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{{Short description|Study of the practices and possibilities of music}}
{{Use dmy dates|date=August 2021}}
[[File:Gaffurio Pythagoras.png|thumb|upright=1.25|[[Jubal (Bible)|Jubal]], [[Pythagoras]] and [[Philolaus]] engaged in theoretical investigations, in a woodcut from [[Franchinus Gaffurius]], ''Theorica musicæ'' (1492)]]

'''Music theory''' is the study of theoretical frameworks for understanding the practices and possibilities of [[music]]. ''[[The Oxford Companion to Music]]'' describes three interrelated uses of the term "music theory": The first is the "[[Elements of music|rudiments]]", that are needed to understand [[Musical notation|music notation]] ([[key signature]]s, [[time signature]]s, and [[Chord chart|rhythmic notation]]); the second is learning scholars' views on music from [[Ancient history|antiquity]] to the present; the third is a sub-topic of [[musicology]] that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built."<ref>{{cite book|last1=Fallows|first1=David|chapter=Theory|url=http://www.oxfordmusiconline.com/subscriber/article/opr/t114/e6759.|title=The Oxford Companion to Music|publisher=Oxford Music Online|access-date=|isbn=978-0199579037|year= 2011}}</ref>

Music theory is frequently concerned with describing how musicians and composers make music, including [[Musical tuning|tuning systems]] and composition methods among other topics. Because of the ever-expanding conception of [[Definition of music|what constitutes music]], a more inclusive definition could be the consideration of any sonic phenomena, including silence. This is not an absolute guideline, however; for example, the study of "music" in the ''[[Quadrivium]]'' [[Liberal arts education|liberal arts university]] curriculum, that was common in [[Middle Ages|medieval Europe]], was an abstract system of proportions that was carefully studied at a distance from actual musical practice.{{refn|See Boethius's ''De institutione musica'',{{sfn|Boethius|1989}} in which he disdains "musica instrumentalis" as beneath the "true" musician who studies music in the abstract: ''Multo enim est maius atque auctius scire, quod quisque faciat, quam ipsum illud efficere, quod sciat'' ("It is much better to know what one does than to do what one knows").|group=n}} But this medieval discipline became the basis for tuning systems in later centuries and is generally included in modern scholarship on the history of music theory.{{refn|See, for example, chapters 4–7 of Christensen, Thomas (2002). ''The Cambridge History of Western Music Theory''. Cambridge, UK: Cambridge University Press.|group=n}}

Music theory as a practical discipline encompasses the methods and concepts that composers and other musicians use in creating and performing music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, [[musical instrument]]s, and other [[Artifact (archaeology)|artifacts]]. For example, ancient instruments from [[Prehistoric music|prehistoric]] sites around the world reveal details about the music they produced and potentially something of the musical theory that might have been used by their makers. In ancient and living cultures around the world, the deep and long roots of music theory are visible in instruments, oral traditions, and current music-making. Many cultures have also considered music theory in more formal ways such as written [[treatise]]s and [[Musical notation|music notation]]. Practical and scholarly traditions overlap, as many practical treatises about music place themselves within a tradition of other treatises, which are cited regularly just as [[scholarly writing]] cites earlier research.

In modern academia, music theory is a subfield of [[musicology]], the wider study of musical cultures and history. [[Guido Adler]], however, in one of the texts that founded musicology in the late 19th century, wrote that "the science of music originated at the same time as the art of sounds",<ref>Guido Adler, "Umfang, Methode und Ziel der Musikwissenschaft", ''Vierteljahrsschrift für Musikwissenschaft'' 1 (1885), p. 5: ''Die Musikwissenschaft entstand gleichzeitig mit der Tonkunst''.</ref> where "the science of music" (''Musikwissenschaft'') obviously meant "music theory". Adler added that music only could exist when one began measuring pitches and comparing them to each other. He concluded that "all people for which one can speak of an art of sounds also have a science of sounds".<ref>''Ibid.''</ref> One must deduce that music theory exists in all musical cultures of the world.

Music theory is often concerned with abstract musical aspects such as [[Musical tuning|tuning]] and tonal systems, [[Scale (music)|scales]], [[consonance and dissonance]], and rhythmic relationships. There is also a body of theory concerning practical aspects, such as the creation or the performance of music, [[orchestration]], [[Ornament (music)|ornamentation]], improvisation, and [[Electronic music|electronic sound]] production.{{sfn|Palisca and Bent|n.d.|loc=Theory, theorists. 1. Definitions}} A person who researches or teaches music theory is a music theorist. University study, typically to the [[Master of Arts|MA]] or [[Doctor of Philosophy|PhD]] level, is required to teach as a tenure-track music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by western music notation. Comparative, descriptive, statistical, and other methods are also used. Music theory [[textbook]]s, especially in the United States of America, often include elements of [[musical acoustics]], considerations of [[musical notation]], and techniques of tonal [[Musical composition|composition]] ([[harmony]] and [[counterpoint]]), among other topics.

==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}}

==Fundamentals of music==
{{Main|Aspect of music}}
Music is composed of [[aural]] phenomena; "music theory" considers how those phenomena apply in music. Music theory considers melody, rhythm, counterpoint, harmony, form, tonal systems, scales, tuning, intervals, consonance, dissonance, durational proportions, the acoustics of pitch systems, composition, performance, orchestration, ornamentation, improvisation, electronic sound production, etc.{{sfn|Palisca and Bent|n.d.}}

===Pitch===
{{Main|Pitch (music)}}
[[File:Middle C.png|thumb|Middle C (261.626&nbsp;Hz)[[File:Middle C.mid]]]]
Pitch is the lowness or highness of a [[Musical tone|tone]], for example the difference between [[middle C]] and a higher C. The frequency of the sound waves producing a pitch can be measured precisely, but the perception of pitch is more complex because single notes from natural sources are usually a complex mix of many frequencies. Accordingly, theorists often describe pitch as a subjective sensation rather than an objective measurement of sound.{{sfn|Hartmann|2005|loc={{Page needed|date=August 2014}}}}

Specific frequencies are often assigned letter names. Today most orchestras assign [[concert A]] (the A above [[middle C]] on the piano) to the frequency of 440&nbsp;Hz. This assignment is somewhat arbitrary; for example, in 1859 France, the same A was tuned to 435&nbsp;Hz. Such differences can have a noticeable effect on the timbre of instruments and other phenomena. Thus, in [[historically informed performance]] of older music, tuning is often set to match the tuning used in the period when it was written. Additionally, many cultures do not attempt to standardize pitch, often considering that it should be allowed to vary depending on genre, style, mood, etc.

The difference in pitch between two notes is called an [[interval (music)|interval]]. The most basic interval is the [[unison]], which is simply two notes of the same pitch. The [[octave]] interval is two pitches that are either double or half the frequency of one another. The unique characteristics of octaves gave rise to the concept of [[pitch class]]: pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring the difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's.{{Sfn|Bartlette and Laitz|2010|loc={{Page needed|date=October 2014}}}}

[[Musical tuning]] systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. In [[Western culture]], there have long been several competing tuning systems, all with different qualities. Internationally, the system known as [[equal temperament]] is most commonly used today because it is considered the most satisfactory compromise that allows instruments of fixed tuning (e.g. the piano) to sound acceptably in tune in all keys.

