C.HA.S. - Harmonic Concept: Conceptual Syntesis

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The octave, which for hundreds of years was believed to be the only key-coordinate, reveals its specific proportional progression and steps down to make way for two new accurate constant coordinates.

The Circular Harmonic System goes beyond the hypothesis of Equal Temperament, according to which the octave is double the frequency of the first note. The Circular Harmonic System discovers the superlative euphonic form that springs from the consistent and progressive increase in tensions (beats coherence times) produced by two sounds. In this way the sound itself strengthens the orders of Regularity and Equilibrium with the qualities of Symmetry, Reversibility and Specularity, which are the necessary conditions for a harmonic, scalar system.
Chord “matter”, now no longer forced into an arbitrary numeric value, releases its harmonic qualities in a united and unanimous way, so that every sound is a “tensor-centre” within the Whole.

Tension - Rhythm and Proportion in Time .............................................................................................................................................................

The Circular Harmonic System - c.ha.s.® rules the true tensorial relationships within any set of two sounds, rather than the numerical values of individual semitones. This is what distinguishes c.ha.s.® as a tuning system from other systems; previous temperaments, at different times in history, have adopted the fifth, the third, and the “pure” octave as the numerical base for division into semitones.

The sound produced by a taut chord constitutes a set, made up of the fundamental and its harmonics in their well-known sequence. The harmonics have a pure relationship with the fundamental, but not amongst themselves. Thus, as we know, a series of three pure major thirds produces a flat octave; pure fifths give a sharp octave and sharp thirds; a pure octave generates the following sequence of increasingly flat steps in relation to the first note (generator): 12th (5th +8th ), 15th (8th +8th ), 19th, 22nd. Consequently, octaves cannot be pure either: like thirds, fifths and all other intervals, the octave becomes a “tensorial factor”. Moreover, it is tension – which we perceive as beats – which enlivens and distinguishes any sound set. Just as vibrato vivifies melodic singing, so beats, in the time dimension, express a specific tension, rhythm and proportion in time.

The c.ha.s.® “RATIO” ...............................................................................................................................................................................................

If no interval can have pure progression, every interval must have its own correct tensorial progression. Beats are the rhythmic quantity to be proportioned in time. Accordingly, the usual sound arc of thirteen notes is expanded out, and opens up towards a new harmonic conception: every sound, with its harmonic tensors, carries its memory and trace in the sound set: the power of a tensorial-harmonic form with an infinite number of sounds.

Our research reveals the existence of a dynamic and tensorial "whole". It is dynamic in the sense that a vibrating chord translates the energy it has received into sound-time. It is tensorial because a small set of two sounds (e.g. 1st and 10th ) is defined by its harmonic tensors, which also determine its melodiosity. This whole finds its highest degree of isomorphism in the tensions of every interval, so that each sound is able both to participate in the Whole and to contribute its memory and trace at the same time, in a harmonic relationship which both takes and gives meaning.

The strength of the c.ha.s.® set lies in the ratio between the tensorial progressions of the various intervals, the univocal sustainers of the Circular Harmonic Form. This appears to be of great value as a truly synergic tensorial system, where the fundamentals and the harmonics are able to free each other and spring off each other again, with perfect synchronism. Univocal tensions, in the c.ha.s.® system’s order, constitute the supporting element of the form. Stretched thirds, fifths and octaves (cf. stretched octave – Ernst Terhardt) correct and temper the progressions of the 2nds and the 4ths and determines the proportional progressions of 3rds and m-6ths, 6ths and m-3rds and 7ths .

Where the constant of Equal Temperament was arbitrary, and established a ratio of 2:1 for octave frequencies, the constants of the Harmonic Temperament are the self-generating products of the proportional progression between the tensions of every interval.
C.ha.s.® system reveals the intrinsic ratio of octave tensorial increase, and of the proportional progression of thirds, whether they are internal or external to the octave (10ths, 17ths); it also respects the mirrored symmetry of the intervals 1st 4th 5th (8^) e 1st 5th 4th.
This is clearly shown in the figures below – coordinates: X Octaves – Y Tension.

Note how Equal Temperament, for intervals larger than an octave, determines an increasing divarication between the ratio of the flat steps, 2nd and 5th , and the sharp steps, 3rd 4th 6th and 7th. This divarication is caused by an exponential increase in beats, generated by the difference in frequency between the “natural” harmonic step, and the “tempered” harmonic step.

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