“The person who seeks to harmonize his own qualities cooperates with the Cosmos. In creating one’s own spiritual image each person perfects universal harmony. The currents of space are intensified through the principle of fusion, a law which governs all universal forces.”*
THE INTERVALS
Among the many highly valuable concepts of Harmonics – think of Space, Rhythm, etc. – the supreme one is that of the Interval. In music the difference in height (or in frequency) between two sounds is called an interval, and it is expressed in acoustics as the relationship between their frequencies or between their wavelengths. Thus Interval means, in the widest sense, Connection or Relationship.
However, careful attention should be given to the following: the Interval is not only the sum, so to speak, of two sounds, but is their synthesis: it is a new sound, which it is impossible to reproduce without the help of two distinct notes, whether instrumental or vocal. It is an entity apart, endowed with its own psychic qualities, produced by the resounding (simultaneous or successive) of the two components. The relationship, the connection are thus clearly recognized in Harmonics as entities which appear to the hearing and to the psyche with their own, distinct characteristics.
The Interval is the intermediary between two sounds, and Harmonics studies this aspect of it, which is numerical, knowable, exact. But one can certainly also speak of an interval between colours, in which case the numerical part is no longer immediately recognizable, but its psychic value is perceptible: a red and a blue, placed side by side, produce a certain interval, which the psyche records and whose qualities it distinguishes.
But the idea of an Interval drawn from music can and must be taken to its furthest consequences, and thus it can be applied in all fields of what is knowable and perceptible to men. All that is relationship is traceable to a certain interval, even logical opposites, complementary principles and energetic transformations.
Interval means consciousness. In infinite and living Space all the elementary charges of Fire (the Points) are in a reciprocal relationship with all the others, and this infinite field of connection is universal consciousness, different from Point to Point but never completely absent. Space is thus established as the whole of the infinite intervals.
It follows that listening to the interval is a real activity of consciousness and the more one exercises it the more one refines and educates it.
In Harmonics it is not so much the sound that dominates as the interval. By its very nature of intermediary, it functions as a bridge and links the shores of two different worlds: the physical and the spiritual. It is the child of the continually changing relationship between spirit and substance.
This statement opens the door to considerations relevant to religion and philosophy, which, to the careful observer, are nothing but fields of application of Harmonics.
It is precisely here, in the very centre of the concept of the interval, that that Path separates and is clarified which, if traversed, leads man far beyond his normal experience; and Harmonics, as a science, shows here its major efficacy, its transcendent utility, since it is the Guide which knows the ways of all relationships, being nothing but the Science of Relationships, or intervals.
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245 – Any harmonic form shines with a marvellous flame of attraction. Thus, when the Magnet extends its forces, the Fire of Space vibrates in resonance.
The Interval has no “thickness”. It is neither long nor wide: it is without dimensions, but it is not without a goal. It is thus a transcendent way, which passes between the opposites and is finer than a cobweb. It is a real ray. The Interval is the basis of that world which, having no dimensions, is called subtle; and, having no quantities, is purely qualitative. This world, being by nature the seat of consciousness and of relationships, is also recognizable as intermediate between substance and essence. If these definitions, which have a strictly logical basis, are accepted, many concepts which cloud the mind are clarified; not only that, one learns that it is possible to move in a world which is usually barred, yet irresistibly attractive because it is superior. It is possible, by penetrating the idea of an Interval, to rise from the world of quantitative exchanges to the sphere of relationships of quality and to learn and know the laws there and perceive the presences which, on account of their universality, it is right to call divine.
Through the intervals, therefore, relationships, qualities and consciousness can be known. That which appears separate, isolated and distinct in the physical world reveals its correlations, often unexpected, with other entities in the sphere of the intervals, so that it demonstrates its belonging to a group. And the idea of a group is typical of the world of qualities and relationships, where it is the authentic basis, or the centre, of all exchanges. In that sphere the group replaces the individual, upon which, on the contrary, the physical world hinges. Thus the concept of an Interval is a typical group concept, since each of them is the whole, or the group, of all the infinite equivalent intervals: for example, these two sounds: C and C’, respectively of frequency 256 and 512, are in a mutual relationship of an octave, since 256/512 = ½; but to this same group all the relationships of that same value belong, whatever their component sounds are.
A great simplification marks the passage from the single sound to the interval: in saying “octave”, for example, the qualities of all the innumerable relationships of that value are identified, even though the individual sounds among them are very different. “Octave” is a group concept and is clear, unmistakeable, exact.
(A semicircle is the Octave of a whole circle)
It goes without saying that between groups, or between intervals, innumerable relationships are of necessity established which, by being such, are still always intervals; and this is true both within the same group or outside, that is between groups of a different nature. For example, this interval CC’, which is of an octave, is in a relationship of a fifth with this other interval: GG’, which by itself is an octave; and that same CC’ is in a relationship always of a fifth with the interval GC’, which by itself is a fourth.
