Editing Music theory (section)

==History==
{{further|History of music}}

===Antiquity===
{{further|Ancient music}}

====Mesopotamia====
{{see also|Music of Mesopotamia}}

Several surviving [[Sumerian language|Sumerian]] and [[Akkadian language|Akkadian]] [[clay tablet]]s include musical information of a theoretical nature, mainly lists of [[Interval (music)|intervals]] and [[Musical tuning|tunings]].<ref>{{harvnb|Mirelman|2010}}; {{harvnb|Mirelman|2013}}; {{harvnb|Wulstan|1968}}; {{harvnb|Kümmel|1970}}; {{harvnb|Kilmer|1971}}; {{harvnb|Kilmer and Mirelman|n.d.}}</ref> The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500&nbsp;BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts [about music] are united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years."{{sfn|Mirelman|2013|loc=43–44}}

====China====
{{see also|Music of China|Chinese musicology}}

Much of Chinese music history and theory remains unclear.<ref name="Lam">{{harvnb|Lam}}</ref>

Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, Five refers to the Pentatonic Scale (primarily uses a 5-note scale), And Eight refers to the eight categories of Chinese Music Instruments; classified by the material they are made from: (Metal, Stone, Silk, Bamboo, Gourd, Clay, Leather, and Wood). The [[Lüshi chunqiu]] from about 238&nbsp;BCE recalls the legend of [[Ling Lun]]. On order of the [[Yellow Emperor]], Ling Lun collected twelve [[bamboo]] lengths with thick and even nodes. Blowing on one of these like a pipe, he found its sound agreeable and named it ''huangzhong'', the "Yellow Bell." He then heard [[Fenghuang|phoenixes]] singing. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes to match the pitches of the phoenixes, producing twelve pitch pipes in two sets: six from the male phoenix and six from the female: these were called the ''lülü'' or later the ''shierlü''.{{sfn|Service|2013}}

<blockquote>Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as the nature and functions of music. The ''[[Record of Music|Yueji]]'' ("Record of music", c1st and 2nd centuries BCE), for example, manifests [[Confucianism|Confucian]] moral theories of understanding music in its social context. Studied and implemented by Confucian scholar-officials [...], these theories helped form a musical Confucianism that overshadowed but did not erase rival approaches. These include the assertion of [[Mozi]] (c. 468 – c. 376&nbsp;BCE) that music wasted human and material resources, and [[Laozi]]'s claim that the greatest music had no sounds. [...] Even the music of the [[Guqin|''qin'' zither]], a genre closely affiliated with Confucian scholar-officials, includes many works with [[Taoism|Daoist]] references, such as ''Tianfeng huanpei'' ("Heavenly Breeze and Sounds of Jade Pendants").<ref name="Lam"/></blockquote>

====India====
{{See also|Music of India}}
The [[Samaveda]] and [[Yajurveda]] (c. 1200 – 1000&nbsp;BCE) are among the earliest testimonies of Indian music, but properly speaking, they contain no theory. The [[Natya Shastra]], written between 200&nbsp;BCE to 200&nbsp;CE, discusses intervals (''[[Shruti (music)|Śrutis]]''), scales (''Grāmas''), consonances and dissonances, classes of melodic structure (''Mūrchanās'', modes?), melodic types (''Jātis''), instruments, etc.<ref>''The Nāțyaśāstra, A Treatise on Hindu Dramaturgy and Histrionics, attributed to Bharata Muni'', translated from the Sanskrit with introduction and notes by Manomohan Ghosh, vol. II, Calcutta, The Asiatic Society, 1961. See particularly pp. 5–19 of the Introduction, ''The Ancient Indian Theory and Practice of Music''.</ref>

====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 }}

===Post-classical or Medieval Period===
{{see also|List of music theorists#Post-classical|List of medieval music theorists}}

====China====
The [[pipa]] instrument carried with it a theory of musical modes that subsequently led to the Sui and Tang theory of 84 musical modes.<ref name="Lam" />

====Arabic countries / Persian countries====

Medieval Arabic music theorists include:{{refn|See the [[List of music theorists#7th–14th centuries]], which includes several Arabic theorists; see also {{harvnb|d'Erlanger|1930–56|loc=1:xv-xxiv}}.|group=n}}

