Elementa harmonica

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Elementa harmonica is a treatise on the subject of musical scales by Aristoxenus, of which considerable amounts are extant. The work dates to the second half of the 4th century BC.[1] It is the oldest substantially surviving work written on the subject of music theory.[2]


The work is generally known as Aristoxenou Harmonika Stoicheia or Elements of Harmonics.[3][4][5] It is also known by the shorter title The Elements, rendering Greek Στοιχεία.[6]

The Work[edit]

Historical context[edit]

Aristoxenus's work departs from prior studies in which music was studied only in relation to an understanding of the kosmos. The study of music in the Pythagorean school c.500 had focused on the mathematical nature of harmonia. Aristotle, whose Peripatetic school Aristoxenus belonged to, addressed the subject in his work On the Soul. Aristoxenus opposed the position of the Pythagoreans; he favoured an intellectual treatment of the subject in Aristotelian terms, i.e. by applying the exercise of inductive logic with attention to empirical evidence.[7][8][9][10][11][12][self-published source][13][14] As such, the Elements is the first and earliest work on music in the classical Greek tradition. Musicology as a discipline comes into being with the systematic study undertaken in the work.


The work is a theoretical treatise concerned with harmony and harmonics, and thus pertains to a burgeoning theory of euphonics. The study of harmonics is especially concerned with treating melody in order to find its components (the Greek word for melody is μέλος).[6][12][15]

In the first sentence of the treatise Aristoxenus identifies Harmony as belonging under the general scope of the study of the science of Melody. Aristoxenus considers notes to fall along a continuum available to auditory perception. Aristoxenus identified the three tetrachords in the treatise as diatonic, the chromatic, and the enharmonic.[3][4][16]

Aristoxenus aims to attempt an empirical study based upon observation. As such, his writing contains criticisms of earlier approaches and attitudes, including those of the Pythagorean and harmonikoi, on the problems of sound perceptible as music.[17][18][19]


The work comprises 3 books. Book II seems not to follow from Book I, and it is quite widely but not unanimously assumed that Book I is a separate work from Book II & III.[19]

The parts of harmonics:[12][19][20]

(1) The Genera - the ways in which the differences between these are determined

(2) Distantia (Intervals) - the distinction of how these are differentiated

(3) Notes - dynameis

(4) Systēmata - enumerating and distinguishing the types, and explaining how they are put together out of Notes and Intervals

(5) Tonoi (Modes) - including the relations between them

(6) Modulation

(7) Construction / Composition


The use of dynamis (pl. dynameis) as a musical term seems to have been originated by Aristoxenus. The term normally denotes power and potentiality. Sidoli contends in his review (cf. ref.) that the initial use of the concept by Aristoxenus was rather "elusive."[21][22][23]

Later Reception[edit]

Vitruvius (circa. mid-20s B.C.[24]) based his understanding of the laws of harmony on the Elements of Aristoxenus.[25]

The Elements was studied earnestly during the Renaissance by theoreticians and musicians.[17] Renaissance thinkers were faced with a choice between following Pythagoras or Aristoxenus.[26]

Editions and Translations[edit]

The first Latin translation was made in 1564 by Antonius Gogavinus.[27]

There are editions of the Greek text by Marcus Meibom (1652); Paul Marquard, Aristoxenou harmonikōn ta sōzomena: Die harmonischen fragmente des Aristoxenus (1868), with German translation; Rudolf Westphal (Leipzig, 1883); and Henry Stewart Macran (Oxford, 1902). An edition was published in Latin during 1954, and another in the same year in Italian, by Typis Publicae Officinae Polygraphicae.[19][28][29][30]

There is an English translation by Andrew Barker in his Greek Musical Writings (volume 1 published 1984, volume 2 1989).[31][32]

Modern Studies[edit]

  • Louis Laloy, Aristoxène de Tarent et la Musique de l'antiquité (Paris, 1904).
  • R.P. Winnington-Ingram, "Aristoxenus and the Intervals of Greek Music," Classical Quarterly 26 (1932), 195-208.
  • Norman Cazden, "Pythagoras and Aristoxenos Reconciled," Journal of Music Theory 32. 1 (1958), 51-73.[33][34]
  • Annie Bélis, Aristoxene de Tarante et Aristote: Le Traité d’harmonique, Études et commentaires 100 (Paris, 1986).[35]
  • John G. Landels, Music in Ancient Greece and Rome (London and New York, 1999). Deals with intervals in The Elements.[20]
  • D. Creese, "Instruments and Empiricism in Aristoxenus' Elementa Harmonica" (2012). Online.[36]

