8-17), proclaimed every fifty years on the tenth day of time seventh month by the trumpeting of the ram’s horn (yobel), signified a fundamental turning point in the
relationship between the Lord and his people, and among the people themselves.
“And ye shall hallow the fiftieth year, and proclaim
liberty throughout all the land unto all the inhabitants: it shall be a jubilee
unto you; and we shall return every man unto his possession,
and to his family. Ye shall not sow,
neither reap, that which groweth of itself in it, nor gather the grapes in
it of thy vine undreased... in this year of this jubilee ye shall return every man unto
his possession. Ye shall
not therefore oppress one another; but thou shalt fear thy God” (Leviticus 25,
The sound of the horn takes on a precise meaning: it
transmits the announcement of freedom from slavery, a sociological turning point.
The necessity to transmit that meaning immediately, reveals how sound is a more
than efficacious method for spreading the
word. Furthermore, the sound of
the horn is useful in giving
solemnity and prestige to an important
occasion, no doubt already present
in the minds of the faithful. The sound of the horn also reaches far distant places. Cheosing such an instrument
probably indicated the people’s knowledge
oh the long distances involved, i.e a fairly clear image
of the geometry of their boundaries
and of their own vital
emphasis of each sound is typical
of traditional Chinese music as a source for philosophical
meditation, and through these passages of sound
we return once again
to the spatial-temporal perception inherent in this kind of culture.
In the novel The virgin in
A. Byatt writes: “The iambic pentameter embodies, if one can put
way, the number of heart
beats between inspiration and exhalation, Shakespeare’s verse is the human heart beat,” claiming that his observation
was inspired by Music practice by
Franchinus Gafurius (l496).
An observation that clearly arises from the assumption, that the human
heart was the
first clock on
which Man placed the time.
Just as metrics unveil the
perception of time, so a
music can do
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[i] Ingenuous psychology is the study of what is usually
called “good common sense”, thanks to which a culture system manages to
control the social dimension of its human relationships. Every culture, in fact,
develops special adaptive strategies within its society to guarantee its own
survival. The explanation (or rationalisation) for these strategies comes
from the core of good common sense.
[ii] The term Utopia is used for the first time by
Sir Thomas More, in his Libellus vere aureus nec minus salutaris quam
festivus de optimo reipubblicae statu deque nova Insula Utopia (Lovanio,
December 1516). The term emerges from the myth of Cronus, from the Golden Age
and from the Garden of Eden, and systemized in Plato’s great
political-philosophical opus The Republic. In the time of the Romans,
characterised by pragmatism adapted to governability, Tacitus touches on Utopia,
comparing the barbaric strength of the invasions to the corruption of Imperial
Rome. The Hebrew view-point, on the other hand, links Utopia to the
awaited coming of the Messiah which is then transferred to the Catholic
Christian eschatological perspective, from the Apocalypse to the Fathers of the
Church. The Middle Ages meet Utopia through the pauperist heresies and
the palingenesian visions of Gioacchino da Fiore (millenarianism or chiliasm);
via tracts of social communism we come to the Reformation with the
Lollards, the Hussites and the Anabaptists. From the zeal of the Puritan concept
in Law of Freedom (1652) by G. Winstanley, through the modern era, we
come to the flowering literature of the Enlightenment. However there are many
cases in which , to use Sorel’s expression, Utopia becomes a work
hypothesis. We are reminded of the technological visions in New Atlantis
(1627) by Bacon and the Commonwealth of Oceania (1656) by J. Harrington.
The Enlightenment vision of history confers on Utopia the task of
resolving the glaring contradictions between Man and Nature, between the town
and the country. In the Code of Nature (1755) by Morelly and the Social
Contract by J.J. Rousseau the myth of the “noble savage” becomes
synonymous with social progress, spanning the French revolution to arrive at the
Restoration and the challenge of romanticism. We witness the advent of the
technical-religious work of Saint Simon (in his Utopian Socialism), of
the egalitarianism and experimentation of R. Owen and C. Fourier. In 1888, E.
