Harmony (Ptolemy)

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Harmonics (αρμονικά) is an important work of music theory in ancient Greece . It was created in the second century by the Greek naturalist Claudius Ptolemy , who also authored significant works on geography, mathematics and astronomy.

Structure and content

The work is divided into three books. In Book I to Book III, 2 the Greek tone systems are presented. Book III, 3–16 deals with the meaning of the acoustic interval numbers for the cosmos and the ethical and physical relationships of people.

Book I, 1 - Book III, 2

In the main part of the work, Ptolemy systematizes the music-theoretical knowledge of his time. It separates tones from sounds (I, 3–4), defines intervals (I, 5–11), sound genres (I, 12 – II, 2), systems formed from fourths and fifths (II, 3 – II, 6) and keys ( tonoi ) (II, 7-III, 2). He mainly depicts the schools of the Pythagoreans and Aristoxenus , both of which he names and strongly criticizes. He accuses the Pythagoreans of getting lost in mere speculation of numbers, and Aristoxenus of relying exclusively on observation, on hearing psychology. Ptolemy tries a synthesis between the Pythagorean, mathematical-logical way of thinking and the acoustic experiment of Aristoxenos on the monochord , but cannot cope with the contradictions.

Book III, 3-11

From Book III, 3 the position of the αρμονικά on the world as a whole, Book III, 4–7 on the human soul and Book III, 8-14 on astronomy, is presented. Relationships between the three consonances - octave , fifth , fourth - and the three soul forces - power to think, feel and live - are established (Book III, 5). The underlying ideas can be found in several ancient authors, including a. Aristotle , Plutarch , Plato . Aristeides Quintilianus developed similar thoughts in his work Von der Musik (3rd book, II, B, b World harmony in the soul ). However, no direct parallels can be established. And since the lifetime of Aristeides Quintilianus cannot be precisely defined, it is not clear whether and in what way an influence took place.

From Book III, 8 Ptolemy turns to astronomical terms. He brings the systema teleion (perfect system = double octave) into agreement with the ecliptic :

  • Book III, 8 The correspondence between the Systema teleion and the ecliptic
  • Book III, 9 Comparison of the symphonic and diaphonic intervals in the tone system and the relationships in the zodiac
  • Book III, 14 List of the smallest numbers according to which the fixed tones of the Systema teleion can be compared with the most important orbits of the planetary system.

The proportions of the 360 ​​° circle of the orbit of the stars are compared with the ratios of the tones, such as the 180 ° of opposition with the octave, or the 12 houses of the zodiac with the approximately 12 whole tones in the two-octave systema teleion (Book III, 9). In a similar way, Aristeides Quintilianus established a connection between the tones and the stars, including the zodiac (Aristeides Quintilianus: From music. 3rd book, II, B, a, 2 The melodic movement of the planets).

Tradition and survival

Just a few decades later, the philosopher Porphyrios wrote an extensive commentary. Anicius Manlius Severinus Boethius used the book in his work Five Books on Music . This can be seen in numerous citations by name, but also in particular in the fact that Boethius adopted chapters 1 and 2 almost entirely as a translation in book 5 / cap.2 + 3. In the following time, music theory was mainly based on this work. Later, however, the thoughts of Ptolemy were taken up again, especially in the 16th century by Vincenzo Galilei and Gioseffo Zarlino For Johannes Kepler , harmony played an important role in his work Harmonice mundi (world harmony). Since the present translation into the Latin language did not seem clear enough to him, he translated Book III, 3 – end from a Greek manuscript into the Latin language.

In 1562 a Latin translation was edited by Antonius Gogavinus in Venice, and the Greek text by John Wallis in Oxford in 1695/1699 . Ingemar Düring created an edition in 1930 and a translation into German in 1934.

Text editions and translations

  • Ingemar Düring: Άρμονικᾀ ed. I. Düring. Gothenburg 1930.
  • Ingemar Düring: Ptolemaios and Porphyrios, about music. Gothenburg, 1934.
  • Oscar Paul : Anicius Manilius Severinus Boetius: Five books on music. Book II, 5–11 - Edition and Translation, Hildesheim / New York 1973.
  • Jon Solomon: Ptolemy. Harmonics. Translation and Commentary, Mnemosyne, Bibliotheca Classica Batava, Supplementum, Leiden: Brill 1999.

literature

  • Franz Boll : Studies on Claudius Ptolemaeus. A contribution to the history of Greek philosophy and astrology. In: New Yearbooks for Philology and Education. Supplementary volume 21.2. Teubner, Leipzig 1894, pp. 49–244.
  • Wilfried Neumaier: What is a sound system? A historical-systematic theory of the occidental sound systems, based on the ank theoreticians, Aristoxenus, Eucleides and Ptolemaios, presented with the means of modern algebra. Frankfurt am Main 1986.

Single receipts

  1. ^ Rudolf Westphal : The music of the Greek antiquity. P. 256.
  2. ^ Rudolf Westphal: The music of the Greek antiquity. Pp. 256-260.
  3. ^ Franz Boll: Studies on Claudius Ptolemaeus. P. 95.
  4. ↑ Wilfried Neumaier: What is a sound system? P. 174 f.
  5. ^ Franz Boll: Studies on Claudius Ptolemaeus. Pp. 102-107.
  6. ^ Franz Boll: Studies on Claudius Ptolemaeus. P. 104, note 5.
  7. ↑ Ingemar Düring: Ptolemaios and Porphyrios, About Music. 10 f.
  8. ^ Franz Boll: Studies on Claudius Ptolemaeus. P. 94, note 1.
  9. ↑ Wilfried Neumaier: What is a sound system? P. 209 f.
  10. ↑ Wilfried Neumaier: What is a tone system ?. P. 180.
  11. ^ Max Caspar : Johannes Kepler: Weltharmonik , Foreword S29 *, Oldenburg 1997
  12. ↑ Johann Kepler, Appendix to V. Book of World Harmonics
  13. ^ Franz Boll: Studies on Claudius Ptolemaeus. P. 93.