cont

CONTENTS

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)