Contents
Volume I
|
Translation Society Preface |
i |
|
Translator’s & Editor’s Preface |
|
|
Foreword |
|
|
Introduction |
xii |
A. The Theorems of the
Tone-Number
|
§1. The Monochord |
1 |
|
§2. Tone-Value and Tone-Number |
3 |
|
§3. Tone-Value |
5 |
|
§4. Tone-Number |
9 |
|
§5. String Lengths – Wavelength |
11 |
|
§6. Vibration-Numbers = Frequencies |
13 |
|
§7. The
Reciprocity of Waves = String Length and Frequency |
14 |
|
§8. Rhythm and Periodicity |
19 |
|
§9. Resonance |
28 |
|
§10. Interference |
32 |
|
§11. Haptic – Ektypic –
Prototype – Value-Form – Theorem, |
41 |
|
§12. Coincidences of the Theorems of Tone-Number and Their |
43 |
B. The Theorems of the Tone
Series
|
§13. The Overtone Series |
46 |
|
§14. The Undertone Series |
54 |
|
§15. The Whole Numbers |
57 |
|
§16. The Quanta |
60 |
|
§17. The Intervals |
67 |
|
§18. Harmonic Logarithms |
80 |
|
§19. Convergence – Divergence And Perspective – Equidistance |
98 |
C. The Theorems of the
Tone-Groups
I.
The Partial-Tone Diagram
|
§20. The Partial-Tone Coordinates |
114 |
|
§21. The Rationing of Partial-Tone Coordinates |
122 |
|
§22. Major and Minor Series of the Partial-Tone Coordinates |
131 |
|
§23. Polarity |
148 |
|
§24. The Equal-Tone Lines |
157 |
|
§25. Value-Forms for 0/0, 1/1, and the Equal-Tone Lines |
176 |
|
§26. Index and Generator |
187 |
|
§27. Parabola, Hyperbola, Ellipse |
195 |
|
§28. The Proportions |
204 |
|
§29. Harmonic Proportions in Architecture |
227 |
|
§30. Trinity |
247 |
II.
The Arrangements
|
§31. Variation Models |
254 |
|
§32. Combination Models |
267 |
|
§33. Polar Diagrams |
287 |
|
§34. Tone-Spirals and Tone Curves |
304 |
|
§35. The Complete Partial-Tone Diagram |
317 |
|
§36. Logarithmic Arrangements |
326 |
|
§37. Tone-Space |
338 |
|
§38. Sound-Images |
359 |
Volume II
D. Selections
|
§39. Scales |
378 |
|
§40. Chords |
416 |
|
§41. Ektypics for Melodies and Chords |
433 |
|
§42. Cadence |
444 |
|
§43. Counterpoint |
446 |
|
§44. Directions |
454 |
|
§45. Interval Powers and Constants |
457 |
|
§46. Symmetry |
468 |
|
§47. Space and Time |
474 |
|
§48. Enharmonics |
482 |
|
§49. Tempering |
490 |
|
§50. Number Symbolism |
494 |
|
§51. Tolerance: a Dialogue (and Review) |
520 |
|
§52. Hierarchy |
531 |
|
§53. Norm |
539 |
|
§54. Harmonic Cosmogony |
554 |
E. History
|
§55. Summary of the History of Harmonics |
594 |
*
|
Afterword |
609 |
|
Partial-Tone Logarithms |
612 |
|
Great Table of Ratios |
621 |
|
The Author’s Publications |
630 |