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Ἑλικών



Measurement

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Diagram

Diagram
Division line
Construction line

Intersections

Diagram shows division
Diagram shows construction
Construction shows division
Construction+Diagram shows division
Division shows further division

Measurement

Selectable point
Selected point

Helikon

String
Bridge

Works Cited

Anticopedie. [n.d.]. ‘How Did Music Sound in Ancient Greece?’ Educational fact sheet. https://anticopedie.fr/download/musique-grecque-gb.pdf (accessed May 2026).

Barbour, J. Murray. 1951. Tuning and Temperament: A Historical Survey. East Lansing: Michigan State College Press.

Barker, Andrew. 1989. Greek Musical Writings. Vol. II: Harmonic and Acoustic Theory. Cambridge: Cambridge University Press.

———. 2000. Scientific Method in Ptolemy’s “Harmonics”. Cambridge: Cambridge University Press.

Bielenberg, Aliosha. 2022. ‘The Reception of Ptolemy’s Harmonics in the Byzantine Manuscript Tradition’. Unpublished paper.

Caleon, Imelda and Subramaniam Ramanathan. 2008. ‘From Music to Physics: The Undervalued Legacy of Pythagoras’. Science and Education 17(4): 449–456.

Capecchi, Danilo. 2015. ‘Epistemology of Greek Harmonics’. Advances in Historical Studies 4(3): 155–171.

Clark, Mitchell. 1997. ‘The Helikon’. Experimental Musical Instruments 12(4): 167.

Clendinning, Jane Piper. 1987. ‘Zarlino and the Helicon of Ptolemy: A Translation with Commentary of Book III, Chapter 3 of Gioseffo Zarlino’s “Sopplimenti Musicali”’. Theoria 2: 39–58.

Creese, David. 2010. The Monochord in Ancient Greek Harmonic Science. Cambridge: Cambridge University Press.

Düring, Ingemar, ed. 1930. Die Harmonielehre des Klaudios Ptolemaios. Göteborg: Elanders Boktryckeri Aktiebolag.

Galilei, Vincenzo. 1581. Dialogo della Musica Antica et della Moderna. Florence: Giorgio Marescotti.

Gogava, Antonio, trans. 1562. Aristoxeni Musici Antiquiss. Harmonicorum Elementorum Libri III. Cl. Ptolemaei Harmonicorum, seu de Musica Libri III. Venice: Vincenzo Valgrisi.

Hagel, Stefan. 2009. Ancient Greek Music: A New Technical History. Cambridge: Cambridge University Press.

Höeg, Carsten. 1930. Review of Die Harmonielehre des Klaudios Ptolemaios, by Ingemar Düring. Gnomon 6: 652–659.

Jorgensen, Owen H. 1991. Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament, Complete with Instructions for Aural and Electronic Tuning. East Lansing: Michigan State University Press.

Mathiesen, Thomas J. 1999. Apollo’s Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages. Lincoln and London: University of Nebraska Press.

Mountford, James Frederick. 1926. ‘The Harmonics of Ptolemy and the Lacuna in II, 14’. Transactions and Proceedings of the American Philological Association 57: 71–96.

Rehding, Alexander. 2016. ‘Instruments of Music Theory’. Music Theory Online 22(4).

Ruelle, C.-É. 1900. ‘Hélicon’. In Dictionnaire des Antiquités Grecques et Romaines, edited by Charles Daremberg and Edmond Saglio. Vol. III.1: 59–60. Paris: Hachette.

Solomon, Jon, trans. 2000. Ptolemy: Harmonics. Translation and Commentary. Leiden: Brill.

Tetlow, Adam. 2021. The Diagram: Harmonic Geometry. Glastonbury: Wooden Books.

Wallis, John, ed. 1682. Claudii Ptolemaei Harmonicorum Libri Tres. Oxford: Sheldonian Theatre.

West, M. L. 1992. Ancient Greek Music. Oxford: Clarendon Press.

Wikipedia contributors. 2026. ‘Vallotti Temperament’. Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/wiki/Vallotti_temperament (accessed 4 June 2026).

Winnington-Ingram, R. P., ed. 1963. Aristidis Quintiliani De Musica Libri Tres. Leipzig: Teubner.

Zarlino, Gioseffo. 1571. Le Dimostrationi Harmoniche. Venice: Francesco de’ Franceschi Senese.

———. 1588. Sopplimenti Musicali. Venice: Francesco de’ Franceschi Sanese.

Manuscripts

Bibliothèque nationale de France, ms. grec 2450. 14th century. Paris.

Bibliothèque nationale de France, ms. grec 2459. 16th century. Paris.

Trinity College Cambridge, MS O.5.16. 17th century. Cambridge.

Options

Reference pitch: Hz
String pitch: Hz: C4

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