* Abū Yūsuf Ya'qūb [[Al-Kindi#Music theory|al-Kindi]] (Bagdad, 873&nbsp;CE), who uses the first twelve letters of the alphabet to describe the twelve frets on five strings of the [[oud]], producing a chromatic scale of 25 degrees.{{sfn|Manik|1969|loc=24–33}}
* [Yaḥyā ibn] al-[[Banu Munajjim|Munajjim]] (Baghdad, 856–912), author of ''Risāla fī al-mūsīqī'' ("Treatise on music", MS GB-Lbl Oriental 2361) which describes a [[Pythagorean tuning]] of the [[oud]] and a system of eight modes perhaps inspired by [[Ishaq al-Mawsili]] (767–850).<ref>{{harvnb|Wright|2001a}}; {{harvnb|Wright|2001b}}; {{harvnb|Manik|1969|loc=22–24}}.</ref>
* Abū n-Nașr Muḥammad [[Al-Farabi#Music|al-Fārābi]] (Persia, 872? – Damas, 950 or 951&nbsp;CE), author of ''[[Kitab al-Musiqa al-Kabir]]'' ("The Great Book of Music").<ref>Rodolphe d'Erlanger, ''La Musique arabe'', vol. I, pp. 1–306; vol. II, pp. 1–101.</ref>
* 'Ali ibn al-Husayn ul-Isfahānī (897–967), known as [[Abu al-Faraj al-Isfahani]], author of ''Kitāb al-Aghānī'' ("The Book of Songs").
* Abū 'Alī al-Ḥusayn ibn ʿAbd-Allāh ibn Sīnā, known as [[Avicenna]] (c. 980 – 1037), whose contribution to music theory consists mainly in Chapter 12 of the section on mathematics of his ''Kitab Al-Shifa'' ("[[The Book of Healing]]").{{sfn|d'Erlanger|1930–56|loc=2:103–245}}
* al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib, author of Kamāl adab al Ghinā' ("The Perfection of Musical Knowledge"), copied in 1225 (Istanbul, Topkapi Museum, Ms 1727).{{sfn|Shiloah|1964}}
* [[Safi al-Din al-Urmawi]] (1216–1294&nbsp;CE), author of the ''Kitabu al-Adwār'' ("Treatise of musical cycles") and ''ar-Risālah aš-Šarafiyyah'' ("Epistle to Šaraf").{{sfn|d'Erlanger|1930–56|loc=3:1–182}}
* Mubārak Šāh, commentator of Safi al-Din's ''Kitāb al-Adwār'' ([[British Museum]], Ms 823).<ref>Anon. LXII in Amnon Shiloah, ''The Theory of Music in Arabic Writings (c. 900–1900): Descriptive Catalogue of Manuscripts in Libraries of Europe and the U.S.A.'', RISM, München, G. Henle Verlag, 1979. See {{harvnb|d'Erlanger|1930–56|loc=3:183–566}}</ref>
* Anon. LXI, Anonymous commentary on Safi al-Din's ''Kitāb al-Adwār''.{{sfn|Ghrab|2009}}
* Shams al-dῑn al-Saydᾱwῑ Al-Dhahabῑ (14th century CE (?)), music theorist. Author of ''Urjῡza fi'l-mῡsῑqᾱ'' ("A Didactic Poem on Music").<ref name="Shiloah-2003">{{Cite book|title=The Theory of Music in Arabic Writings (c. 900–1900)|last=Shiloah|first=Amnon|publisher=G. Henle Verlag Munchen|year=2003|isbn=978-0-8203-0426-7|location=Germany|pages=[https://archive.org/details/sacredharp00buel/page/48 48, 58, 60–61]|url=https://archive.org/details/sacredharp00buel/page/48}}</ref>

====Europe====
The Latin treatise ''De institutione musica'' by the Roman philosopher [[Boethius]] (written c. 500, translated as ''Fundamentals of Music''{{sfn|Boethius|1989}}) was a touchstone for other writings on music in medieval Europe. Boethius represented Classical authority on music during the Middle Ages, as the Greek writings on which he based his work were not read or translated by later Europeans until the 15th century.{{sfn|Palisca and Bent|n.d.|loc=§5 Early Middle Ages}} This treatise carefully maintains distance from the actual practice of music, focusing mostly on the mathematical proportions involved in tuning systems and on the moral character of particular modes. Several centuries later, treatises began to appear which dealt with the actual composition of pieces of music in the [[plainchant]] tradition.<ref>{{harvnb|Palisca and Bent|n.d.|loc=Theory, theorists §5 Early Middle Ages}}: "Boethius could provide a model only for that part of theory which underlies but does not give rules for composition or performance. The first surviving strictly musical treatise of Carolingian times is directed towards musical practice, the Musica disciplina of Aurelian of Réôme (9th century)."</ref> At the end of the ninth century, [[Hucbald]] worked towards more precise pitch notation for the [[neume]]s used to record plainchant.

