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Index

Introduction

1. Theoretical framework

1.1 The intervals that create more harmonic tension are those of M3 and tritone

1.2 The notes that form the M3 intervals (CE/EC) and/or tritone (EB¬/A#E) locally resolve to the notes F or B, or to the chords that have these fundamentals.

1.3 The fifth of the fundamental is the less important note as regards the chord's harmonic function.

1.4 The 7M3 structure produces a tonal vector.

1.5 The htonal and Phrygian resolutions of M3 and tritone account for most cadences, secondary dominants and cadential harmonic progressions.

1.6 A fundamental and its main harmonics also have a 7M3 structure.

1.7 Most chords may be separated into one or two chords having the harmonic CEGB¬ complete or partial structure.

1.7.1 We may summarise the harmonic tension of most chords with one or two fundamentals, which results in eight large families of chords.

1.7.2 We can apply the fundamental symbology of chords to create or find local relaxed progressions of chords.

1.8 The reduction of tonal functions to three (tonic, subdominant and dominant) may be explained by means of the tensions of M3 and tritone intervals.

2. The harmonics of a sound as the basis of musical perception

2.1 Significant harmonics for the human auditory system

2.2 Virtual fundamental

2.3 Harmonic 2f

2.4 Harmonic 3f

2.5 Harmonic 5f

2.6 Formation of music scales

2.7 Minor chord and minor mode

2.8 Harmonic 7f


3. Functional study of chords

3.1 Classification of chords according to their harmonic tensions. The fundamental symbology

3.1.1 Major chord family

3.1.2 Minor chord family

3.1.3 Dominant chords (unitonal)

3.1.4 Augmented chords

3.1.5 Symmetric dominant chords

3.1.6 Major-minor chords

3.1.7 Cluster chords

3.1.8 Suspended chords

3.1.9 Other chords

3.2 The functionality of chord families

3.3 Correspondence between the main known chords and the fundamental symbology

3.4 Chord inversions and their optional symbology

4. Secondary relaxions and other successions of fundamentals

4.1 "Locrian" relaxion

4.2 "Dorian" relaxion

4.3 Successions of fundamentals without homotonic tension

4.4 Summary of homotonic tensions and relaxions

4.5 Homotonic relaxions and tonal axis theory

5. Tonality

5.1 The tonal field and its vectors

5.2 Tonality and the 7M3 structure

5.3 Tonal functions and their symbols (functional symbology)

5.4 Tonality and tonal axes

5.5 Cadences

5.6 Functional symbology in inversions

5.7 Modulation

5.8 Recapitulation

6. Examples of harmonic progressions with homotonic relaxions

6.1 Relaxions between chords with a single functional fundamental

6.1.1 Htonal relaxions following the circle of fifths

6.1.2 Phrygian relaxions following the 12 tones of the chromatic scale


6.1.3 Combinations of htonal and Phrygian relaxions

6.1.4 Using the full palette of chords

6.2 Relaxions with one or more functional fundamentals

6.2.1 Two functional fundamentals separated by a tritone (symmetrical dominant chords)

6.2.2 Two functional fundamentals separated by a M2 (dominant chords family)

6.2.3 Two functional fundamentals separated by a P5 (major chords family)

6.2.4 Two functional fundamentals separated by a M3 (augmented chords)

6.2.5 Other chords

6.3 Locrian homotonic relaxion

7. Examples of homotonic and tonal analyses

Annex 1
8. Morphogenesis of chords and scales

8.1 Equivalence level between chords

8.2 Equivalence level between scales

8.3 `Chords classes' and `Scale classes' tables

8.4 How to find the fundamentals or the fundamental symbology of the chords

Chord/Scale class Tables

Annex 2
9. Modes of the first eight 7-note scale classes

Annex 3
10. Cyclical chord/scale classes

Annex 4
11. Symmetrical modes and chords

11.1 Symmetry between chords

11.2 Internal symmetries inside an octave

Bibliography

Introduction