Ptolemy Harmonics

CONTENTS

Preface ........................................................................................................ ix Abbreviations ............................................................................................ xiii Introduction ............................................................................................... xxi Ptolemy Harmonics Book I .................................................................................................... 1 Book II................................................................................................... S9 Book III ................................................................................................. 127 Bibliography ........................................................................................ Index of Greek Terms ................................................................................ Index of Manuscripts and Papyri Cited ..................................................... General Index ............................................................................................

167 181 183 184

BOOK I

Summary I. 2. 3. 4. 5.

6. 7. 8.

9. 10. II.

12. 13. 14. 15. 16.

On the Criteria in Harmonics. What is the Purpose of the Harmonicist? How Highness and Lowness in Sounds Exists. On Notes and Their Differences. On the Pythagoreans' Positions Concerning the Hypotheses of the Consonances. That the Pythagoreans did not Investigate About the Consonances Properly. How the Ratios ofthe Consonances Could Be More Properly Defined. In What Way the Ratios of the Consonances Will Be Demonstrated Con-fidently via the Monochord Canon. That the Aristoxenians Incorrectly Calculated the Consonances by the Intervals and Not by the Notes. That They Improperly Suppose the Consonance of the Diatessaron to Contain Two and One-halfTones. How by means of the Octochord Canon the Diapason Could Be Shown to One's Perceptions to be Smaller than Six Tones. On the Aristoxenian Division of the Genera and the Tetrachords in Each. On Archytas' Division of the Genera and the Tetrachords. Proof that Neither of These Divisions Preserves the Real Emmelic Interval. On the Rational and Audible Tetrachordal Division by Genus. How Many and Which Genera Are More Familiar to the Hearing.