===Scales and modes===
{{Main|Musical scale| Musical mode}}
[[File:C major scale.png|thumb|upright=1.3|A pattern of whole and half steps in the Ionian mode or major scale on C[[File:Ionian mode C.mid]]]]
Notes can be arranged in a variety of [[scale (music)|scale]]s and [[musical mode|modes]]. Western music theory generally divides the octave into a series of twelve pitches, called a [[chromatic scale]], within which the interval between adjacent tones is called a [[semitone]], or half step. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales.{{sfn|Touma|1996|loc={{Page needed|date=August 2014}}}}

The most commonly encountered scales are the seven-toned [[major scale|major]], the [[harmonic minor]], the [[melodic minor]], and the [[natural minor]]. Other examples of scales are the [[octatonic scale]] and the [[pentatonic]] or five-tone scale, which is common in [[folk music]] and [[blues]]. Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classical [[Ottoman classical music|Ottoman]], [[Persian classical music|Persian]], [[Indian classical music|Indian]] and [[Arabic music|Arabic]] musical systems often make use of multiples of quarter tones (half the size of a semitone, as the name indicates), for instance in 'neutral' seconds (three quarter tones) or 'neutral' thirds (seven quarter tones)—they do not normally use the quarter tone itself as a direct interval.{{sfn|Touma|1996|loc={{Page needed|date=August 2014}}}}

In traditional Western notation, the scale used for a composition is usually indicated by a [[key signature]] at the beginning to designate the pitches that make up that scale. As the music progresses, the pitches used may change and introduce a different scale. Music can be [[Transposition (music)|transposed]] from one scale to another for various purposes, often to accommodate the range of a vocalist. Such transposition raises or lowers the overall pitch range, but preserves the intervallic relationships of the original scale. For example, transposition from the key of C major to D major raises all pitches of the scale of C major equally by a [[whole tone]]. Since the interval relationships remain unchanged, transposition may be unnoticed by a listener, however other qualities may change noticeably because transposition changes the relationship of the overall pitch [[range (music)|range]] compared to the range of the instruments or voices that perform the music. This often affects the music's overall sound, as well as having technical implications for the performers.{{sfn|Forsyth|1935|loc=73–74}}

The interrelationship of the keys most commonly used in Western tonal music is conveniently shown by the [[circle of fifths]]. Unique key signatures are also sometimes devised for a particular composition. During the Baroque period, emotional associations with specific keys, known as the [[doctrine of the affections]], were an important topic in music theory, but the unique tonal colorings of keys that gave rise to that doctrine were largely erased with the adoption of equal temperament. However, many musicians continue to feel that certain keys are more appropriate to certain emotions than others. [[Indian classical music]] theory continues to strongly associate keys with emotional states, times of day, and other extra-musical concepts and notably, does not employ equal temperament.

===Consonance and dissonance===
{{Main|Consonance and dissonance}}
{{multiple image
| align = right
| image1 = Perfect octave on C.png
| width1 = 175
| alt1 = A consonance
| caption1 = [[Perfect octave]], a consonant interval[[File:Perfect octave on C.mid]]
| image2 = Minor second on C.png
| width2 = 175
| alt2 = A dissonance
| caption2 = [[Minor second]], a dissonant interval[[File:Minor second on C.mid]]
| footer =
}}
[[Consonance and dissonance]] are subjective qualities of the sonority of intervals that vary widely in different cultures and over the ages. Consonance (or concord) is the quality of an interval or chord that seems stable and complete in itself. Dissonance (or discord) is the opposite in that it feels incomplete and "wants to" resolve to a consonant interval. Dissonant intervals seem to clash. Consonant intervals seem to sound comfortable together. Commonly, perfect fourths, fifths, and octaves and all major and minor thirds and sixths are considered consonant. All others are dissonant to a greater or lesser degree.{{sfn|Latham|2002|loc={{Page needed|date=August 2014}}}}

Context and many other aspects can affect apparent dissonance and consonance. For example, in a Debussy prelude, a major second may sound stable and consonant, while the same interval may sound dissonant in a Bach fugue. In the [[Common practice period|Common practice era]], the perfect fourth is considered dissonant when not supported by a lower third or fifth. Since the early 20th century, [[Arnold Schoenberg]]'s concept of "emancipated" dissonance, in which traditionally dissonant intervals can be treated as "higher," more remote consonances, has become more widely accepted.{{sfn|Latham|2002|loc={{Page needed|date=August 2014}}<!--Better would be the title of the article in this dictionary, added to the entry in the list of references, in which case a page number would be superfluous.-->}}

===Rhythm===
{{Main|Rhythm}}
[[File:Metric levels.svg|thumb|upright=1.3|[[Metric level]]s: beat level shown in middle with division levels above and multiple levels below]]
Rhythm is produced by the sequential arrangement of sounds and silences in time. [[Metre (music)|Meter]] measures music in regular pulse groupings, called [[Bar (music)|measures or bars]]. The [[time signature]] or meter signature specifies how many beats are in a measure, and which value of written note is counted or felt as a single beat.

Through increased stress, or variations in duration or articulation, particular tones may be accented. There are conventions in most musical traditions for regular and hierarchical accentuation of beats to reinforce a given meter. [[Syncopation|Syncopated]] rhythms contradict those conventions by accenting unexpected parts of the beat.<ref>{{cite book|chapter=Syncopation|title=The Oxford Dictionary of Music |url=https://www.oxfordreference.com/display/10.1093/acref/9780199579037.001.0001/acref-9780199579037-e-6605?rskey=S0uJUr&result=1 |quote=Syncopation is achieved by accenting a weak instead of a strong beat, by putting rests on strong beats, by holding on over strong beats, and by introducing a sudden change of time‐signature.|isbn=978-0199578108|publisher=Oxford University Press|year= 2013}}</ref> Playing simultaneous rhythms in more than one time signature is called [[polyrhythm]].<ref>{{cite web|title=Polyrhythm|url=http://www.oxfordmusiconline.com/subscriber/article/grove/music/22059|website=Grove Music Online |publisher= Oxford University Press|access-date=11 August 2017|quote=The superposition of different rhythms or metres.}}</ref>

In recent years, rhythm and meter have become an important area of research among music scholars. The most highly cited of these recent scholars are [[Maury Yeston]],{{sfn|Yeston|1976}} [[Fred Lerdahl]] and [[Ray Jackendoff]],{{sfn|Lerdahl and Jackendoff|1985}} [[Jonathan Kramer]],{{sfn|Kramer|1988}} and Justin London.{{sfn|London|2004}}

===Melody===
{{Main|Melody}}
[[File:Pop Goes the Weasel melody.PNG|thumb|upright=1.3|"[[Pop Goes the Weasel]]" melody{{sfn|Kliewer|1975|loc={{Page needed|date=September 2012}}}}[[File:Pop Goes the Weasel.ogg]]]]
A [[melody]] is a group of musical sounds in agreeable succession or arrangement.<ref>{{Cite web |title=Definition of melody {{!}} Dictionary.com |url=https://www.dictionary.com/browse/melody |access-date=2023-01-11 |website=www.dictionary.com |language=en}}</ref> Because melody is such a prominent aspect in so much music, its construction and other qualities are a primary interest of music theory.

The basic elements of melody are pitch, duration, rhythm, and tempo. The tones of a melody are usually drawn from pitch systems such as [[Musical scale|scales]] or [[Musical mode|modes]]. Melody may consist, to increasing degree, of the figure, motive, semi-phrase, antecedent and consequent phrase, and period or sentence. The period may be considered the complete melody, however some examples combine two periods, or use other combinations of constituents to create larger form melodies.{{sfn|Stein|1979|loc=3–47}}

