Elementa harmonica

{{Main|Harmony#Etymology and definitions|Harmonic}}

The work is generally known as Aristoxenou Harmonika Stoicheia or Elements of Harmonics.{{cite book |author=M.C. Howatson|title=The Oxford Companion to Classical Literature |page=73|publisher=Oxford University Press (reprint) |date=22 August 2013 |isbn=978-0199548552}} Oxford Paperback Reference{{cite book|url=https://books.google.com/books?id=3TseQjV_wogC&dq=translations+of+Aristoxenus+Elements+of+Harmony&pg=PA165|author=Aristoxenus, Henry Stewart Macran|title=Harmonika Stoicheia (The Harmonics of Aristoxenus)|publisher=Georg Olms Verlag |year=1902 |isbn=978-3487405100|access-date=2015-05-04}}(and [https://www.worldcat.org/oclc/123175755 World Cat])The Perseus Catalog - [http://catalog.perseus.org/catalog/urn:cts:greekLit:tlg0088.tlg001 Elementa Harmonica] Tufts University, University of Leipzig [Retrieved 2015-05-04] It is also known by the shorter title The Elements, rendering Greek Στοιχεία.

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.{{cite book |url=https://books.google.com/books?id=5vi10r5k5eEC&dq=Aristoxenus+Elements+Harmony&pg=PA69|author=C.H. Kahn|title=Pythagoras and the Pythagoreans: A Brief History |page=69|publisher=Hackett Publishing |date=1 January 2001 |isbn=978-0872205758 |access-date=2015-05-04}}Sophie Gibson - [https://books.google.com/books?id=JAUSBAAAQBAJ&dq=Aristoxenus+of+Tarentum+and+the+Birth+of+Musicology&pg=PA3 Aristoxenus of Tarentum and the Birth of Musicology (p. 6)] Routledge, 8 April 2014 Studies in Classics {{ISBN|1135877475}} [Retrieved 2015-05-03]{{cite book |url=https://books.google.com/books?id=LZDBAgAAQBAJ&q=Aristoxenus|author=C.A. Huffman|title=Aristoxenus of Tarentum: Discussion|publisher=Transaction Publishers, 2012 |access-date=2015-05-03|isbn=9781412843010|year=2012}}(p. 254){{cite book |url=https://books.google.com/books?id=w-eqL7oLyigC&dq=Aristoxenus+Elements&pg=PA365|author=H Partch|title=Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments|publisher=Da Capo Press |date=5 August 2009 |isbn=978-0786751006 |access-date=2015-05-04}}{{cite book |url=https://books.google.com/books?id=-wYVAAAAQAAJ&dq=Aristoxenus+Elements&pg=PA66|author=J. Hawkins|title=General history of the science and practice of music. [With] vol. of portraits, Volume 1|publisher=J.Alfred Novello 1858 |access-date=2015-05-04|year=1858}}{{cite book |url=https://books.google.com/books?id=pyZduhclFkoC&q=Aristoxenus|author=Mitzi Dewhitt|title=Aristoxenus's Ghost|publisher=Xlibris Corporation |date=7 September 2004 |isbn=978-1465332059 |access-date=2015-05-03}}{{Self-published inline|certain=yes|date=January 2018}}{{cite book |url=https://books.google.com/books?id=YSk-LjJNp8QC&dq=Elementa+Harmonica&pg=PA11|author=L.M. Zbikowski Associate Professor of Music University of Chicago|title=Conceptualizing Music : Cognitive Structure, Theory, and Analysis: Cognitive Structure, Theory, and Analysis|publisher=Oxford University Press |date=18 October 2002 |isbn=978-0198032175 |access-date=2015-05-03}} AMS Studies in Music Series{{cite book |url=https://books.google.com/books?id=02rFSecPhEsC&q=The+Harvard+Dictionary+of+Music|author=D.M. Randel|title=The Harvard Dictionary of Music|publisher=Harvard University Press, Volume 16 of Harvard University Press reference library |year=2003 |isbn=978-0674011632|page=358 |access-date=2015-05-04}} 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).{{cite book |url=https://books.google.com/books?id=bVWcAQAAQBAJ&dq=Burnyeat+translation+Aristoxenus&pg=PA163|author=A.D. Barker|title=The Oxford Classical Dictionary (edited by S Hornblower, A Spawforth, E Eidinow) |pages=163–164|publisher=Oxford University Press |date=29 March 2012 |isbn=978-0199545568 |access-date=2015-05-08}}{{cite book |url=https://books.google.com/books?id=KBNGAH9-0YAC&dq=Aristoxenus+Elements+Harmony&pg=PA140|author=D Obbink|title=Philodemus and Poetry : Poetic Theory and Practice in Lucretius, Philodemus and Horace |page=140|publisher=Oxford University Press |date=9 May 1995 |isbn=978-0195358544 |access-date=2015-05-04}}(additionally using American Heritage® Dictionary of the English Language, Fifth Edition at thefreedictionary.com)

