Platos Timaeus and the Missing Fourth Guest Finding the Harmony of the Spheres (Studies in Platonism, Neoplatonism, and the Platonic Tradition, 21)

In Plato's Timaeus and the Missing Fourth Guest, Donna M. Altimari Adler offers an original account of Plato's Timaeus from 35a-36d, yielding a new interpretation of the Timaeus scale and cosmic harmony imbedded in the text. ‎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 Parts ‎Chapter 4. The Sesquioctave Operation within the Sesquitertian Parts ‎1. 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 Disdiapason ‎6. First Octave of the Model Diatonic Octave Chain Containing Chromatic Elements ‎7. 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 Genera ‎9. Possibilities for Modulation among Different Perfect Systems Arising within the Timaeus Numbers ‎10. 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 Scale ‎15. Orderly Rise and Fall of Fifth Periodicity with the Decay of the Primary Scale ‎16. 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 Fabric ‎3.1. Preliminary Observations ‎3.2. A Note on the Obvious ‎3.3. The Enharmonic Phenomena ‎Chapter 7. The Musical Data of the Timaeus Vis-à-vis the Cutting of the Fabric, the Making of the “Chi,” and the Cosmic Orbits ‎1. Division of the Material ‎2. Forming the χ Figure ‎3. Bending the Arms to Form Circular Shapes ‎3.1. Volume ‎3.2. Surface Area ‎4. The Uniform Motion of the Whole without Variation ‎5. Separation of the Arms into an Outer and Inner Circle ‎6. Separation and Definition of the Motions of Same and Different ‎6.1. The Outer Band’s Motion of the Same ‎6.2. The Inner Band’s Motion of the Different ‎6.3. The Fitting Relationship of the Outer and Inner Bands ‎7. Elevation of the Motion of the Same to Primacy ‎8. Sixfold Split of the Inner Movement of the Different, i.e., the Octave Movement ‎Chapter 8. Plato’s Generalization of the Timaean Harmonia in Laws ‎Concluding Remarks ‎Appendices ‎Appendix 1. Verification of the Diesis Remaining after Insertion of Two Sesquioctave Intervals into a Sesquitertian Part for the Sample Sesquitertian Part, 2:8/3 ‎Appendix 2. The Archytan Alternative in the Pythagorean School ‎Appendix 3. Greater and Lesser Perfect Systems and Associated Questions ‎Appendix 4. Alternative Perfect Systems ‎Appendix 5. Two Overlapping Sequences of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Chromatic Factors of 1719926784 ‎Appendix 6. Two Overlapping Sequences of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Chromatic Nonfactors of 1719926784 ‎Appendix 7. Continuously Overlapping and Contiguous Chains of Doubles, Including Coincident Diatonic Octaves within Each, Bounded Entirely by Model Scale Numbers and Their Multiples ‎Appendix 8. Chromatic Scale Tables ‎Appendix 9. Specification of Trihemitones and Chromatic Scales in Which They Manifest ‎Appendix 10. Enharmonic Scale Tables ‎Glossary of Musical Terms and Concepts ‎Selected Bibliography ‎Subject Matter Index In "Plato's 'Timaeus' and the Missing Fourth Guest", Donna M. Altimari Adler proposes a new Timaeus scale structure. She finds the harmonic cosmos in Plato's text, mathematically, regarding it as a number generator. Plato's primary number sequence, she argues, yields a matrix defining a sophisticated harmony of the spheres. She stresses the Decad as the pattern governing both human perception and the generation of all things, in the text, including the World Soul and musical scale symbolizing it. She precisely identifies Plato's "fabric" and its locus of severance and solves other thorny problems of interpretation, e.g., properly naming the sets of three and four bands, born of splitting the band of difference, and explaining their differing motions and speeds In Plato's Timaeus and the Missing Fourth Guest, Donna M. Altimari Adler proposes a new Timaeus scale structure. She finds the harmonic cosmos, mathematically, at 35 A-36 D, regarding the text as a number generator. Plato's primary number sequence, she argues, yields a matrix defining a sophisticated harmony of the spheres. She stresses the Decad as the pattern governing both human perception and the generation of all things, in the Timaeus, including the World Soul and musical scale symbolizing it. She precisely identifies Plato's'fabric'and its locus of severance and solves other thorny problems of textual interpretation.