Elementa harmonica is a treatise on the subject of musical scales by Aristoxenus, of which substantial amounts are extant.
The work dates apparently to c.300 B.C.
The work is known variously as Aristoxenou (or Aristoxenoy) Armonika (or Harmonika) Stoicheia i.e. Aristoxenou Armonika Stoicheia, Aristoxenou Harmonika Stoicheia etc. All of these translate as The Harmonics of Aristoxenus. Elementa harmonica translates as Elements of Harmonics. The work is otherwise rendered as The Elements, or Elements, the latter translates into Greek as .
The Elements is held to be the work founding a tradition of the study of music based on practice, which is, to understand music by study to the ear. Musicology as a discipline achieved nascency with the systematic study undertaken in the work, which treated music independently of those prior studies which held it in a position of something purely and only in relation to an understanding of the kosmos. In-as-much, the Elements is the first and earliest work on music in the classical Greek tradition. Earliest considerations arose within the Pythagorean school c.500 and thinking dwelled on the mathematical nature of harmonia. Aristotle, whose Peripatetic school Aristoxenus belonged to, addressed the subject in his work On the Soul. Dewhitt thinks Aristoxenus treatment of the subject was essentially to attempt to describe and locate the elements of the soul, and provide mathematical proofs for these. Aristoxenus is thought contrary to the position of the Pythagoreans, he favoured an intellectual treatment of the subject which Aristotle had set out in his work, which is the exercise of inductive logic with attention to empirical evidence.
Aristoxenus is thought the first to consider music in this respect, as a separate subject, due to this 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 ).
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.
The general considered attitude of Aristoxenus was to attempt an empirical study based therefore upon observation. In-as-much his writing contains criticisms of predecessing appreciations and attitudes, of the Pythagorean and harmonikoi, on the problems of sound percptable as music.
Translation into Latin for the first time, during 1564, was made by Antonius Gogavinus.
Editions were published by Meibom, Marquard (1868) Aristoxenou harmonik?n ta s?zomena: Die harmonischen fragmente des Aristoxenus, published in Greek and German translation, and Westphal. Henry Stewart Macran edition was published during 1902 by Clarendon Press, Oxford. An edition was published in Latin during 1954, and another in the same year in Italian, by Typis Publicae Officinae Polygraphicae.
History of scholarship
Vitruvius (circa. mid-20's B.C. ) based his understanding of the laws of harmony on the Elements of Aristoxenus.
The Elements was studied seriously and earnestly during the Renaissance, by theoreticians and musicians, because of the necessary choice which Renaissance intellectuals and thinkers had to make of deciding where to make concordance with, of the reality of the theory on music made by either Pythagoras or Aristoxenus. All the events belonging to the Renaissance Period as an approximate whole occurred within a time some time prior to and including the 15th and 16th centuries 
The work was known to Meibomius, who was born 1611.
Loloy made a study which was published during 1904. Annie Bélis composed a study Aristoxene de Tarante et Aristote: Le Traité d'harmonique, Études et commentaires 100, published during 1986.
Norman Cazden wrote the article Pythagoras and Aristoxenos Reconciled which was published 1958 by the Journal of Music Theory.
W.B.Stanford' The Sound of Greek (1967) cites the work.
Andrew Barker has made a translation, published in Greek Musical Writings (volume 1 published 1984, volume 2 1989).
Landels' Music in Ancient Greece and Rome (1999) deals with intervals in The Elements.
Kuntz (2000) thinks Aristoxenus to have provided a superior understanding to the Pythagorean treatment of the harmonic problem.
D Creese 2012 work concerns itself with Aristoxenus' consideration of the perfect fourth.
The work comprises 3 books.Book II seems not to follow from Book I,it is quite widely but not unanimously the shared opinion Book I is separate work from Book II & III.
The parts of harmonics:
(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) Syst?mata - 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
(7) Construction / Composition
The term dynamis seems to have been originated by Aristoxenus. Dynamis (dynameis) are conventionally understood to have, amongst other meanings, power and potentiality. Sidoli contends in his review (c.f. ref.) that the initial use of the concept by Aristoxenus was rather "elusive" in the context of the meaning intended by him.
- ^ Rotman Institute of Philosophy Western University [Retrieved 2015-05-04]
- ^ a b M.C. Howatson. The Oxford Companion to Classical Literature (p.73). Oxford University Press, 22 Aug 2013 (reprint) ISBN 0199548552 Oxford Paperback Reference.
- ^ a b Aristoxenus, Henry Stewart Macran. Harmonika Stoicheia (The Harmonics of Aristoxenus). Georg Olms Verlag 1902 ISBN 3487405105. Retrieved .(and World Cat)
- ^ The Perseus Catalog - Elementa Harmonica Tufts University , University of Liepzig [Retrieved 2015-05-04]
- ^ a b A.D. Barker. The Oxford Classical Dictionary (edited by S Hornblower, A Spawforth, E Eidinow) p.163-4. Oxford University Press, 29 Mar 2012 ISBN 0199545561. Retrieved .
- ^ C.H. Kahn. Pythagoras and the Pythagoreans: A Brief History (p.69). Hackett Publishing, 1 Jan 2001 ISBN 0872205754. Retrieved .
- ^ Sophie Gibson - Aristoxenus of Tarentum and the Birth of Musicology (p.6) Routledge, 8 Apr 2014 Studies in Classics ISBN 1135877475 [Retrieved 2015-05-03]
- ^ C.A. Huffman. Aristoxenus of Tarentum: Discussion. Transaction Publishers, 2012. Retrieved .(p.254)
- ^ H Partch. Genesis of a Music: An Account of a Creative Work, Its Roots, and Its Fulfillments. Da Capo Press, 5 Aug 2009 ISBN 0786751002. Retrieved .