{{Clear}}

===Chord===
{{Main|Chord (music)}}
[[File:C triad.svg|thumb|upright=0.7|C major triad represented in [[staff notation]].<br />{{Audio|Just major triad on C.mid|Play}} in [[just intonation]]<br />{{Audio|Major triad on C.mid|Play}} in [[Equal temperament]]<br />{{Audio|Quarter-comma meantone major chord on C.mid|Play}} in [[Meantone temperament|1/4-comma meantone]]<br />{{Audio|Young temperament major chord on C.mid|Play}} in [[Young temperament]]<br />{{Audio|Pythagorean major chord on C.mid|Play}} in [[Pythagorean tuning]] ]]
A chord, in music, is any [[harmony|harmonic]] set of three or more [[Musical note|note]]s that is heard as if sounding [[Simultaneity (music)|simultaneously]].{{sfn|Benward and Saker|2003}}{{rp|pp. 67, 359|quote=A chord is a harmonic unit with at least three different tones sounding simultaneously." "A combination of three or more pitches sounding at the same time.}}{{sfn|Károlyi|1965|}}{{rp|p. 63|quote=Two or more notes sounding simultaneously are known as a chord.}} These need not actually be played together: [[arpeggio]]s and broken chords may, for many practical and theoretical purposes, constitute chords. Chords and [[Chord progression|sequences of chords]] are frequently used in modern Western, West African,{{sfn|Mitchell|2008}} and Oceanian{{sfn|Linkels|n.d.|loc={{Page needed|date=July 2015}}<!--Specific page citation within this twelve-page article needed.-->}} music, whereas they are absent from the music of many other parts of the world.{{sfn|Malm|1996}}{{rp|p. 15|quote=Indeed this harmonic orientation is one of the major differences between Western and much non-Western music.}}

The most frequently encountered chords are [[Triad (music)|triads]], so called because they consist of three distinct notes: further notes may be added to give [[seventh chord]]s, [[extended chord]]s, or [[added tone chord]]s. The most [[Common chord (music)|common chord]]s are the ''[[major chord|major]]'' and ''[[minor chord|minor]] [[Triad (music)|triads]]'' and then the ''[[augmented triad|augmented]]'' and ''[[diminished triad|diminished]] [[Triad (music)|triads]]''. The descriptions ''major'', ''minor'', ''augmented'', and ''diminished'' are sometimes referred to collectively as chordal ''quality''. Chords are also commonly classed by their [[root (chord)|root]] note—so, for instance, the chord '''C''' major may be described as a triad of major quality built on the note '''C'''. Chords may also be classified by [[Inverted chord|inversion]], the order in which the notes are stacked.

A series of chords is called a [[chord progression]]. Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing [[Key (music)|key]] in [[Common practice harmony|common-practice harmony]]. To describe this, chords are numbered, using [[Roman numerals]] (upward from the key-note),{{sfn|Schoenberg|1983|loc=1–2}} per their [[diatonic function]]. Common ways of [[#Notation|notating or representing chords]]{{sfn|Benward and Saker|2003|loc=77}} in western music other than conventional [[staff notation]] include [[Roman numerals#Music theory|Roman numerals]], [[figured bass]] (much used in the [[Baroque music|Baroque era]]), [[chord letter]]s (sometimes used in modern [[musicology]]), and various systems of [[chord chart]]s typically found in the [[lead sheet]]s used in [[Chord names and symbols (popular music)|popular music]] to lay out the sequence of chords so that the musician may play accompaniment chords or improvise a solo.

===Harmony===
{{Main|Harmony}}
[[File:US Navy 080615-N-7656R-003 Navy Band Northwest's Barbershop Quartet win the hearts of the audience with a John Philip Sousa rendition of.jpg|thumb|[[Barbershop quartet]]s, such as this US Navy group, sing 4-part pieces, made up of a melody line (normally the second-highest voice, called the "lead") and 3 harmony parts.]]
In music, harmony is the use of simultaneous [[pitch (music)|pitches]] ([[timbre|tones]], [[note (music)|notes]]), or [[chord (music)|chords]].{{sfn|Malm|1996|}}{{rp|p. 15|quote=Homophonic texture... is more common in Western music, where tunes are often built on chords (harmonies) that move in progressions. Indeed this harmonic orientation is one of the major differences between Western and much non-Western music.}} The study of harmony involves chords and their construction and [[chord progression]]s and the principles of connection that govern them.{{sfn|Dahlhaus|2009}} Harmony is often said to refer to the "vertical" aspect of music, as distinguished from [[melody|melodic line]], or the "horizontal" aspect.{{sfn|Jamini|2005|loc=147}} [[Counterpoint]], which refers to the interweaving of melodic lines, and [[polyphony]], which refers to the relationship of separate independent voices, is thus sometimes distinguished from harmony.<ref>{{cite web |url=http://sites.fas.harvard.edu/~lab51/theory/html/struct8.html |title=Pitch Structure: Harmony and Counterpoint |author=Faculty of Arts & Sciences |work=Theory of Music – Pitch Structure: The Chromatic Scale |publisher=Harvard University |access-date=2 October 2020 }}</ref>

In [[popular harmony|popular]] and [[jazz harmony]], chords are named by their [[root (chord)|root]] plus various terms and characters indicating their qualities. For example, a [[lead sheet]] may indicate chords such as C major, D minor, and G dominant seventh. In many types of music, notably Baroque, Romantic, modern, and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively [[Consonance and dissonance|dissonant interval]] in relation to the bass. It is part of a chord, but is not one of the chord tones (1 3 5 7). Typically, in the classical [[common practice period]] a dissonant chord (chord with tension) "resolves" to a consonant chord. [[Harmonization]] usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and "relaxed" moments.<ref>{{cite web|url=https://shodhganga.inflibnet.ac.in/bitstream/10603/14206/6/06_chapter%202.pdf|title=Chapter 2 Elements and concepts of music (With reference to Hindustani and Jazz music)|website=Shodhganga.inflibnet.ac.in|access-date=3 March 2022}}</ref>{{unreliable source?|date=November 2019|reason=Self-contradictory, self-published?}}

===Timbre===
{{Main|Timbre}}
[[File:9577 Guitarz1970 Clean E9 Guitar Chord (Mike Tribulas).jpg|thumb|right|[[Spectrogram]] of the first second of an E9 chord played on a Fender Stratocaster guitar with noiseless pickups. Below is the E9 chord audio:
[[File:9577 Guitarz1970 Clean E9 Guitar Chord (Mike Tribulas).ogg]] ]]Timbre, sometimes called "color", or "tone color," is the principal phenomenon that allows us to distinguish one instrument from another when both play at the same pitch and volume, a quality of a voice or instrument often described in terms like bright, dull, shrill, etc. It is of considerable interest in music theory, especially because it is one component of music that has as yet, no standardized nomenclature. It has been called "... the psychoacoustician's multidimensional waste-basket category for everything that cannot be labeled pitch or loudness,"{{sfn|McAdams and Bregman|1979|loc=34}} but can be accurately described and analyzed by [[Fourier analysis]] and other methods{{sfn|Mannell|n.d.}} because it results from the combination of all sound [[Audio frequency|frequencies]], attack and release envelopes, and other qualities that a tone comprises.

[[Timbre]] is principally determined by two things: (1) the relative balance of [[overtones]] produced by a given instrument due its construction (e.g. shape, material), and (2) the [[Envelope (waves)|envelope]] of the sound (including changes in the overtone structure over time). Timbre varies widely between different instruments, voices, and to lesser degree, between instruments of the same type due to variations in their construction, and significantly, the performer's technique. The timbre of most instruments can be changed by employing different techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, the player changes their embouchure, or volume.{{Citation needed|date=July 2015}}

A voice can change its timbre by the way the performer manipulates their vocal apparatus, (e.g. the shape of the vocal cavity or mouth). Musical notation frequently specifies alteration in timbre by changes in sounding technique, volume, accent, and other means. These are indicated variously by symbolic and verbal instruction. For example, the word ''dolce'' (sweetly) indicates a non-specific, but commonly understood soft and "sweet" timbre. ''Sul tasto'' instructs a string player to bow near or over the fingerboard to produce a less brilliant sound. ''Cuivre'' instructs a brass player to produce a forced and stridently brassy sound. Accent symbols like ''marcato'' (^) and dynamic indications (''pp'') can also indicate changes in timbre.<ref>{{Cite web|url=https://www.sheffield.k12.oh.us/Downloads/IMG.pdf|title=How Loud? How Soft?|website=Sheffield-Sheffield Lake City Schools}}</ref>

====Dynamics====
{{Unreferenced section|date=July 2015}}
{{Main|Dynamics (music)}}
[[File:Music hairpins.svg|thumb|upright=1.3|Illustration of hairpins in musical notation]]
In music, "[[dynamics (music)|dynamics]]" normally refers to variations of intensity or volume, as may be measured by physicists and audio engineers in [[decibels]] or [[phon]]s. In music notation, however, dynamics are not treated as absolute values, but as relative ones. Because they are usually measured subjectively, there are factors besides amplitude that affect the performance or perception of intensity, such as timbre, vibrato, and articulation.