See also[edit]


  1. ^ Rotman Institute of Philosophy Archived 2015-04-21 at the Wayback Machine Western University [Retrieved 2015-05-04]
  2. ^ Aristoxenus, Henry Stewart Macran (1902). Harmonika Stoicheia (The Harmonics of Aristoxenus). Georg Olms Verlag. ISBN 978-3-487-40510-0. OCLC 123175755.
  3. ^ a b M.C. Howatson (22 August 2013). The Oxford Companion to Classical Literature. Oxford University Press (reprint). p. 73. ISBN 978-0199548552. Oxford Paperback Reference
  4. ^ a b Aristoxenus, Henry Stewart Macran (1902). Harmonika Stoicheia (The Harmonics of Aristoxenus). Georg Olms Verlag. ISBN 978-3487405100. Retrieved 4 May 2015.(and World Cat)
  5. ^ The Perseus Catalog - Elementa Harmonica Tufts University, University of Leipzig [Retrieved 2015-05-04]
  6. ^ a b A.D. Barker (29 March 2012). The Oxford Classical Dictionary (edited by S Hornblower, A Spawforth, E Eidinow). Oxford University Press. pp. 163–164. ISBN 978-0199545568. Retrieved 8 May 2015.
  7. ^ C.H. Kahn (1 January 2001). Pythagoras and the Pythagoreans: A Brief History. Hackett Publishing. p. 69. ISBN 978-0872205758. Retrieved 4 May 2015.
  8. ^ Sophie Gibson - Aristoxenus of Tarentum and the Birth of Musicology (p. 6) Routledge, 8 April 2014 Studies in Classics ISBN 1135877475 [Retrieved 2015-05-03]
  9. ^ C.A. Huffman (2012). Aristoxenus of Tarentum: Discussion. Transaction Publishers, 2012. ISBN 9781412843010. Retrieved 3 May 2015.(p. 254)
  10. ^ H Partch (5 August 2009). Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments. Da Capo Press. ISBN 978-0786751006. Retrieved 4 May 2015.
  11. ^ J. Hawkins (1858). General history of the science and practice of music. [With] vol. of portraits, Volume 1. J.Alfred Novello 1858. Retrieved 4 May 2015.
  12. ^ a b c Mitzi Dewhitt (7 September 2004). Aristoxenus's Ghost. Xlibris Corporation. ISBN 978-1465332059. Retrieved 3 May 2015.
  13. ^ L.M. Zbikowski Associate Professor of Music University of Chicago (18 October 2002). Conceptualizing Music : Cognitive Structure, Theory, and Analysis: Cognitive Structure, Theory, and Analysis. Oxford University Press. ISBN 978-0198032175. Retrieved 3 May 2015. AMS Studies in Music Series
  14. ^ D.M. Randel (2003). The Harvard Dictionary of Music. Harvard University Press, Volume 16 of Harvard University Press reference library. p. 358. ISBN 978-0674011632. Retrieved 4 May 2015.
  15. ^ D Obbink (9 May 1995). Philodemus and Poetry : Poetic Theory and Practice in Lucretius, Philodemus and Horace. Oxford University Press. p. 140. ISBN 978-0195358544. Retrieved 4 May 2015.(additionally using American Heritage® Dictionary of the English Language, Fifth Edition at thefreedictionary.com)
  16. ^ Cristiano M.L. Forster - Musical Mathematics : on the art and science of acoustic instruments CHAPTER 10: WESTERN TUNING THEORY AND PRACTICE Chrysalis Foundation [Retrieved 2015-05-04]
  17. ^ a b R Katz, C Dahlhaus (1987). Contemplating Music: Substance. ISBN 9780918728609. Retrieved 4 May 2015.(p. 273)
  18. ^ J Godwin (1 November 1992). The Harmony of the Spheres: The Pythagorean Tradition in Music. Inner Traditions / Bear & Co. ISBN 978-1620550960. Retrieved 4 May 2015.
  19. ^ a b c d A. Barker (13 September 2007). The Science of Harmonics in Classical Greece. Cambridge University Press. ISBN 978-1139468626. Retrieved 3 May 2015.(p. 187 "Meibom, Westphal")