[[Guido d'Arezzo]] wrote a letter to Michael of Pomposa in 1028, entitled ''Epistola de ignoto cantu'',<ref>{{cite web|url=http://www.hs-augsburg.de/~harsch/gui_epi.html|title=Guy Aretini's letter to the unknown : modern translation of the letter|website=Hs-augsburg.de|access-date=3 March 2022}}</ref> in which he introduced the practice of using syllables to describe notes and intervals. This was the source of the hexachordal [[solmization]] that was to be used until the end of the Middle Ages. Guido also wrote about emotional qualities of the modes, the phrase structure of plainchant, the temporal meaning of the neumes, etc.; his chapters on polyphony "come closer to describing and illustrating real music than any previous account" in the Western tradition.{{sfn|Palisca and Bent|n.d.|loc=§5 Early Middle Ages}}

During the thirteenth century, a new rhythm system called [[mensural notation]] grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatise ''Ars cantus mensurabilis'' ("The art of measured chant") by [[Franco of Cologne]] (c. 1280). Mensural notation used different note shapes to specify different durations, allowing scribes to capture rhythms which varied instead of repeating the same fixed pattern; it is a proportional notation, in the sense that each note value is equal to two or three times the shorter value, or half or a third of the longer value. This same notation, transformed through various extensions and improvements during the Renaissance, forms the basis for rhythmic notation in [[European classical music]] today.

===Modern===
====Middle Eastern and Central Asian countries====

* Bāqiyā Nāyinῑ (Uzbekistan, 17th century CE), Uzbek author and music theorist. Author of ''Zamzama e wahdat-i-mῡsῑqῑ'' ["The Chanting of Unity in Music"].<ref name="Shiloah-2003" />
* Baron Francois Rodolphe d'Erlanger (Tunis, Tunisia, 1910–1932&nbsp;CE), French musicologist. Author of ''La musique arabe'' and ''Ta'rῑkh al-mῡsῑqᾱ al-arabiyya wa-usῡluha wa-tatawwurᾱtuha'' ["A History of Arabian Music, its principles and its Development"]

D'Erlanger divulges that the Arabic music scale is derived from the Greek music scale, and that Arabic music is connected to certain features of Arabic culture, such as astrology.<ref name="Shiloah-2003" />

====Europe====
* '''Renaissance'''
{{further |List of music theorists#15th and 16th centuries}}
* '''Baroque'''
{{further |List of music theorists#17th century}}
{{further |List of music theorists#18th century}}
* '''1750–1900'''
** As Western musical influence spread throughout the world in the 1800s, musicians adopted Western theory as an international standard—but other theoretical traditions in both textual and oral traditions remain in use. For example, the long and rich musical traditions unique to ancient and current cultures of Africa are primarily oral, but describe specific forms, genres, performance practices, tunings, and other aspects of music theory.{{sfn|Kubik|2010|loc=passim}}{{sfn|Ekwueme|1974|loc=passim}}
** [[Sacred harp]] music uses a different kind of scale and theory in practice. The music focuses on the solfege "fa, sol, la" on the music scale. Sacred Harp also employs a different notation involving "shape notes", or notes that are shaped to correspond to a certain solfege syllable on the music scale. Sacred Harp music and its music theory originated with Reverend Thomas Symmes in 1720, where he developed a system for "singing by note" to help his church members with note accuracy.<ref>{{Cite book|title=The Sacred Harp: A Tradition and Its Music|last=Cobb|first=Buell E. Jr.|publisher=The University of Georgia Press Athens|year=1978|isbn=978-0-8203-0426-7|location=United States of America|pages=[https://archive.org/details/sacredharp00buel/page/4 4–5, 60–61]|url=https://archive.org/details/sacredharp00buel/page/4}}</ref>

{{further |List of music theorists#19th century}}

===Contemporary===
{{see also|List of music theorists#20th century|List of music theorists#21st century}}