The conventional indications of dynamics are abbreviations for Italian words like ''forte'' ('''''f''''') for loud and ''piano'' ('''''p''''') for soft. These two basic notations are modified by indications including ''mezzo piano'' ('''''mp''''') for moderately soft (literally "half soft") and ''mezzo forte'' ('''''mf''''') for moderately loud, ''sforzando'' or ''sforzato'' ('''''sfz''''') for a surging or "pushed" attack, or ''fortepiano'' ('''''fp''''') for a loud attack with a sudden decrease to a soft level. The full span of these markings usually range from a nearly inaudible ''pianissississimo'' ('''''pppp''''') to a loud-as-possible ''fortissississimo'' ('''''ffff''''').

Greater extremes of '''''pppppp''''' and '''''fffff''''' and nuances such as '''''p+''''' or ''più piano'' are sometimes found. Other systems of indicating volume are also used in both notation and analysis: dB (decibels), numerical scales, colored or different sized notes, words in languages other than Italian, and symbols such as those for progressively increasing volume (''crescendo'') or decreasing volume (''diminuendo'' or ''decrescendo''), often called "[[Dynamics (music)|hairpins]]" when indicated with diverging or converging lines as shown in the graphic above.

====Articulation====
{{Unreferenced section|date=July 2015}}
{{Main|Articulation (music)}}
[[File:Notation accents1.png|thumb|upright=1.4|Examples of articulation marks. From left to right: [[staccato]], [[staccatissimo]], [[martellato]], [[Accent (music)|accent]], [[tenuto]].]]
Articulation is the way the performer sounds notes. For example, ''[[staccato]]'' is the shortening of duration compared to the written note value, ''[[legato]]'' performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation.

For example, ''staccato'' is often referred to as "separated" or "detached" rather than having a defined or numbered amount by which to reduce the notated duration. Violin players use a variety of techniques to perform different qualities of ''staccato.'' The manner in which a performer decides to execute a given articulation is usually based on the context of the piece or phrase, but many articulation symbols and verbal instructions depend on the instrument and musical period (e.g. viol, wind; classical, baroque; etc.).

There is a set of articulations that most instruments and voices perform in common. They are—from long to short: ''legato'' (smooth, connected); ''[[tenuto]]'' (pressed or played to full notated duration); ''[[marcato]]'' (accented and detached); ''staccato'' ("separated", "detached"); ''[[martelé (bowstroke)|martelé]]'' (heavily accented or "hammered").{{Contradictory inline|date=March 2020|reason=The accompanying illustration names "staccato", "tenuto", and three other articulations not listed here. Are these synonyms and, if so, which are synonyms of which? Neither list is cited to a reliable source.}} Many of these can be combined to create certain "in-between" articulations. For example, ''[[portato]]'' is the combination of ''tenuto'' and ''staccato''. Some instruments have unique methods by which to produce sounds, such as ''[[spiccato]]'' for bowed strings, where the bow bounces off the string.

===Texture===
{{Main|Musical texture}}
[[File:Sousa - "Washington Post March," m. 1-7.png|thumb|upright=1.2|Introduction to [[John Philip Sousa|Sousa]]'s "[[The Washington Post (march)|Washington Post March]]," mm. 1–7 features [[octave doubling]]{{Sfn|Benward and Saker|2003|p=133}} and a homorhythmic texture[[File:Sousa - "Washington Post March," m. 1-7.mid]]]]
In music, texture is how the [[melody|melodic]], [[rhythm]]ic, and [[harmony|harmonic]] materials are combined in a [[musical composition|composition]], thus determining the overall quality of the sound in a piece. Texture is often described in regard to the density, or thickness, and [[range (music)|range]], or width, between lowest and highest pitches, in relative terms as well as more specifically distinguished according to the number of voices, or parts, and the relationship between these voices. For example, a thick texture contains many "layers" of instruments. One of these layers could be a string section, or another brass.

The thickness also is affected by the number and the richness of the instruments playing the piece. The thickness varies from light to thick. A lightly textured piece will have light, sparse scoring. A thickly or heavily textured piece will be scored for many instruments. A piece's texture may be affected by the number and character of parts playing at once, the [[timbre]] of the instruments or voices playing these parts and the harmony, [[tempo]], and rhythms used.{{sfn|Benward and Saker|2003|loc={{Page needed|date=July 2015}}}} The types categorized by number and relationship of parts are analyzed and determined through the labeling of primary textural elements: primary melody, secondary melody, parallel supporting melody, static support, harmonic support, rhythmic support, and harmonic and rhythmic support.{{sfn|Isaac and Russell|2003|loc=136}}{{incomplete short citation|date=December 2021}}

Common types included [[Monophony|monophonic]] texture (a single melodic voice, such as a piece for solo soprano or solo flute), biphonic texture (two melodic voices, such as a duo for bassoon and flute in which the bassoon plays a drone note and the flute plays the melody), [[polyphonic]] texture and [[Homophony|homophonic]] texture (chords accompanying a melody).{{Citation needed|date=August 2015}}<!--Especially for the drone accompaniment, which is usually regarded as a type of monophony.-->

===Form or structure===
[[File:Canon example.png|thumb|A musical [[canon (music)|canon]]. ''Encyclopaedia Britannica'' calls a "canon" both a compositional technique and a musical form.<ref>{{Britannica URL|art/canon-music|title=Canon: music}}</ref>]]
{{Main|Musical form}}
The term musical form (or musical architecture) refers to the overall structure or plan of a piece of music, and it describes the layout of a composition as divided into sections.{{sfn|Brandt|2007}} In the tenth edition of ''[[The Oxford Companion to Music]]'', [[Percy Scholes]] defines musical form as "a series of strategies designed to find a successful mean between the opposite extremes of unrelieved repetition and unrelieved alteration."{{sfn|Scholes|1977}} According to [[Richard Middleton (musicologist)|Richard Middleton]], musical form is "the shape or structure of the work." He describes it through difference: the distance moved from a [[Repetition (music)|repeat]]; the latter being the smallest difference. Difference is quantitative and qualitative: ''how far'', and ''of what type'', different. In many cases, form depends on statement and [[Restatement (music)|restatement]], unity and variety, and [[contrast (music)|contrast]] and connection.{{sfn|Middleton|1999|loc={{Page needed|date=July 2015}}}}

===Expression===
{{Main|Musical expression}}
[[File:1Francisco20violinista.jpg|thumb|right|220px|A violinist performing]]
Musical expression is the art of playing or singing music with emotional communication. The elements of music that comprise expression include dynamic indications, such as forte or piano, [[Musical phrasing|phrasing]], differing qualities of timbre and articulation, color, intensity, energy and excitement. All of these devices can be incorporated by the performer. A performer aims to elicit responses of sympathetic feeling in the audience, and to excite, calm or otherwise sway the audience's physical and emotional responses. Musical expression is sometimes thought to be produced by a combination of other parameters, and sometimes described as a transcendent quality that is more than the sum of measurable quantities such as pitch or duration.

