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The Myth of Invariance, the Origin of the Gods, Mathematics, and Music from the Ṛg Veda to Plato

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Author: Ernest G. McClain

Harmonical analysis is a technique for synthesizing the tonal, arithmetical, and geometrical imagery of ancient civilizations. It aims at the reconstruction of the esoteric diagrams which gave the sacred symbols of particular cultures their enduring and magical powers and furnished philosophy with a ground of certainty. The technique is applicable to all cultures which considered tone and number twin keys to the secrets of the universe, and practicable wherever a sufficient mythology and cosmology have survived. I have made explicit the objective elements of that harmonic technique ; it is based on the habits of ancients like Plato, Plutarch, Ptolemy, and Nicomachus, and on principles enunciated anew in our time by men like Brumbaugh, de Nicolás, Levarie, and Levy.


Charts and Tables
Introduction by Siegmund Levarie
Glossary of Terms

1. Introduction: the problem ; de Nicolás' challenge; a
musical hypothesis; procedure

2. Tone Maṇḍala and Sun's Chariot: the Hindu-Greek
diatonic scale

3. Musical Generation: God and Mother; Fathers and
Sons; Indra and the Aśvin Pair; Indra as Dancer and
Lord of the Five Tribes

4. The Tonal Calendar: 360 "like pegs"; Vision in Long

5. Algebraic Yantras: star hexagon and drum of Śiva; the
holy mountain ; origins of geometry

6. Expansion of the Tone-Number Field: the Bṛhaspati
and Prajāpati cycles of 3,600 and 216,000 years
7. Cosmic Cycles: the four Yugas; Kalpa and Brahmā
cycles; the birth of Agni, incarnate savior; the chariot of
the gods; the duration of the universe

8. Music and the Calendar: arithmetic and geometric
coincidences; Ptolemy's tonal zodiac

9. The Book of Revelation: the meeting of East and West;
New Jerusalem; the Choir of 144,000; the Holy City as
12,0003; the Divine Mother; conclusions; postscript on

10. Babylon and Sumer: the Pythagorean achievement of
ancient Semitic cultures; sexagesimal arithmetic; God on
the Mountain; Babylonian and Hebrew floods; Old
Testament arithmology; Mayan cosmology; Mt. Meru

11. Lost Atlantis: Plato's musical cities; Gilbert Ryle's
hypothesis; the Muses' Jest; the Plain of Atlantis; the
Islands of Atlantis; Callipolis and Ancient Athens;
Egyptian derivation; Egyptian music, Egyptian
mathematics; The Book of the Dead; the Underworld;

12. Conclusions: the myth of invariance; a mathematical
perspective; codetta


I Conversion Tables
II Multiplication Tables for Numbers 3p5q
III Simplified Acoustical Theory for Fretted Instruments


Thanks so much for this!