The first of these examples illustrates a relationship inside a group; the other one outside a group.
The science of the Intervals – that is, the science of that which is “Between” two things or beings – reveals itself as the science of groups and the idea of a group has in this sense nothing indefinite or vague but possesses a real, mathematical clarity. There is no possible uncertainty in defining a group: and its components are clearly identified. Every one of its members (that is, every single interval) can however belong by right and by intrinsic nature to other groups: going back to the example set out above, the interval GG’ is by right a member of the Octave group but simultaneously, by its inner essence, it also always belongs to the sphere of the Fifths, and so on.
In brief, the groups are interwoven and merge together without being confused and leaving completely free the relationships of the individual components: a world which is orderly and organized, hierarchical and free.
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Before evaluating any physical phenomenon, whether a natural process, an event or a human undertaking, one should examine the values of the intervals which appear in it, which would certainly reveal the degree of cohesion, beauty and solidity. Any creative project or programme should be imagined beforehand on the basis of the certain laws of the subtle world. Better proportioned works and activities would result, but also more stable and lasting ones, better results for the benefit of many people.
But these are not suitable times for such applications. Today it is possible only to put down the first seeds of an overturning which will shake the world from the inside, building a more advanced future without demolishing anything worthy and noble that was achieved in the past.
The world of the intervals, as has been said, is the world of consciousness, intermediate between substance and spirit. It is a dual environment, since every interval, though being a unitary and collective value has always originated of necessity from two terms, of which it is in every way the relationship. In short, in the idea of an interval, a component of bipolarity is present, in so far as the two creating elements can be represented as energetic entities of an opposite kind, which form between them a magnetic or force field. In this field, lines of flux can be distinguished, just like those studied by physics, along which the material particles which make up the structure, or the connective tissues of form, are arranged. 
By this is meant that the “subtlety” of the interval generates a field of force, orderly, different and characteristic for each one of them, which in its turn is the origin of the arrangement of material forms – whether they are natural forms, or historical events, or human behaviour. This explains the inextricable presence of qualities in all the quantitative compositions of the physical world; not only that, but it places such qualities at the right level, superior and conditioning rather than in a subject and passive state, as is usually done. It is even useless to make it known that the combination of the intervals among themselves can be very complex and that it is regulated by the laws of affinity, by which like attracts like and repels what is different.
These are the first laws, the first discoveries, the first treasures of the world of the intervals. But the best still remains hidden. Their power is still only recognizable in theory. One day, men and the other creatures will feed on intervals and, with the strength generated by them, mechanisms will be moved and great structures will be built, amazing in their boldness, durability and lightness, yet in perfect harmony with nature and the environment.
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Where does the middle world of the intervals lead?
If it is the seat of every connection and the substance is on one side, it must be possible – as has already been written – to touch the other bank, that is the spirit, that world that many human documents call the world of Fire. It is not appropriate to deal with it here, not even in brief. Let a few hints suffice, to direct the mind to that goal. As the birth of a relationship between two entities (between two sounds) reveals a superior sphere, whose main points we have described in these pages, so at the most secret centre of the interval is a nucleus of Fire, a charge of vital energy. This energy, supreme and creative, is unitary, real, everlasting, unlimited and inextinguishable. Every interval expresses and accentuates certain of its qualities, but it dwells there in its entirety. The world of Fire is unitary and transcends time and distance. The great interval of a fifth reveals, for example, its innovative and stimulating qualities and the octave the receptive and constructive ones. But the Fire is one alone and is the origin of everything and every process.
In setting out these remarks we have passed from the physical laws to the psychic ones and now we are casting a glance at the spiritual realities. But really the path is the opposite: from a stimulus of Fire two entities are produced, which completely describe it with their reciprocal relationship (interval): from this then precipitates, in time and space, the external form which the senses perceive. This is the only direction in which any creation proceeds – while the movement in the opposite direction is developed which leads from the form to the meaning and thence to the Value, by means of the senses and intelligent understanding. It is a question, after all, of that double and simultaneous act of “writing” and “reading”, which has been discussed previously.
The person who is concerned with Harmonics is thus invited to recognize that the Interval hinges on a central, unitary Fire, of which it is the first, partial message and which is then manifested, limited by numbers and forms, in the kingdom of quantities and appearances.
The world of the intervals is clear and simple: three of them dominate and are supreme: another four, of lesser power, assist them; all the others are lost little by little in indistinctness, as far as the human perceptive faculty is concerned, without however losing their individual gifts.
The first three have all been always recognized by all the peoples of history. As far as they are concerned, no doubts or uncertainties exist. They are exact, incontrovertible, primordial, universal. They express completely the Trinity of Being, the three great Persons of the unitary divinity. They are the Unison, the Octave and the Fifth, in the very unsuitable terms of contemporary musicology.
The other four lesser intervals are the Fourth, the Third (major and minor), the Sixth (major and minor) and the Tone (major and minor).
We are now preparing to illustrate the principal qualities of each one of these.