Expression on instruments can be closely related to the role of the breath in singing, and the voice's natural ability to express feelings, sentiment and deep emotions.{{clarify|date=July 2015}}<!--Does this mean that keyboard and stringed instruments are essentially inexpressive?--> Whether these can somehow be categorized is perhaps the realm of academics, who view expression as an element of musical performance that embodies a consistently recognizable [[emotion]], ideally causing a [[emotional contagion|sympathetic emotional response]] in its listeners.{{sfn|London|n.d.}} The emotional content of musical expression is distinct from the emotional content of specific sounds (e.g., a startlingly-loud 'bang') and of learned associations (e.g., a [[national anthem]]), but can rarely be completely separated from its context.{{Citation needed|date=July 2015}}

The components of musical expression continue to be the subject of extensive and unresolved dispute.{{sfn|Avison|1752|loc={{Page needed|date=July 2015}}<!--Where does Avison say there is a continuing and unresolved dispute?-->}}{{sfn|Christiani|1885|loc={{Page needed|date=July 2015}}<!--Where does Christiani say there is a continuing and unresolved dispute?-->}}{{sfn|Lussy|1892|loc={{Page needed|date=July 2015}}<!--On what page(s) does Lussy state there is an extensive and unresolved dispute, or indeed that there is any dispute at all?-->}}{{sfn|Darwin|1913|loc={{Page needed|date=July 2015}}<!--Where does Darwin state that there is a continuing and unresolved dispute?-->}}{{sfn|Sorantin|1932|loc={{Page needed|date=July 2015}}<!--On what page(s) does Sorantin contend that there is an extensive and unresolved dispute on thesubject?-->}}{{sfn|Davies|1994|loc={{Page needed|date=July 2015}}<!--On what page does Davies say the components of expression continue to be subject to unresolved dispute? He mentions particular disputes on pp. 105, 136, 213, and 364, but characterises none of them as "extensive", nor does he say whether these disputes are resolved or not.-->}}

===Notation===
{{Main|Musical notation|Sheet music}}
[[File:Tibetanmusicalscore.jpg|thumb|[[Tibet]]an musical score from the 19th century]]
Musical notation is the written or symbolized representation of music. This is most often achieved by the use of commonly understood graphic symbols and written verbal instructions and their abbreviations. There are many systems of music notation from different cultures and different ages. Traditional Western notation evolved during the Middle Ages and remains an area of experimentation and innovation.{{Sfnm|Read|1969|1loc={{Page needed|date=August 2014}}|Stone|1980|2loc={{Page needed|date=August 2014}}}} In the 2000s, computer [[file formats]] have become important as well.{{sfn|Castan|2009}} Spoken language and [[Kodály Method#Hand signs|hand signs]] are also used to symbolically represent music, primarily in teaching.

In standard Western music notation, tones are represented graphically by symbols (notes) placed on a [[Staff (music)|staff]] or staves, the vertical axis corresponding to pitch and the horizontal axis corresponding to time. Note head shapes, stems, flags, ties and dots are used to indicate duration. Additional symbols indicate keys, dynamics, accents, rests, etc. Verbal instructions from the conductor are often used to indicate tempo, technique, and other aspects.

In Western music, a range of different music notation systems are used. In Western Classical music, conductors use printed scores that show all of the instruments' parts and orchestra members read parts with their musical lines written out. In popular styles of music, much less of the music may be notated. A rock band may go into a recording session with just a handwritten [[chord chart]] indicating the song's [[chord progression]] using chord names (e.g., C major, D minor, G7, etc.). All of the chord voicings, rhythms and accompaniment figures are improvised by the band members.

==As academic discipline==
The scholarly study of music theory in the twentieth century has a number of different subfields, each of which takes a different perspective on what are the primary phenomenon of interest and the most useful methods for investigation.

===Analysis===
{{Main|Musical analysis|Schenkerian analysis|Transformational theory}}
[[File:Debussy Pelleas et Melisande prelude opening.PNG|thumb|upright=1.3|Typically a given work is analyzed by more than one person and different or divergent analyses are created. For instance, the first two bars of the prelude to [[Claude Debussy]]'s ''[[Pelléas et Mélisande (opera)|Pelléas et Melisande]]''
are analyzed differently by Leibowitz, Laloy, van Appledorn, and Christ. Leibowitz analyses this succession harmonically as D minor:I–VII–V, ignoring melodic motion, Laloy analyses the succession as D:I–V, seeing the G in the second measure as an [[musical ornamentation|ornament]], and both van Appledorn and Christ analyse the succession as D:I–VII.
{{audio|Debussy Pelleas et Melisande-prelude opening.mid|Play}}]]
Musical analysis is the attempt to answer the question ''how does this music work?'' The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to [[Ian Bent]], "analysis, as a pursuit in its own right, came to be established only in the late 19th century; its emergence as an approach and method can be traced back to the 1750s. However, it existed as a scholarly tool, albeit an auxiliary one, from the [[Middle Ages]] onwards."{{sfn|Bent|1987|loc=6}}{{incomplete short citation|date=December 2021}} [[Adolf Bernhard Marx]] was influential in formalising concepts about composition and music understanding towards the second half of the 19th century. The principle of analysis has been variously criticized, especially by composers, such as [[Edgard Varèse]]'s claim that, "to explain by means of [analysis] is to decompose, to mutilate the spirit of a work".<ref>Quoted in {{harvnb|Bernard|1981|loc=1}}</ref>

[[Schenkerian analysis]] is a method of musical analysis of tonal music based on the theories of [[Heinrich Schenker]] (1868–1935). The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work and to help reading the score according to that structure. The theory's basic tenets can be viewed as a way of defining [[tonality]] in music. A Schenkerian analysis of a passage of music shows hierarchical relationships among its pitches, and draws conclusions about the structure of the passage from this hierarchy. The analysis makes use of a specialized symbolic form of musical notation that Schenker devised to demonstrate various [[Schenkerian analysis#Techniques of prolongation|techniques of elaboration]]. The most fundamental concept of Schenker's theory of tonality may be that of ''tonal space''.<ref>Schenker described the concept in a paper titled ''Erläuterungen'' ("Elucidations"), which he published four times between 1924 and 1926: ''Der Tonwille'' (Vienna, Tonwille Verlag, 1924) vol. 8–9, pp. 49–51, vol. 10, pp. 40–42; ''Das Meisterwerk in der Musik'' (München, Drei Masken Verlag), vol. 1 (1925), pp. 201–05; 2 (1926), pp. 193–97. English translation, ''Der Tonwille'', Oxford University Press, vol. 2, pp. 117–18 (the translation, although made from vols. 8–9 of the German original, gives as original pagination that of ''Das Meisterwerk'' 1; the text is the same). The concept of tonal space is still present in {{harvtxt|Schenker|1979|loc=especially p. 14, § 13}}, but less clearly than in the earlier presentation.</ref> The intervals between the notes of the tonic triad form a ''tonal space'' that is filled with passing and neighbour notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached.

Although Schenker himself usually presents his analyses in the generative direction, starting from the [[fundamental structure]] (''Ursatz'') to reach the score, the practice of Schenkerian analysis more often is reductive, starting from the score and showing how it can be reduced to its fundamental structure. The graph of the ''Ursatz'' is arrhythmic, as is a strict-counterpoint cantus firmus exercise.{{sfn|Schenker|1979|loc=p. 15, § 21}} Even at intermediate levels of the reduction, rhythmic notation (open and closed noteheads, beams and flags) shows not rhythm but the hierarchical relationships between the pitch-events. Schenkerian analysis is ''subjective''. There is no mechanical procedure involved and the analysis reflects the musical intuitions of the analyst.{{sfn| Snarrenberg|1997|loc={{Page needed|date=July 2015}}}} The analysis represents a way of hearing (and reading) a piece of music.

