Editing Major second (section)

==''Epogdoon''<!--[[Epogdoon]] redirects directly here-->==
{{multiple image
| align = right
| direction = vertical
| width = 200
| image1 = Epogdoon.jpg
| caption1 = Diagram showing relations between ''epogdoon'', ''[[perfect fourth|diatessaron]]'', ''[[perfect fifth|diapente]]'', and ''[[octave|diapason]]''
| image2 = Epogdoon translation.png
| caption2 = Translation
}}
[[Image:Epogdoon-Raphael.JPG|thumb|left|200px|Detail of Raphael's ''[[The School of Athens|School of Athens]]'' showing Pythagoras with ''epogdoon'' diagram ]]

In [[Pythagorean tuning|Pythagorean]] music theory, the '''''epogdoon''''' ({{langx|grc|ἐπόγδοον}}) is the [[interval (music)|interval]] with the ratio 9 to 8. The word is composed of the prefix ''epi''- meaning "on top of" and ''ogdoon'' meaning "one eighth"; so it means "one eighth in addition". For example, the natural numbers are 8 and 9 in this relation ({{nowrap|8+(<math>\tfrac{1}{8}</math>×8){{=}}9}}).

According to [[Plutarch]], the Pythagoreans hated  the number 17 because it separates the 16 from its Epogdoon 18.<ref>{{cite web|url=https://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html |title=Plutarch • Isis and Osiris (Part 3 of 5) |publisher=Penelope.uchicago.edu |access-date=2015-02-25}}</ref>

"[''Epogdoos''] is the 9:8 ratio that corresponds to the tone, [''hêmiolios''] is the 3:2 ratio that is associated with the musical fifth, and [''epitritos''] is the 4:3 ratio associated with the musical fourth. It is common to translate '''''epogdoos''''' as 'tone' [major second]."<ref>{{cite web|url=http://philpapers.org/archive/BALPCO |title=Proclus : Commentary on Plato's Timaeus |publisher=Philpapers.org |access-date=25 February 2015}}</ref>

===Further reading===
* [[Andrew Barker (classicist)|Barker, Andrew]] (2007). ''The Science of Harmonics in Classical Greece''. Cambridge University Press. {{ISBN|9780521879514}}.
* Plutarch (2005). ''Moralia''. Translated by Frank Cole Babbitt. Kessinger Publishing. {{ISBN|9781417905003}}.