The chromatic scale is the set of twelve notes of the tempered system. In the symbolic system of Solaria, it is represented through the cycle of fifths, understood not as a simple theoretical succession of pitches, but as a relational space in which each note can assume different functions depending on the configuration observed.
Arranging the twelve notes on the cycle of fifths makes it possible to visualise relationships of proximity, opposition and complementarity between sounds, showing how the chromatic total is not merely a sum of notes, but a system of mobile relationships.
From this structure derive two fundamental states of the musical and symbolic world: the complete world and the incomplete world.
In the complete world, the chromatic total appears as a dynamic interweaving of nature and consciousness. Its structure can be summarised in the formula:
12 = 5 + 2 + 5
The two groups of five notes correspond to two complementary sigma chords, placed at a tritone distance from each other, representing the two polarities of the five natural elements. The two remaining notes form the tritone: it is excluded from the two sigmas, but completes the chromatic total and represents the human being as self-consciousness and standpoint.
The incomplete world is instead the state in which this tension is reduced. A sigma chord transforms into a pentatonic, compressing its internal dissonance and producing a more consonant but also more closed structure. Corresponding to this reduction is an opposite closure in the complementary sigma, so that the chromatic total no longer presents itself as a dynamic interweaving, but as a division between two consonant and separate worlds. Facing this fracture stands the tritone, no longer as a simple standpoint before nature, but as the figure of consciousness placed before the division.
Complete World
In the complete world, two complementary sigma chords, placed at a tritone distance from each other, form a structure of ten notes. To these is added the tritone excluded from the two sigmas, which completes the chromatic total of twelve sounds.
The general structure can be described as follows:
| Element | Symbolic function |
|---|---|
| First sigma chord | One polarity of the five natural elements |
| Second sigma chord | Complementary polarity of the five natural elements |
| Tritone | Human being, self-consciousness, standpoint |
In this arrangement, the world is not divided between consonance and dissonance, but contains both. Nature is not conceived as a pacified and uniform system, but as a field of relationships, tensions and complementarities. The tritone is excluded from the sigma chord, but not from the chromatic total: it is what allows the world to be observed, questioned and understood.
The complete world is therefore an interwoven world: each note can be part of a sigma chord or of a tritone, depending on the standpoint assumed in the cycle of fifths. No note possesses a definitive and isolated meaning; every sound can become nature or consciousness, matter or question, element or observer.
Twelve Rotations
The structure of the complete world does not present itself only once. It can be rotated along the cycle of fifths, generating twelve possible configurations. In each rotation, the notes assume different roles: a note that in one configuration belongs to a sigma chord may, in another, belong to the tritone; a note that represents a natural polarity may, by changing perspective, become part of the consciousness that observes.
This continuous rotation makes the complete world a perspectival structure. There is no single definitive centre: the meaning of each note depends on the relationship in which it is placed.
For this reason the complete world can be defined as a world in which everything is everything: each element is itself, but can assume different functions within a broader order. Nature and humanity, matter and consciousness, consonance and dissonance are not rigidly separated, but transform into one another according to the standpoint.
Interweaving of Harmony and Dissonance
In the complete world, harmony does not coincide with pure consonance. Completeness arises instead from the interweaving of consonance and dissonance, stability and tension, similarity and otherness.
The sigma chord is central precisely because it contains almost all the possible distances within the octave, but leaves out the tritone. This means that nature is rich, articulated and almost complete, but not self-sufficient. The missing tritone indicates the presence of a consciousness that does not allow itself to be fully absorbed by nature: it observes it, questions it, interprets it.
Incomplete World
The incomplete world arises when a sigma chord reduces its internal tension by transforming itself into a pentatonic. In this transformation, a note placed at a tritone distance is brought back to a more consonant position. The structure thereby loses its intervallic richness and becomes simpler, more stable, but also more closed.
For example, the sigma of D:
D–E–A–C–D♭
can be reduced to the pentatonic of C:
C–D–E–G–A
through the substitution of D♭ with G.
The passage is minimal, as it concerns only one note, but its effect is profound. The pentatonic obtained is more consonant than the sigma, but contains less internal difference. Where the sigma was fertile because traversed by tension, the pentatonic becomes a more pacified world, but also poorer in relationships.
Closure of the Polarities
The reduction of one sigma does not remain isolated. Since every sigma chord possesses a complementary sigma placed at a tritone distance, the transformation of one entails a corresponding closure in the other.
Two complementary pentatonics thus arise, for example:
C–D–E–G–A
and
G♭–A♭–B♭–D♭–E♭
These two structures occupy ten notes of the chromatic total, but the two notes of the tritone remain excluded:
F–B
The two pentatonics are both consonant, ordered and self-sufficient. However, precisely because each closes itself within its own sonic field, they are no longer able to construct a genuine relationship. Their consonance becomes isolation.
The Individual Facing the Message
In the incomplete world, the tritone assumes a dramatic function. It no longer represents simply the consciousness that observes the complete nature, but the individual placed before the division.
The two complementary pentatonics become two closed worlds, two polarities that do not communicate. The remaining tritone, formed by two notes such as F–B, then represents consciousness facing the fracture: an individual placed before two consonant but opposing orders.
In this sense, the incomplete world is the world of choice, uncertainty and responsibility. The individual does not face a harmony already composed, but a separation. They must ask which is the right path, how to traverse the division, how to re-establish a relationship between worlds that have closed themselves to one another.
Related Entries
Sigma Chord
Complementary Chord
Tritone
Tritone and the Sigma Chord
Pentatonic Scale
The σεα (sea) System
Seven Elements