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.Cristiano M.L. Forster - [http://www.chrysalis-foundation.org/Philolaus_and_Euclid.htm Musical Mathematics : on the art and science of acoustic instruments CHAPTER 10: WESTERN TUNING THEORY AND PRACTICE] Chrysalis Foundation [Retrieved 2015-05-04]

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.{{cite book |url=https://books.google.com/books?id=1WpnAwAAQBAJ&dq=Aristoxenus+Elements+Harmony&pg=PT402|author=J Godwin|title=The Harmony of the Spheres: The Pythagorean Tradition in Music|publisher=Inner Traditions / Bear & Co |date=1 November 1992 |isbn=978-1620550960 |access-date=2015-05-04}}

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.{{cite book |url=https://books.google.com/books?id=xRM9WLpswiEC&dq=Elementa+Harmonica&pg=PA113 |author=A. Barker|title=The Science of Harmonics in Classical Greece|publisher=Cambridge University Press |date=13 September 2007 |isbn=978-1139468626 |access-date=2015-05-03}}(p. 187 "Meibom, Westphal")

The parts of harmonics:{{cite book |url=https://books.google.com/books?id=buEm81wj7VkC&dq=Aristoxenus+Elements&pg=PA145|author=A Briggman|title=Irenaeus of Lyons and the Theology of the Holy Spirit|publisher=Oxford University Press, Oxford Early Christian Studies |date=12 January 2012 |isbn=978-0199641536 |access-date=2015-05-04}}("Distantia & Landels")

(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."Erik Nis Ostenfeld, Plato (The Republic - Ergon and dynamis)- [https://books.google.com/books?id=bqu1BwAAQBAJ&dq=dynameis++definition&pg=PT268 Forms, Matter and Mind] Volume 10 of Martinus Nijhoff philosophy library Springer Science & Business Media, 1982 {{ISBN|940097681X}} [Retrieved 2015-05-08]definitions taken from [http://biblehub.com/greek/1411.htm bible hub] - Strong's Concordance & [http://www.merriam-webster.com/dictionary/dynamis Merriam-Webster] [Retrieved 2015-05-08]{{cite journal |url=http://bmcr.brynmawr.edu/2009/2009-10-38.html|author=Nathan Sidoli, Andrew Barker |title=Andrew Barker, The Science of Harmonics in Classical Greece reviewed by Nathan Sidoli, Waseda University|journal=Bryn Mawr Classical Review |publisher=Bryn Mawr Classical Review 2009.10.38 |access-date=2015-05-08|date=October 2009}}

Vitruvius's concepts of architectural and machine design draw heavily on the Elements of Aristoxenus.D.K.S. Walden - [http://booksandjournals.brillonline.com/content/journals/10.1163/22129758-12341255 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]

