Editing Music theory (section)

====Greece====
{{see also|Musical system of ancient Greece|List of music theorists#Antiquity}}

Early preserved Greek writings on music theory include two types of works:<ref>{{cite book |first=T.J.|last=Mathiesen |author-link=Thomas J. Mathiesen |year=2002 |section=Greek music theory |title=The Cambridge History of Western Music Theory |editor-first=T. |editor-last=Christensen |place=Cambridge, UK |publisher=Cambridge University Press |pages=112–113}}</ref>
* technical manuals describing the Greek musical system including notation, scales, consonance and dissonance, rhythm, and types of musical compositions;
* treatises on the way in which music reveals universal patterns of order leading to the highest levels of knowledge and understanding.
Several names of theorists are known before these works, including [[Pythagoras]] ({{circa|570}} ~ {{circa|495&nbsp;{{sc|BCE}}}}), [[Philolaus]] ({{circa|470 ~ ({{circa|385&nbsp;{{sc|BCE}}}}), [[Archytas]] (428–347&nbsp;{{sc|BCE}}}}), and others.

Works of the first type (technical manuals) include
* {{cite book |author=Anonymous (erroneously attributed to [[Euclid]]) |trans-title=Division of the Canon |title={{math|Κατατομή κανόνος}} |orig-year=4th–{{nobr|3rd century {{sc|BCE}}}} |year=1989 |editor-first=Andrew |editor-last=Barker |series=Greek Musical Writings |volume=2: Harmonic and Acoustic Theory |place=Cambridge, UK |publisher=Cambridge University Press |pages=191–208 |id=English trans.}}
* {{cite book |author=Theon of Smyrna |author-link=Theon of Smyrna |orig-year= |id=115–140&nbsp;{{sc|CE}} |trans-title=On the Mathematics Useful for Understanding Plato |title={{math|Τωv κατά τό μαθηματικόν χρησίμων είς τήν Πλάτωνος άνάγνωσις}} |language=el }}
* {{cite book |author-link=Nicomachus#Manual of Harmonics |author=Nicomachus of Gerasa  |orig-year= |id=100–150&nbsp;{{sc|CE}} |trans-title=Manual of Harmonics |title={{math|Άρμονικόν έγχειρίδιον}} }}
* {{cite book |author=Cleonides |author-link=Cleonides |orig-year= |id={{nobr|2nd century {{sc|CE}}}} |trans-title=Introduction to Harmonics |title=Είσαγωγή άρμονική |language=el }}
* {{cite book |author=Gaudentius |author-link=Gaudentius (music theorist) |orig-year= |id=3rd or {{nobr|4th century {{sc|CE}}}} |trans-title=Harmonic Introduction |title={{math|Άρμονική είσαγωγή}} |language=el }}
* {{cite book |author=Bacchius Geron |trans-title=Introduction to the Art of Music |title={{math|Είσαγωγή τέχνης μουσικής}} |orig-year= |id={{nobr|4th century {{sc|CE}}}} or later}}
* {{cite book |author=Alypius of Alexandria |author-link=Alypius of Alexandria |orig-year= |id=4th–{{nobr|5th century {{sc|CE}}}} |trans-title=Introduction to Music |title={{math|Είσαγωγή μουσική}} |language=el }}

More philosophical treatises of the second type include

* {{cite book |author=Aristoxenus |author-link=Aristoxenus |orig-year= |id=375~360&nbsp;{{sc|BCE}}, before 320&nbsp;{{sc|BCE}} |trans-title=Harmonic Elements |title={{math|Άρμονικά στοιχεία}} |language=el }}
* {{cite book |author=Aristoxenus |author-link=Aristoxenus |orig-year= |trans-title=Rhythmic Elements |title={{math|Ρυθμικά στοιχεία}} |language=el }}
* {{cite book |first=Claudius |last=Ptolemaios ({{math|Πτολεμαίος}}) |author-link=Ptolemy |orig-year= |id=127–148&nbsp;{{sc|CE}} |trans-title=Harmonics |title={{math|Άρμονικά}} |language=el }}
* {{cite book |author=Porphyrius |author-link=Porphyry (philosopher) |orig-year= |id={{circa|232~233}} – {{circa|305&nbsp;{{sc|CE}}}} |trans-title=On Ptolemy's Harmonics|title={{math|Είς τά άρμονικά Πτολεμαίον ύπόμνημα}} |language=el }}