- ^ a b J. Hawkins. General history of the science and practice of music. [With] vol. of portraits, Volume 1. J.Alfred Novello 1858. Retrieved .
- ^ a b c Mitzi Dewhitt. Aristoxenus's Ghost. Xlibris Corporation, 7 Sep 2004 ISBN 1465332057. Retrieved .
- ^ L.M. Zbikowski Associate Professor of Music University of Chicago. Conceptualizing Music : Cognitive Structure, Theory, and Analysis: Cognitive Structure, Theory, and Analysis. Oxford University Press, 18 Oct 2002 ISBN 019803217X AMS Studies in Music Series. Retrieved .
- ^ D.M. Randel. The Harvard Dictionary of Music. Harvard University Press, 2003 Volume 16 of Harvard University Press reference library ISBN 0674011635. Retrieved .(p.358)
- ^ Lilian Voudouri
- ^ D Obbink. Philodemus and Poetry : Poetic Theory and Practice in Lucretius, Philodemus and Horace: Poetic Theory and Practice in Lucretius, Philodemus and Horace (p.140). Oxford University Press, 9 May 1995 ISBN 0195358546. Retrieved .(additionally using American Heritage® Dictionary of the English Language, Fifth Edition at thefreedictionary.com)
- ^ 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]
- ^ a b R Katz, C Dahlhaus. Contemplating Music: Substance. Retrieved .(p.273)
- ^ J Godwin. The Harmony of the Spheres: The Pythagorean Tradition in Music. Inner Traditions / Bear & Co, 1 Nov 1992 ISBN 1620550962. Retrieved .
- ^ a b c d A. Barker. The Science of Harmonics in Classical Greece. Cambridge University Press, 13 Sep 2007 ISBN 1139468626. Retrieved .(p.187 "Meibom, Westphal")
- ^ S.J. Livesey (John of Reading). 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(p.25). BRILL, 1989 ISBN 9004090231. Retrieved .
- ^ Aristoxenus, P Marquard - Aristoxenou harmonik?n ta s?zomena: Die harmonischen fragmente des Aristoxenus Weidmann, 1868 [Retrieved 2015-05-04]
- ^ H.S. Macran - The harmonics of Aristonexus The Boston Library Consortium - Northeastern University Libraries [Retrieved 2015-05-04]
- ^ the Internet Archive - Open Library ID : OL14785002M University of Toronto MARC record [Retrieved 2015-05-08]
- ^ I. Kagis McEwen - Vitruvius: Writing the Body of Architecture, MIT Press 2003, p.1 of 493 pages, ISBN 026263306X [Retrieved 2015-12-16]
- ^ 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]
- ^ J. Prins - Echoes of an Invisible World: Marsilio Ficino and Francesco Patrizi on Cosmic Order and Music Theory BRILL, 28 Nov 2014, 476 pages, History, ISBN 9004281762, Brill's Studies in Intellectual History [Retrieved 2015-12-16]
- ^ P. Van Ness Myers - facsimile of Mediæval and Modern History published by Boston: Ginn and Company, 1905 - p.251 published online by Sam Houston State University [Retrieved 2015-12-16]
- ^ Alexander Chalmers - The General biographical dictionary, Printed for J. Nichols 1815, Volume 22 of The General Biographical Dictionary: Containing an Historical and Critical Account of the Lives and Writings of the Most Eminent Persons in Every Nation (Original from the University of Michigan Digitized 31 Aug 2007) [Retrieved 2015-12-16]
- ^ Lilian Voudouri - Music Library of Greece Friends of Music Society (Athens) [Retrieved 2015-05-04]
- ^ M Litchfield. Aristoxenus and Empiricism: A Reevaluation Based on His Theories. Journal of Music Theory Vol. 32, No. 1 (Spring, 1988), pp. 51-73 Published by: Duke University Press. Retrieved .
- ^ N Cazden. Pythagoras and Aristoxenos Reconciled. Journal of the American Musicological Society Vol. 11, No. 2/3 (Summer - Autumn, 1958), pp. 97-105 Published by: University of California Press. Retrieved .
- ^ T.G.Rosenmeyer - Elegiac and Elegos (in) California Studies in Classical Antiquity, Volume 1 (p.221) University of California Press & Cambridge University Press (ed. T.S.Brown, W.K.Pritchett)[Retrieved 2015-05-04]
- ^ T.J. Mathiesen. Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages. University of Nebraska Press, 1999 ISBN 0803230796 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. Retrieved .
- ^ A. Barker - staff profile University of Birmingham [Retrieved 2015-05-04]
- ^ a b A Briggman. Irenaeus of Lyons and the Theology of the Holy Spirit. Oxford University Press, 12 Jan 2012 ISBN 0199641536 Oxford Early Christian Studies. Retrieved .("Distantia & Landels")
- ^ P.G. Kuntz - Whitehead's Category of Harmony: Analogous Meanings in Every Realm of Being and Culture - part.XX Process Studies, pp.43-65, Vol. 29, Number 1, Spring-Summer, 2000. Process Studies is published quarterly by the Center for Process Studies [Retrieved 2015-05-04]
- ^ D Creese - Instruments and Empiricism in Aristoxenus' Elementa harmonica Newcastle University - School of History Classics and Archaeology 2012 [Retrieved 2015-05-04]
- ^ 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]
- ^ definitions taken from bible hub - Strong's Concordance & Merriam-Webster [Retrieved 2015-05-08]
- ^ Nathan Sidoli, Andrew Barker. Andrew Barker, The Science of Harmonics in Classical Greece reviewed by Nathan Sidoli, Waseda University. Bryn Mawr Classical Review 2009.10.38. Retrieved .