The Elements was studied earnestly during the Renaissance by theoreticians and musicians.{{cite book |url=https://books.google.com/books?id=64ADtnjmEpQC&dq=Aristoxenus+Elements+Harmony&pg=PA272|author=R Katz, C Dahlhaus|title=Contemplating Music: Substance |access-date=2015-05-04|isbn=9780918728609|year=1987}}(p. 273) Renaissance thinkers were faced with a choice between following Pythagoras or Aristoxenus.J. Prins - [https://books.google.com/books?id=XXWjBQAAQBAJ&dq=Aristoxenus+the+Renaissance&pg=PA56 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]

Antonius Gogavinus translated the book into Latin as Elementa Harmonica in 1564.{{cite book |url=https://books.google.com/books?id=eLFulMIdGjAC&dq=Aristoxenus+Elements&pg=PA25|author=S.J. Livesey (John of Reading)|title=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 |page=25 |publisher=BRILL |year=1989 |isbn=978-9004090231 |access-date=2015-05-04}}

Marcus Meibom included Aristoxenus' text in Antiquae musicae auctores septem (1652), his series of Latin translations of Greek music theory.

Paul Marquard translated it into German as Aristoxenou harmonikōn ta sōzomena: Die harmonischen fragmente des Aristoxenus (1868). Rudolf Westphal also created a German edition (Leipzig, 1883).

Henry Stewart Macran was the first to translate Elementa Harmonica into English (Oxford, 1902).H.S. Macran - [https://archive.org/details/harmonicsofarist00aris The harmonics of Aristonexus] The Boston Library Consortium - Northeastern University Libraries [Retrieved 2015-05-04]

An edition was published in Latin during 1954, and another in the same year in Italian, by Typis Publicae Officinae Polygraphicae.Aristoxenus, P Marquard - [https://books.google.com/books?id=-dyxQXD4cdIC Aristoxenou harmonikōn ta sōzomena: Die harmonischen fragmente des Aristoxenus] Weidmann, 1868 [Retrieved 2015-05-04]the Internet Archive - [https://openlibrary.org/books/OL14785002M/Elementa_harmonica Open Library ID : OL14785002M] University of Toronto MARC record [Retrieved 2015-05-08]

There is an English translation by Andrew Barker in his Greek Musical Writings (volume 1 published 1984, volume 2 1989).{{cite book |url=https://books.google.com/books?id=Td5odzctae8C&dq=Meibom%2C+Marquard%2C+Westphal&pg=PA306|author=T.J. Mathiesen|title=Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages|publisher=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|year=1999 |isbn=978-0803230798|access-date=2015-05-04}}

• Bélis, Annie, Aristoxene de Tarante et Aristote: Le Traité d’harmonique, Études et commentaires 100 (Paris, 1986).
• Cazden, Norman. "Pythagoras and Aristoxenos Reconciled", Journal of Music Theory 32. 1 (1958), 51–73.
• Huffman, Carl A. Aristoxenus of Tarentum : Discussion. Transaction Publishers, 2012.
• Laloy, Louis. Aristoxène de Tarent et la Musique de l'antiquité (Paris, 1904).
• Landels, John G. Music in Ancient Greece and Rome (London and New York, 1999).
• Litchfield, Malcolm. "Aristoxenus and Empiricism: A Reevaluation Based on His Theories". Journal of Music Theory, Vol. 32, No. 1. (Spring, 1988). Duke University Press: 51–73. doi:10.2307/843385. JSTOR 843385.
• Winnington-Ingram, R.P. "Aristoxenus and the Intervals of Greek Music", Classical Quarterly 26 (1932), 195–208.

• {{section link|Musical system of ancient Greece|Aristoxenian tonoi}}

{{Reflist|2}}

Manuscripts

• [https://digi.vatlib.it/view/MSS_Vat.gr.191/0629 Elementa Harmonica], Vat.gr.191 in the Vatican Library.
• [https://digi.vatlib.it/view/MSS_Vat.gr.221/0015 Elementa Harmonica], Vat.gr.221 in the Vatican Library.

Category:Ancient Greek philosophical literature

Category:Music theory