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CONTENTS

Introduction

*Axis System

Axis substitution
Tonal reflections
On the meaning of functions
The relationship of the three functions
Tonal ’asymmetrical’ and atonal ’symmetrical’ elements
Nature Symbolism
*Golden section
*Fibonacci series
Harmonic Principles
     The pentatonic–chromatic system
         Alpha chords
         Models 1:2, 1:3, 1:5
1:2 model
1:2 model harmonic turns
1:5 model
1:3 model
Complementary (annihilating) keys
          Equidistant scales
Fourth chords
Tonic–antitonic relations in pentatonic scales
Omega chords
     The diatonic–overtone system
Acoustic (overtone) chord
Hypermajor and hyperminor
Alpha inversion
Authentic and Plagal Thinking
DO system and MI system
The complementary relation of the two systems
Inverted relation of the two systems
Consonance and dissonance
Openness and closedness
Duality and synthesis
The Quadrophonic Stage of the Music for Strings, Percussion and Celesta
Polymodal Chromaticism
Major triad — minor triad
Polar chords (DI + MA tension)
Major — minor — subminor
     On the ’Tristan chord’
Function
Diminished sevenths
Substitute chords
     Remarks on Verdi’s colour chords
*Tonality: Modality: Atonality
Summary
The Ethos of the Axis System (tonal serialism)
Pole–counterpole relations
The symmetrical correspondences of the system
Relations between parallel keys
Polar major and minor chords
Relations in content between substitute keys
Relations in content between complementary (annihilating) keys
Function
Natural and modified keys
Upper and lower spheres
The potentialities of the axis system
Overtone relations
Wie lenkt’ ich sicher den Kiel (modal serialism)
Computer Language of Music
The ’Sprecher’ Scene of The Magic Flute
Appendix (Relative Solmization)
Editors‘ Postscript (Miklós Szabó–Miklós Mohay)
 
 

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