  20. ^ a b A Briggman (12 January 2012). Irenaeus of Lyons and the Theology of the Holy Spirit. Oxford University Press, Oxford Early Christian Studies. ISBN 978-0199641536. Retrieved 4 May 2015.("Distantia & Landels")
  21. ^ Erik Nis Ostenfeld, Plato (The Republic - Ergon and dynamis)- Forms, Matter and Mind Volume 10 of Martinus Nijhoff philosophy library Springer Science & Business Media, 1982 ISBN 940097681X [Retrieved 2015-05-08]
  22. ^ definitions taken from bible hub - Strong's Concordance & Merriam-Webster [Retrieved 2015-05-08]
  23. ^ Nathan Sidoli, Andrew Barker (October 2009). "Andrew Barker, The Science of Harmonics in Classical Greece reviewed by Nathan Sidoli, Waseda University". Bryn Mawr Classical Review. Bryn Mawr Classical Review 2009.10.38. Retrieved 8 May 2015.
  24. ^ I. Kagis McEwen - Vitruvius: Writing the Body of Architecture, MIT Press 2003, p. 1 of 493 pages, ISBN 026263306X [Retrieved 2015-12-16]
  25. ^ D.K.S. Walden - Frozen Music: Music and Architecture in Vitruvius’ De Architectura 2014 Greek and Roman Musical Studies, Volume 2, Issue 1, pages 124 – 145 DOI: 10.1163/22129758-12341255 [Retrieved 2015-05-04]
  26. ^ J. Prins - Echoes of an Invisible World: Marsilio Ficino and Francesco Patrizi on Cosmic Order and Music Theory BRILL, 28 November 2014, 476 pages, History, ISBN 9004281762, Brill's Studies in Intellectual History [Retrieved 2015-12-16]
  27. ^ S.J. Livesey (John of Reading) (1989). Theology and Science in the Fourteenth Century: Three Questions on the Unity and Subalternation of the Sciences from John of Reading's Commentary on the Sentences. BRILL. p. 25. ISBN 978-9004090231. Retrieved 4 May 2015.
  28. ^ Aristoxenus, P Marquard - Aristoxenou harmonikōn ta sōzomena: Die harmonischen fragmente des Aristoxenus Weidmann, 1868 [Retrieved 2015-05-04]
  29. ^ H.S. Macran - The harmonics of Aristonexus The Boston Library Consortium - Northeastern University Libraries [Retrieved 2015-05-04]
  30. ^ the Internet Archive - Open Library ID : OL14785002M University of Toronto MARC record [Retrieved 2015-05-08]
  31. ^ T.J. Mathiesen (1999). Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages. University of Nebraska Press, ACLS Humanities E-Book Volume 2 of Center for the History of Music Theory and Literature Bloomington, Ind: Publications of the Center for the History of Music Theory and Literature. ISBN 978-0803230798. Retrieved 4 May 2015.
  32. ^ A. Barker - staff profile University of Birmingham [Retrieved 2015-05-04]
  33. ^ M Litchfield (1988). "Aristoxenus and Empiricism: A Reevaluation Based on His Theories". Journal of Music Theory. Journal of Music Theory Vol. 32, No. 1 (Spring, 1988), pp. 51-73 Published by: Duke University Press. 32 (1): 51–73. doi:10.2307/843385. JSTOR 843385.
  34. ^ N Cazden (1958). "Pythagoras and Aristoxenos Reconciled". Journal of the American Musicological Society. Journal of the American Musicological Society Vol. 11, No. 2/3 (Summer - Autumn, 1958), pp. 97-105 Published by: University of California Press. 11 (2/3): 97–105. doi:10.2307/829897. JSTOR 829897.
  35. ^ Lilian Voudouri - Music Library of Greece Friends of Music Society (Athens) [Retrieved 2015-05-04]
  36. ^ D Creese - Instruments and Empiricism in Aristoxenus' Elementa harmonica Archived 2015-05-18 at the Wayback Machine Newcastle University - School of History Classics and Archaeology 2012 [Retrieved 2015-05-04]