Bellamy with his book Looking backward introduces into Western
philosophical thought the idea of a sociological Utopia, which blossoms with
Nietzsche and Spengler into negative antipositivistic thought. In the 20th
century the Utopian question acquires particular importance in the
Frankfurt School, especially with E. Bloch and his Spirit of Utopia and The
Principle of Hope in 1918. Agnes Heller in her Radical Philosophy of
1978 brings to our notice how the Utopian idea at this period is intimately
connected to the Rousseauian and Kantian concept. In fact, Rousseau himself was
the first, in Emile, to attack the realists, who in order to
protect what is realizable end by defending what they do. With Kant, Utopia
acquires value because associated with the regulating function of transcendental
ideas. Even if the ideas of reason do not constitute the basis of experience
(unlike those of the intellect), they direct human actions towards noumenonic
concepts, thanks to which positive law imposes itself on brute force, and peace
on war. Thus we reach H. Marcuse who, in his The end of Utopia, reminds
us that the social sciences of today must rediscover the Utopian attitude in
order to elaborate hypothesis and conduct theoretical research directed towards
the well-being of the whole of humanity.
[iii] Charles Darwin sustains the all animal species evolve
and are not immutable. The evolutive process is determined by: a) spontaneous
variation, i.e. by individual differences in a species produced by chance; b)
the struggle for existence, originating in the fact that more individuals
are born than is the number that can survive; c) natural selection or survival
of the fittest, in which case the favourable variations are maintained
and the unfavourable ones eliminated spontaneously. Darwinian biology exerted an
influence on the psychology of the time, with particular reference to the theory
of a possible continuity in the mental processes animal-man. This resulted in
considerable change in the objectives of psychology. William James, for example,
took into consideration the eventual functions carried out by the conscience,
and no longer the individualisation of its components. Again thanks to Darwin,
the concept of individual differences is introduced into
psychology with the consequential study of the differences between various human
minds, above all from the functionalistic point of view. In his Great Man and
the Environment of 1880 William James maintains that Darwin was the first to
distinguish between causes of production and causes of conservation,
with reference to the extraordinary qualities which characterise human beings
and animals. In other words, Darwin, in isolating the causes of production
defining them as tendencies to spontaneous variation and
relegating them to a physiological cycle, places his attention on the causes of
conservation and, with the expressions natural selection and sexual
selection, regards them as functions of the environmental cycle.
[iv] The answer to this question dominated the speculations
of Spencer and Haeckel, who promptly formulated the theory of “Social
[v] This cognitive effective course is possible precisely
due to the synergic action of mirror neurons, and the intervention of the
neuronal populations in the frontal and prefrontal lobe and in the limbic
[vi] The interval is the difference of pitch between two
notes within a scale, so it concerns the relation of frequency.
[vii] If the frequency in Hertz, of the fundamental note do
is indicated with n, the other notes of the natural scale have frequencies as
shown in the following table:
where the last line gives (in decimal form) the
relation of frequency for each note with respect to the note C, assumed as
fundamental (we indicate this note with C0): i.e. the connection
between the frequency of each note and the frequency of central C. The note C1,
which has double the frequency of C0, initiates another series of
seven indicated thus:
These seven notes have the same relationship of
frequency between them as the previous ones. Another C follows which indicate as
C2, and which as double the frequency of C1 (The frequency
of C2 is therefore equal to 4n). With C2 another series of
seven notes is initiated and so on… The interval of one octave is always equal
The sharp of
a note has with the note itself an interval of 25/24. The flat of a note has with the note itself an interval of 24/25. Until
now of course we have been talking about the natural scale and its seventeen
notes. In the Temperate Scale the interval of a semitone, i.e. the relationship
between the frequency of any two successive notes among the 12 existing ones, is
Clearly in the temperate scale all the intervals and
therefore frequencies of the same notes are altered from those of the natural
scale. For example:
9/8n = 1,125n
Up to here we have been talking about the relationship
between music played by only one instruments or sung by only one voice, the
absolute values of these frequencies would be of no importance. However to
perform pieces with more that instrument or one voice, clearly the instruments
would have to be tuned to the same note, one with a well established frequency:
this note is also called normal note or diapason. For this purpose the A0
has bee chosen with an established frequency fro 440 vibrations a second (440
Hz). For the international standard the normal diapason or pitch is used,
oscillating with a frequency of 435 Hz, and deposited at the Office of Weigths
and Measures in Sèvres (Paris).