Transformational theory is a branch of music theory developed by [[David Lewin]] in the 1980s, and formally introduced in his 1987 work, ''Generalized Musical Intervals and Transformations''. The theory, which models [[Transformation (music)|musical transformations]] as elements of a [[Group theory|mathematical group]], can be used to analyze both [[tonality|tonal]] and [[atonal music]]. The goal of transformational theory is to change the focus from musical objects—such as the "C [[major chord]]" or "G major chord"—to relations between objects. Thus, instead of saying that a C major chord is followed by G major, a transformational theorist might say that the first chord has been "transformed" into the second by the "[[dominant (music)|Dominant]] operation." (Symbolically, one might write "Dominant(C major) = G major.") While traditional [[set theory (music)|musical set theory]] focuses on the makeup of musical objects, transformational theory focuses on the [[interval (music)|intervals]] or types of musical motion that can occur. According to Lewin's description of this change in emphasis, "[The transformational] attitude does not ask for some observed measure of extension between reified 'points'; rather it asks: 'If I am ''at'' s and wish to get to t, what characteristic ''gesture'' should I perform in order to arrive there?'"{{sfn|Lewin|1987|loc=159}}

===Music perception and cognition===
{{Further|Music psychology|Fred Lerdahl|Ray Jackendoff}}

Music psychology or the psychology of music may be regarded as a branch of both [[psychology]] and [[musicology]]. It aims to explain and understand musical [[behavior]] and [[experience]], including the processes through which music is perceived, created, responded to, and incorporated into everyday life.{{sfn|Tan, Peter, and Rom|2010|loc=2}}{{sfn|Thompson|n.d.|loc=320}} Modern music psychology is primarily [[Empirical research|empirical]]; its knowledge tends to advance on the basis of interpretations of data collected by systematic [[observation]] of and interaction with [[Human subject research|human participants]]. Music psychology is a field of research with practical relevance for many areas, including music [[musical technique|performance]], [[music composition|composition]], [[music education|education]], [[music criticism|criticism]], and [[music therapy|therapy]], as well as investigations of human [[aptitude]], skill, [[intelligence]], creativity, and [[social behavior]].

Music psychology can shed light on non-psychological aspects of [[musicology]] and musical practice. For example, it contributes to music theory through investigations of the [[perception]] and [[Cognitive musicology|computational modelling]] of musical structures such as [[melody]], [[harmony]], [[tonality]], [[rhythm]], [[Meter (music)|meter]], and [[Musical form|form]]. Research in [[music history]] can benefit from systematic study of the history of [[musical syntax]], or from psychological analyses of composers and compositions in relation to perceptual, affective, and social responses to their music.

===Genre and technique===
{{Main|Music genre|Musical technique}}
[[File:Bundesarchiv B 145 Bild-F008930-0019, Beethovenhalle Bonn, Kammerkonzert Kölner Trio.jpg|thumb|A Classical [[piano trio]] is a group that plays [[chamber music]], including [[sonata]]s. The term "piano trio" also refers to works composed for such a group.]]
A music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions.{{sfn|Samson|n.d.}} It is to be distinguished from ''[[musical form]]'' and ''musical style'', although in practice these terms are sometimes used interchangeably.{{sfn|Wong|2011}}{{Failed verification|date=December 2014}}<!--An electronic search of this web article finds only one occurrence of the word "form", as part of the compound expression; the word "style" does not occur at all. As a result, this citation confirms neither the claim that genre should be distinguished from form and style, nor the claim that they are sometimes used interchangeably in practice.-->

Music can be divided into different [[genres]] in many different ways. The artistic nature of music means that these classifications are often subjective and controversial, and some genres may overlap. There are even varying academic definitions of the term ''genre ''itself. In his book ''Form in Tonal Music'', Douglass M. Green distinguishes between genre and [[Musical form|form]]. He lists [[madrigal (music)|madrigal]], [[motet]], [[canzona]], [[ricercar]], and dance as examples of genres from the [[Renaissance music|Renaissance]] period. To further clarify the meaning of ''genre'', Green writes, "Beethoven's Op. 61 and Mendelssohn's Op. 64 are identical in genre—both are violin concertos—but different in form. However, Mozart's Rondo for Piano, K. 511, and the ''Agnus Dei'' from his Mass, K. 317 are quite different in genre but happen to be similar in form."{{sfn|Green|1979|loc=1}} Some, like [[Peter van der Merwe (musicologist)|Peter van der Merwe]], treat the terms ''genre'' and ''style'' as the same, saying that ''genre'' should be defined as pieces of music that came from the same style or "basic musical language."{{sfn|van der Merwe|1989|loc=3}}

Others, such as Allan F. Moore, state that ''genre'' and ''style'' are two separate terms, and that secondary characteristics such as subject matter can also differentiate between genres.{{sfn|Moore|2001|loc=432–33}} A music genre or subgenre may also be defined by the [[musical technique]]s, the style, the cultural context, and the content and spirit of the themes. Geographical origin is sometimes used to identify a music genre, though a single geographical category will often include a wide variety of subgenres. Timothy Laurie argues that "since the early 1980s, genre has graduated from being a subset of popular music studies to being an almost ubiquitous framework for constituting and evaluating musical research objects".{{sfn|Laurie|2014|loc=284}}

Musical technique is the ability of [[musical instrument|instrumental]] and vocal musicians to exert optimal control of their instruments or [[vocal cords]] to produce precise musical effects. Improving technique generally entails practicing exercises that improve muscular sensitivity and agility. To improve technique, musicians often practice fundamental patterns of notes such as the [[Natural minor|natural]], [[Minor scale|minor]], [[Major scale|major]], and [[chromatic scale]]s, [[Minor triad|minor]] and [[major triad]]s, [[Dominant seventh chord|dominant]] and [[diminished seventh]]s, formula patterns and [[arpeggio]]s. For example, [[Triad (music)|triads]] and [[Seventh chord|sevenths]] teach how to play chords with accuracy and speed. [[Scale (music)|Scales]] teach how to move quickly and gracefully from one note to another (usually by step). Arpeggios teach how to play [[broken chord]]s over larger intervals. Many of these components of music are found in compositions, for example, a scale is a very common element of classical and romantic era compositions.{{citation needed|date=July 2015}}

[[Heinrich Schenker]] argued that musical technique's "most striking and distinctive characteristic" is [[repetition (music)|repetition]].{{sfn|Kivy|1993|loc=327}} Works known as [[étude]]s (meaning "study") are also frequently used for the improvement of technique.

===Mathematics===
{{Main|Music and mathematics}}
Music theorists sometimes use mathematics to understand music, and although music has no [[axiomatic]] foundation in modern mathematics, mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical".{{sfn|Smith Brindle|1987|loc=42–43}} The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of [[set theory]], [[abstract algebra]] and [[number theory]]. Some composers have incorporated the [[golden ratio]] and [[Fibonacci numbers]] into their work.{{sfn|Smith Brindle|1987|loc=chapter 6, ''passim''}}{{sfn|Garland and Kahn|1995|loc={{Page needed|date=July 2015}}}} There is a long history of examining the relationships between music and mathematics. Though ancient Chinese, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound,{{sfn|Smith Brindle|1987|loc=42}} the [[Pythagoreanism|Pythagoreans]] (in particular [[Philolaus]] and [[Archytas]]){{sfn|Purwins|2005|loc=22–24}} of ancient Greece were the first researchers known to have investigated the expression of [[musical scale]]s in terms of numerical [[ratio]]s.
[[File:HarmonicIdentities.Names.Frequencies.svg|thumb|right|400px|The first 16 harmonics, their names and frequencies, showing the exponential nature of the octave and the simple fractional nature of non-octave harmonics]]
In the modern era, musical [[set theory]] uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such as [[transposition (music)|transposition]] and [[Melodic inversion|inversion]], one can discover deep structures in the music. Operations such as transposition and inversion are called [[isometries]] because they preserve the intervals between tones in a set. Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. For example, the pitch classes in an equally tempered octave form an [[abelian group]] with 12 elements. It is possible to describe [[just intonation]] in terms of a [[free abelian group]].{{sfn|Wohl|2005}}

