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

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 s...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Altimari-Adler, Donna M. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Leiden ; Boston : Brill, [2020]
Colección:Studies in Platonism, Neoplatonism, and the Platonic tradition ; v. 21.
Temas:
Plato. > Timaeus.
Timaeus (Plato)
To 500
Musical intervals and scales > Greece > History > To 500.
Harmony of the spheres.
Harmonie cosmique.
Musical intervals and scales.
Greece.
History.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 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

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