Ernest G. McClain - The myth of invariance, the origin of the gods, mathematics, and music from the Ṛg Veda to Plato
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From the Book ''Conclusion'' 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 ob ancients like Plato, Plutarch, Ptolemy, and Nicomachus, and on principles enunciated anew in our time by men like Brumbaugh, de Nicolás, Levarie, and Levy. |
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CONTENTS Charts and Tables Introduction by Siegmund Levarie Acknowledgments 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 Darkness 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 vii 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; postsc Genesis 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; Khepura 12. Conclusions: the myth of invariance; a mathematical perspective; codetta Appendices I Conversion Tables II Multiplication Tables for Numbers 3p5q III Simplified Acoustical Theory for Fretted Instruments |
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