===Serial composition and set theory===
[[File:Berg's Lyric Suite Mov. I tone row B-P.PNG|thumb|Tone row from [[Alban Berg]]'s ''[[Lyric Suite (Berg)|Lyric Suite]]'', movement I[[File:Berg's Lyric Suite Mov. I tone row B-P.mid]]]]
{{Further|Serialism|Set theory (music)|Arnold Schoenberg|Milton Babbitt|David Lewin|Allen Forte}}
In music theory, serialism is a method or technique of [[Musical composition|composition]] that uses a series of values to manipulate different [[aspect of music|musical elements]]. Serialism began primarily with [[Arnold Schoenberg]]'s [[twelve-tone technique]], though his contemporaries were also working to establish serialism as one example of [[atonality|post-tonal]] thinking. Twelve-tone technique orders the twelve notes of the [[chromatic scale]], forming a [[tone row|row]] or series and providing a unifying basis for a composition's [[melody]], [[harmony]], structural progressions, and [[variation (music)|variations]]. Other types of serialism also work with [[set (music)|sets]], collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "[[parameter (music)|parameters]]"), such as [[duration (music)|duration]], [[Dynamics (music)|dynamics]], and [[timbre]]. The idea of serialism is also applied in various ways in the visual arts, design, and architecture<ref>{{harvnb|Bandur|2001|loc=5, 12, 74}}; {{harvnb|Gerstner|1964|loc=passim}}</ref>

"Integral serialism" or "total serialism" is the use of series for aspects such as duration, dynamics, and register as well as pitch.{{Sfn|Whittall|2008|loc=273}} Other terms, used especially in Europe to distinguish post-World War II serial music from twelve-tone music and its American extensions, are "general serialism" and "multiple serialism".{{sfn|Grant|2001|loc=5–6}}

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by [[Howard Hanson]] (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as [[Allen Forte]] (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.{{Citation needed|date=July 2015}}

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as [[Transposition (music)|transposition]], [[Melodic inversion|inversion]], and [[Complement (music)|complementation]]. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.{{Citation needed|date=July 2015}}

===Musical semiotics===
{{Further|Music semiology|Jean-Jacques Nattiez}}
[[File:Roman Jakobson.jpg|thumb|upright|Semiotician [[Roman Jakobson]]]]
Music semiology ([[semiotics]]) is the study of signs as they pertain to music on a variety of levels. Following [[Roman Jakobson]], [[Kofi Agawu]] adopts the idea of musical semiosis being introversive or extroversive—that is, musical signs within a text and without.{{Citation needed|date=July 2015}} "Topics", or various musical conventions (such as horn calls, dance forms, and styles), have been treated suggestively by Agawu, among others.{{Citation needed|date=July 2015}} The notion of [[Musical Gestures|gesture]] is beginning to play a large role in musico-semiotic enquiry.{{Citation needed|date=July 2015}}

:"There are strong arguments that music inhabits a semiological realm which, on both [[ontogenetic]] and [[phylogenetic]] levels, has developmental priority over verbal language."{{sfn|Middleton|1990|loc=172}}{{sfn|Nattiez|1976}}{{sfn|Nattiez|1990}}{{sfn|Nattiez1989}}{{sfn|Stefani|1973}}{{sfn|Stefani|1976}}{{sfn|Baroni|1983}}{{sfn|''Semiotica''|1987|loc=66:1–3}}{{incomplete short citation|date=December 2021}}{{clarify |date=November 2018|reason=The quotation cannot stem from all these references at once!}}

Writers on music semiology include Kofi Agawu (on topical theory,{{Citation needed|date=July 2015}} [[Heinrich Schenker]],{{sfn|Dunsby|Stopford|1981|loc=49–53}}{{sfn|Meeùs|2017|loc=81–96}} Robert Hatten (on topic, gesture){{Citation needed|date=July 2015}}, [[Raymond Monelle]] (on topic, musical meaning){{Citation needed|date=July 2015}}, [[Jean-Jacques Nattiez]] (on introversive taxonomic analysis and ethnomusicological applications){{Citation needed|date=July 2015}}, [[Anthony Newcomb]] (on narrativity){{Citation needed|date=July 2015}}, and [[Eero Tarasti]]{{Citation needed|date=July 2015}}.

[[Roland Barthes]], himself a semiotician and skilled amateur pianist, wrote about music in ''Image-Music-Text,''{{Full citation needed|date=July 2015}} ''The Responsibilities of Form,''{{Full citation needed|date=July 2015}} and ''Eiffel Tower,''{{Full citation needed|date=July 2015}} though he did not consider music to be a semiotic system{{Citation needed|date=August 2015}}.

Signs, meanings in music, happen essentially through the connotations of sounds, and through the social construction, appropriation and amplification of certain meanings associated with these connotations. The work of [[Philip Tagg]] (''Ten Little Tunes'',{{Full citation needed|date=July 2015}} ''Fernando the Flute'',{{Full citation needed|date=July 2015}} ''Music's Meanings''{{Full citation needed|date=July 2015}}) provides one of the most complete and systematic analysis of the relation between musical structures and connotations in western and especially popular, television and film music. The work of [[Leonard B. Meyer]] in ''Style and Music''{{Full citation needed|date=July 2015}} theorizes the relationship between ideologies and musical structures and the phenomena of style change, and focuses on romanticism as a case study.

===Education and careers===
[[File:Pat Carpenter picture.JPG|thumb|[[Columbia University]] music theorist [[Patricia Carpenter (music theorist)|Pat Carpenter]] in an undated photo]]
Music theory in the practical sense has been a part of education at conservatories and music schools for centuries, but the status music theory currently has within academic institutions is relatively recent. In the 1970s, few universities had dedicated music theory programs, many music theorists had been trained as composers or historians, and there was a belief among theorists that the teaching of music theory was inadequate and that the subject was not properly recognised as a scholarly discipline in its own right.{{sfn|McCreless|n.d.}} A growing number of scholars began promoting the idea that music theory should be taught by theorists, rather than composers, performers or music historians.{{sfn|McCreless|n.d.}} This led to the founding of the [[Society for Music Theory]] in the United States in 1977. In Europe, the French ''Société d'Analyse musicale'' was founded in 1985. It called the First European Conference of Music Analysis for 1989, which resulted in the foundation of the ''Société belge d'Analyse musicale'' in Belgium and the ''Gruppo analisi e teoria musicale'' in Italy the same year, the ''Society for Music Analysis'' in the UK in 1991, the ''Vereniging voor Muziektheorie'' in the Netherlands in 1999 and the ''Gesellschaft für Musiktheorie'' in Germany in 2000.{{sfn|Meeùs|2015|loc=111}} They were later followed by the Russian Society for Music Theory in 2013, the Polish Society for Music Analysis in 2015 and the ''Sociedad de Análisis y Teoría Musical'' in Spain in 2020, and others are in construction. These societies coordinate the publication of music theory scholarship and support the professional development of music theory researchers. They formed in 2018 a network of European societies for Theory and/or Analysis of Music, the [https://europeanmusictheory.eu/ EuroT&AM]

As part of their initial training, music theorists will typically complete a [[B.Mus]] or a [[Bachelor of Arts|B.A.]] in music (or a related field) and in many cases an M.A. in music theory. Some individuals apply directly from a bachelor's degree to a PhD, and in these cases, they may not receive an M.A. In the 2010s, given the increasingly interdisciplinary nature of university graduate programs, some applicants for music theory PhD programs may have academic training both in music and outside of music (e.g., a student may apply with a B.Mus. and a Masters in Music Composition or Philosophy of Music).

