Plato's Timaeus and the missing fourth guest : finding the harmony of the spheres /

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Includes bibliographical references and index.Intro; Contents; Preface; Acknowledgments; List of Figures and Tables; Introduction: Plato's Missing Fourth Guest; Chapter 1. The Timaeus, the Decad, and the Harmonia: an Overview; Chapter 2. Plato's Construction of the World Soul: the Text as a Number Generator from 35 A to a Conundrum in 36 B; 1. Timaeus 35 A; 2. End of Timaeus 35 A-Beginning of Timaeus 35 C; 3. Timaeus 35 C and 36 A; 4. Timaeus 36 A (con't) and 36 B; Chapter 3. Solving the 36 B Conundrum: Deriving the Set of Sesquitertian Parts to Be Filled by Sesquioctave Intervals; 1. Derivation of the Sesquitertian PartsChapter 4. The Sesquioctave Operation within the Sesquitertian Parts1. Deriving Matrix Numbers Not Generable from the 2:8/3 Interval; 2. Special Mathematical Features of the Number Set Reflected in Table 24; Chapter 5. The Musical Significance of Plato's Number Matrix: the Primary Timaeus Scale; 1. Numerical Arrangement of the Timaeus Numbers with Key; 2. The First Cognizable Fourth of Any Kind; 3. The First Diatonic and Enharmonic Fourth; 4. The "Model" Octave and the Perfect Disdiapason; 5. Rise to the Perfect Disdiapason6. First Octave of the Model Diatonic Octave Chain Containing Chromatic Elements7. First Instances of Standard GPS, LPS, Diatonic UPS, and UPS in All Genera; 7.1. Standard GPS; 7.2. Standard LPS; 7.3. Standard Diatonic UPS; 7.4. Unacceptable Modulation; 7.5. Standard Combined UPS in All Three Octave Genera; 8. First Instances of Properly Timaean GPS, LPS, Diatonic UPS, and UPS in All Genera; 8.1. The Timaeus GPS; 8.2. The Timaeus LPS; 8.3. Diatonic Timaeus UPS; 8.4. Timaeus Combined UPS in All Genera9. Possibilities for Modulation among Different Perfect Systems Arising within the Timaeus Numbers10. The Primary Timaeus Scale; 11. Some Other Modern Interpretations of the Timaeus Numbers and Timaeus Scale; 12. The Feature of Ascending/Descending Ambiguity in Plato's Scale; 13. Significance of the Chromatic Invasion for the Primary Timaeus Scale; 13.1. Emergence of the Entire Unmodulating System in All Three Genera; 13.2. Other Diatonic Possibilities Coincident with the Primary Timaeus Scale; 14. The Orderliness of the Chromatic Invasion within the Primary Scale15. Orderly Rise and Fall of Fifth Periodicity with the Decay of the Primary Scale16. Grammar of Chromaticity in the Rise and Fall of Fifth Periodicity; 17. Another Look at the Crantor Matrix; 18. The Decad in the Rise, Wax, and Wane of the Primary Timaeus Scale; Chapter 6. The Further Musical Significance of Plato's Number Matrix: the Many Secondary Timaeus Scales and Associated Musical Phenomena; 1. The Many Secondary Diatonic Timaeus Scales Hidden in the Fabric; 2. The Many Chromatic Timaeus Scales Hidden in the Fabric; 3. The Many Enharmonic Timaeus Scales Hidden in the FabricOnline resource; title from digital title page (viewed on February 07, 2020).