Epistemology of Greek Harmonics

Danilo Capecchi

Dipartimento di ingegneria strutturale e geotecnica, University of Rome, Rome, Italy.

DOI: 10.4236/ahs.2015.43014                

Abstract

Greek harmonics is the theory of the organization of notes with respect to the highness or lowness of their pitches. This was a mathematical science, a thorough knowledge of which was not necessary for the professional musician and was thus cultivated essentially by mathematicians and philosophers. For them, harmonics was mixed mathematics, the mix being between experimental assertions derived from hearing and propositions derived from reason, that was, mathematics. This classification was maintained through the Middle Ages and the Renaissance. Despite the important role played by harmonics in ancient science, little consideration has been given by historians of science. This study shows that harmonics merits a careful study and that its methods are the same as other sciences. Particular attention was devoted to Ptolemy who applied the same approach to harmonics as he did to astronomy, astrology and geography.

Keywords

Harmonics, Epistemology, History of Science, Greek Music, Mixed Mathematics

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Aristoxenus (1902). The Harmonics of Aristoxenus. Edited and Translated into English by H. S. Macran Oxford: Clarendon Press.
[2]	Aristoxenus (1954). Aristoxeni Elementa harmonica. Edited and Translated into Italian by R. Da Rios. Rome: Publicae Officinae polygraphicae
[3]	Barbera, C. A. (1977). Arithmetic and Geometric Divisions of the Tetrachord. Journal of Music Theory, 21, 294-323. http://dx.doi.org/10.2307/843492
[4]	Barker, A. (1978). Music and Perception: A Study in Aristoxenus. The Journal of Hellenic Studies, 98, 9-16. http://dx.doi.org/10.2307/630189
[5]	Barker, A. (1989). Greek Musical Writings (Vol. 2). Cambridge: Cambridge University Press.
[6]	Barker, A. (1994). Ptolemy’s Phytagoreans, Architas, and Plato’s Conception of Mathematics. Phronesis, 39, 113-135. http://dx.doi.org/10.1163/156852894321052135
[7]	Barker, A. (2006). Scientific Method in Ptolemy’s Harmonics. Cambridge: Cambridge University Press.
[8]	Comotti, G. (1991). La musica nella cultura greca e romana. Turin: E.D.T.
[9]	De Pace, A. (1993). Le matematiche e il mondo. Milan: Francoangeli.
[10]	Drake, S. (1970). Renaissance Music and Experimental Science. Journal of the History of Ideas, 31, 483-500. http://dx.doi.org/10.2307/2708256
[11]	Drake, S. (1978). Ptolemy, Galileo, and Scientific Method. Studies in History and Philosophy of science, 9, 99-115. http://dx.doi.org/10.1016/0039-3681(78)90002-X
[12]	Düring, I. (1930). Die Harmonielehre des Klaudios Ptolemaios. Porphyrios Kommentar Zur Harmonielehre Des Ptolemaios. PhD Dissertation, Göthenburg: University of Göthenburg.
[13]	Düring, I. (1956) Greek Music: Its Fundamental Features and Its Significance. Journal of World History, 3, 302-329.
[14]	Feke, J. (2009). Ptolemy in Philosophical Context. Ph.D. Dissertation, Toronto: University of Toronto.
[15]	Laloy, L. (1904) Aristoxéne the Tarente et la musique de l’antiquité. Paris: Societé Français d’Imprimerie et de Libraire.
[16]	Litchfield, M. (1988). Aristoxenus and Empiricism: A Reevaluation Based on His Theories. Journal of Music Theory, 32, 51-73. http://dx.doi.org/10.2307/843385
[17]	Manolova, D. (2014). Discourse of Science and Philosophy in the Letters of Nikephoros Gregoras. Ph.D. Dissertation, Budapest: Central European University.
[18]	Palisca, C. V. (1961). Scientific Empiricism in Musical Thought. In: H. H. Rhys (Ed.), Seventeen Science and the Arts (pp. 91-137). Princeton, NJ: Princeton University Press.
[19]	Palisca, C. V. (1985). Humanism in Italian Renaissance. Musical Thought. New Haven, CT: Yale University Press.
[20]	Ptolemy, C. (2000). Ptolemy Harmonics. Translated and commented by J. Solomon. Leiden: Brill.