This book could seem, at first sight, excessively complex for a lot of people. But, I think that if it is read without any haste, the concepts introduced can be easy to understand. In spite of this advice, for the reader who only wants to look through it, we give here again the definition of some new musical terms that appear in the pages of this work and we specify for everybody the precise meaning given to other known musical terms which can have different interpretations.

Cadence: distension or harmonic resolution which can be passing or conclusive, but in any case it evolves to the end of a segment, phrase or musical section. Cadences can be produced by homotonic, sonance or tonal relaxions.

Chord-mode class: in simplified form is the group of chord inversions (or the group of modes of a scale) with its transpositions in any internal combination of notes, vertical or horizontal. In the equal tempered gamma there are only 351 possible chord-mode classes. A chord-mode class, whatever its manifestation as a chord or scale, has a unique, characteristic decomposition into convergent chords.

Chord-mode class tables: tables containing the 351 chord-mode classes of the equal tempered gamma classified according to their harmonic convergent chords.

Convergent chord: it can be summarized in a simplified way, as a chord with dominant seventh or first especie structure, complete or parcial in any inversion. It is the result of considering the only significative harmonic trails for the ear (prime harmonic trails 2, 3, 5 and 7). They are the only chords that have an unique fundamental (See Fig. 3 below).

Fundamental: the note (real or virtual) on which a convergent chord converges. Most of the chords used in music –included pantonal music– can be separated as the addition of one or two convergent chords. So most chords can have one or two fundamentals. The term root is applied only in its tradicional meaning as the bass of a triadic structure or as the main fundamental.

Fundamental figure: way of representing a chord showing the potency and relationship of the two fundamentals that generate the majority of chords. The fundamental figure gives a first approach to the functional and sonance particularities of a chord.

Gamma: each collection of tuned intervals or notes, theoric or practical, historic or actual, of the different human cultures. For example, Pythagorean gamma, Zarlinian gamma, equal tempered gamma and so forth.

Harmonic field: sum of harmonic forces that act at each moment of a musical work. This field can be decomposed into three closely interrelated sub-fields which are the local harmonic tensions (homotonic tensions) field, the sonance tensions field and the tonal field –harmonic memory–. Melodic tensions are separated in another field.

Harmonic relaxion: the opposite of harmonic tension, that is, a sensation of resting, relaxation, resolution.... Harmonic relaxion can be of three types: homotonic, by sonance or tonal.

Harmonic trail: every harmonic produced by a vibrating body has its own series of harmonics. The resulting harmonic series can be decomposed as the sum of the harmonics in prime position (with all its own harmonics). Each of these prime harmonics together with its attendent multiple harmonics are known as a harmonic trail (See Fig. 3 below).

Homotonic (dis)tension: local harmonic tension or relaxion produced between ywo chords, arpeggios or groups of notes, considered independently from sonance of chords and tonal memory. There are two main homotonic relaxions between chord fundamentals: they are produced by the jump of fundamental by a rising 4th. (or descending 5th.) –1st. order– and a jump of fundamental by a descending minor 2nd. (or rising major 7th.) –2nd. order–.

Inversion: we give to this word the meaning found in the harmony treatises, that is to say, it means the different manifestations of a chord depending on the note put as the bass. It never refers to the meaning given when talking about intervalic symmetry in a chord. In these cases we use the term "symmetric chord".

Scaling: type of equivalence between modes in cancelling the dependence upon ordered degrees (there is not a hierarchic structure, a beginning or an end). It can also be defined as the group of modes of a scale. For example, two different scalings are the white and black keys in the piano. In the equal tempered gamma there is a total of 351 possible scalings. There is an isomorphisme between scalings and chord-mode classes.

Sonance: sound quality of a chord: terms of consonance and dissonance used in a generic way. We could define it as the "timbre" of a chord class.

Tonal axis: a space closed by consecutive minor thirds. Not as a chord or scale structure but as a harmonic-functional region. The equal tempered gamma can be divided into three tonal axes that maintain among them a similar relationship as to the subdominant, tonic or dominant. Between two fundamentals of the same tonal axis there is no homotonic tension. Among two fundamentals of different tonal axes there is always homotonic tension in some direction.