It is simple to deduce from the tables above that if A0
has a frequency of 440 Hz, C0 has a frequency equal to:
The frequencies of do in the diverse octaves are
with a frequency of 33 Hz is the lowest C0
that the ear Can hear (cf. Bertirotti A., 2003: 24-27).
[viii] “Life is the combination of functions that resist
death. A tautological definition, it contains basic truth: the resistance of
living creatures to any form of aggression, and special reactions of tactics or
flight; the productions of antibodies or toxins; phenomena of anabiosis or
slowing down of the chemical functions; the production of protective membranes,
of cists, spores, or shells; reflexive paralysis in face of predator, etc.
Natural examples are practically infinite” (Bertirotti A., Larosa A.,
2005:221).What is more “life, at least as we know it on this Earth, is linked
to the recombination of 5 nucleotides (the pyramiding and purine bases) linked
to each other by a sugar (deoxyribose) by means of a phosphoric bond. As is
known, the combination in series of these three elements constitutes the genetic
code; a polymer endowed with a self-duplicating capacity able to codify the
sequence of amminoacids in the proteins and so function as a matrix for the
production of basic biological material. This polymer with self-duplicating
capacity known as deoxyribonucleic acid (the famous DNA) is life” (Chiarelli
B., 2003, vol. II:454).
[ix] Also at biological level, the proximity of a cell to
other cells determines social behaviour. It is thanks to cellular redundancy that an adult staminal cell, placed next to for
example, an hepatic cell, will fall under its influence and begin specialising
as an hepatocyte.
[x] The term idea
has the etymological meaning of vision,
thereby preserving a subjective and partial dimension. It follows therefore that
the concept of dominant idea is
without foundation because visions are always contemporary. The believe that a
dominant idea exists in the diverse cognitive processes is because it has been
confused (in a process of assimilation) with that selected by the perception as
the more significative at that precise moment of time and space. Cfr. Mercadante
[xi] Human symbolism is a combination of
signs whose comprehension is fundamental to interpreting what they describes.
The sign is a possibility and
cognitive necessity (real-ideal) for adapting to the environment. The sign and
its utilisation become a module through which it is possible to identity the
communicative code and semantics of a more general group of collective
descriptions. The use of signs is founded on the real capacity they have as
instrumental objects, i.e. adapted to following the objective that the user has
established beforehand. If the sign is adequate it can be used to achieve the
objective in a given situation. “Sign can be used as a means of making money,
obtaining social prestige, control over others, to deceive, inform or amuse, to
comfort, reassure or stimulate; to refer, describe, or predict; to satisfy some
needs or create others, to resolve problems objectively and obtain partial
satisfaction in a conflict that the organism can not resolve completely; to
secure the help of others and strengthen its own independence; to show itself
and to hide itself” (Morris C., 1963:96).
The creation of awareness of an even is the result
of a complex cognitive
At the moment
that an action is curried out our brain is directly linked to the activation of
automatic mechanisms which enable the execution of the action itself, while a
part of it is linked to the planning necessary to bring the task to completion.
The formation of awareness of an action that has taken place is typical of
which depicts the action just completed. In other words, the
greatest degree of awareness of finished actions comes through the verbalization
of the contents characterized the action,
not during execution of the action itself.
[xiii] In the Old Testament the stretched cord (or measuring
cord) is often mentioned. For the Free Masons the stretched cord is liked to the
“sisaro” one of the work tools of the Third Degree. It represents
undeviatingly upright conduct that leads to the search for immortality. The
“sisaro” is a cord support turning on a central pivot. This instrument was
given its name only after the United Grand Lodge of 1813 and became a Masonic
term not diffuse outside the Institution. When the cord is unrolled quickly the
“sisaro” emits an acute sound.