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The Symbolism of the Harmonic and Subharmonic Series

Undertones

Dissonance Representing Evil

Whether or not undertones actually exist is irrelevant to their symbolic appreciation

  • Overtones = “microscopic” diminution of time and space

  • Undertones = "astronomical" expansion

=

Represents the universal forces of contraction and expansion

Louis-Claude de Saint-Martin (1743-1803)

  • Duality of the Third – the major triad is the foundation of all music
  • Dominant Seventh Chord – “The ‘image of the Principle’ should be a perfect octave, but before the beginning of time it diverged, asserting its own will and separating itself from the First Principle to become the origin of all evil”

Bettina Brentano von Arnim (1785-1859)

  • “The flat seventh does not harmonize certainly, and is without sensible basis; it is the divine leader,—the mediator between sensual and heavenly nature…the flat seventh by its resolution leads all tones, which pray to it for delivery, in a thousand different ways, to their source—divine spirit.”

Subharmonic Series

Harmonic Series

Werckmeister’s Divine Revelation Harmonic Scheme

Octave I 1, 2 God the Father before Creation

Octave II 2, 3, 4 Old Testament (Trinity Concealed)

Octave III 4, 5, 6, 8 New Testament (Trinity Revealed)

Octave IV 8, 9, 10, 12, 15, 16 Melody of the Christian Life

Excludes 7, 11, 13, 14 (Dissonance = sin)

Andreas Werckmeister

  • 1645-1706
  • Music originated from the divine mind and its purpose was to praise God
  • Cosmos works harmonically (inspired by Kepler)

Werckmeister's Creation-Based Harmonic Scheme

  • Day 1 Heaven & Earth Unison/Fundamental
  • Day 2 Water/Dry Land Octave
  • Day 3 Plants Adds Fifth to the Octave
  • Day 4 Planets/Stars Fills in Complete Harmony
  • Day 5 Animals Both Good and Bad Notes
  • Day 6 Man Musician Bringing Order
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