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Full Description
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.
Contents
Preface
Acknowledgements
List of Figures and Tables
Introduction: Plato's Missing Fourth Guest
1 The Timaeus, the Decad, and the Harmonia: an Overview
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
3 Solving the 36 B Conundrum: Deriving the Set of Sesquitertian Parts to Be Filled by Sesqui-Octave Intervals
1 Derivation of the Sesquitertian Parts
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
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 Unmodulating Perfect System, and Unmodulating Perfect System in All Genera
8 First Instance of Properly Timaean GPS, LPS, Diatonic Unmodulating Perfect System, and Unmodulating Perfect System 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
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
6 The Further Musical Significance of Plato's Number Matrix: the Many "Secondary" Timaeus Scales and Asociated Musical Phenomena
1 The Many "Secondary" Diatonic 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
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
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
7 Elevation of the Motion of the Same to Primacy
8 Sixfold Split of the Inner Movement of the Different, i.e., Octave Movement
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
Selected Bibliography
Index