Most music theorists work as instructors, lecturers or professors in colleges, universities or [[Music school|conservatories]]. The job market for tenure-track professor positions is very competitive: with an average of around 25 tenure-track positions advertised per year in the past decade, 80–100 PhD graduates are produced each year (according to the Survey of Earned Doctorates) who compete not only with each other for those positions but with job seekers that received PhD's in previous years who are still searching for a tenure-track job.<!--How competitive is "very"? As competitive as for, say, a position as an airline pilot?--> Applicants must hold a completed PhD or the equivalent degree (or expect to receive one within a year of being hired—called an "ABD", for "[[All But Dissertation]]" stage) and (for more senior positions) have a strong record of publishing in peer-reviewed journals. Some PhD-holding music theorists are only able to find insecure positions as [[sessional lecturer]]s. The job tasks of a music theorist are the same as those of a professor in any other humanities discipline: teaching undergraduate and/or graduate classes in this area of specialization and, in many cases some general courses (such as [[Music appreciation]] or Introduction to Music Theory), conducting research in this area of expertise, publishing research articles in peer-reviewed journals, authoring book chapters, books or textbooks, traveling to conferences to present papers and learn about research in the field, and, if the program includes a graduate school, supervising M.A. and PhD students and giving them guidance on the preparation of their theses and dissertations. Some music theory professors may take on senior administrative positions in their institution, such as [[Dean (education)|Dean]] or Chair of the School of Music.

==See also==
* [[List of music theorists]]
* [[Music psychology]]
* [[Musicology]]
* [[Theory of painting]]

==Notes==
{{Reflist|group=n|colwidth=45em}}

==References==
{{Reflist}}

===Sources===
{{div col|colwidth=45em}}
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* {{cite book|last=Kramer|first=Jonathan D.|author-link=Jonathan Kramer|title=The Time of Music: New Meanings, New Temporalities, New Listening Strategies|date=1988|publisher=Schirmer Books|location=New York}}
* {{wikicite|ref={{harvid|Kubik|2010}}|reference=[[Gerhard Kubik|Kubik, Gerhard]] (2010). ''Theory of African Music'', 2 vols. Chicago: University of Chicago Press. {{ISBN|0-226-45691-9}}.}}
* {{wikicite|ref={{harvid|Kümmel|1970}}|reference={{ill|Hans Martin Kümmel|de|lt=Kümmel, H. M.}} (1970). "Zur Stimmung der babylonischen Harfe". ''Orientalia'' 39:252–263.}}
* {{cite encyclopedia|last=Lam|first=Joseph S. C.|title=China, §II, History and Theory|encyclopedia=[[Grove Music Online]]|publisher=Oxford University Press<!-- |access-date=15 November 2015 -->|url=http://www.oxfordmusiconline.com/subscriber/article/grove/music/43141pg2}}
* {{wikicite|ref={{harvid|Latham|2002}}|reference=Latham, Alison (ed.) (2002). ''The Oxford Companion to Music''. Oxford and New York: Oxford University Press. {{ISBN|0-19-866212-2}}.}}
* {{wikicite|ref={{harvid|Laurie|2014}}|reference=Laurie, Timothy (2014). "Music Genre as Method". ''Cultural Studies Review'' 20, no. 2:283–292.}}
* {{wikicite|ref={{harvid|Lerdahl and Jackendoff|1985}}|reference=[[Fred Lerdahl|Lerdahl, Fred]], and [[Ray Jackendoff]] (1985). ''A Generative Theory of Tonal Music''. Cambridge, Massachusetts: MIT Press.}}{{ISBN|0262260913}}
* {{wikicite|ref={{harvid|Lewin|1987}}|reference=[[David Lewin|Lewin, David]] (1987). ''Generalized Musical Intervals and Transformations''. New Haven: Yale University Press.}}
* {{wikicite|ref={{harvid|Linkels|n.d.}}|reference=Linkels, Ad. n.d. "The Real Music of Paradise". In ''World Music'', Vol. 2: Latin & North America, Caribbean, India, Asia and Pacific, edited by Simon Broughton and Mark Ellingham, with James McConnachie and Orla Duane, 218–229. {{Full citation needed|date=July 2015|reason=Place of publication needed.}}: Rough Guides, Penguin Books. {{ISBN|1-85828-636-0}}.}}
* {{cite book|last=London|first=Justin|title=Hearing in Time: Psychological Aspects of Musical Meter|date=2004|publisher=Oxford University Press|location=Oxford and New York}}{{ISBN needed|date=October 2017}}
* {{wikicite|ref={{harvid|London|n.d.}}|reference=London, Justin (n.d.), "[https://www.escom.org/proceedings/ICMPC2000/Tue/London.htm Musical Expression and Musical Meaning in Context]. ICMPC2000 Proceedings Papers.}}
* {{wikicite|ref={{harvid|Lussy|1892}}|reference=Lussy, Mathis (1892). ''Musical Expression: Accents, Nuances, and Tempo, in Vocal and Instrumental Music'', translated by Miss M. E. von Glehn. Novello, Ewer, and Co.'s Music Primers 25. London: Novello, Ewer and Co.; New York: H. W. Gray}}
* {{wikicite|ref={{harvid|McAdams and Bregman|1979}}|reference=McAdams, Stephen, and [[Albert Bregman]] (1979). "Hearing Musical Streams". ''[[Computer Music Journal]]'' 3, no. 4 (December): 26–43, 60. {{JSTOR|4617866}}}}
* {{wikicite|ref={{harvid|McCreless|n.d.}}|reference=McCreless, Patrick. n.d. "Society for Music Theory", ''[[Grove Music Online]]''. Oxford University Press.}}
* {{wikicite|ref={{harvid|Malm|1996}}|reference=[[William P. Malm|Malm, William P.]] (1996). ''Music Cultures of the Pacific, the Near East, and Asia'', third edition. {{ISBN|0-13-182387-6}}.}}
* {{wikicite|ref={{harvid|Manik|1969}}|reference=Manik, Liberty (1969). ''Das Arabische Tonsystem im Mittelalter''. Leiden: E. J. Brill.}}
* {{cite web|last=Mannell|first=Robert|date=n.d.|title=Spectral Analysis of Sounds|url=http://clas.mq.edu.au/speech/acoustics/frequency/spectral.html|website=Macquarie University}}
* {{wikicite|ref={{harvid|Meeùs|2015}}|reference=Meeùs, Nicolas (2015). "Épistémologie d’une musicologie analytique". ''Musurgia'' 22, nos. 3–4:97–114.}}
* {{wikicite|ref={{harvid|Meeùs|2017}}|reference=Meeùs, Nicolas (2017). "Schenker's ''Inhalt'', Schenkerian Semiotics. A Preliminary Study". ''The Dawn of Music Semiology. Essays in Honor of Jean-Jacques Nattiez'', J. Dunsby and J. Goldman ed. Rochester: Rochester University Press:81–96.}}
* {{wikicite|ref={{harvid|Middleton|1990}}|reference=[[Richard Middleton (musicologist)|Middleton, Richard]] (1990). ''Studying Popular Music''. Milton Keynes and Philadelphia: Open University Press. {{ISBN|978-0335152766|978-0335152759}} (cloth & pbk).}}
* {{wikicite|ref={{harvid|Middleton|1999}}|reference=Middleton, Richard (1999). "Form". In ''[https://books.google.com/books?id=gY-w68zIQWQC Key Terms in Popular Music and Culture]'', edited by Bruce Horner and [[Thomas Swiss]].{{Page needed|date=July 2015|reason=Inclusive page numbers of Middleton's chapter are needed.}} Malden, Massachusetts: Blackwell Publishing. {{ISBN|0-631-21263-9}}.}}
* {{wikicite|ref={{harvid|Mirelman|2010}}|reference=Mirelman, Sam (2010). "A New Fragment of Music Theory from Ancient Iraq". ''[[Archiv für Musikwissenschaft]]'' 67, no. 1:45–51.}}
* {{wikicite|ref={{harvid|Mirelman|2013}}|reference=Mirelman, Sam (2013). "[http://www.aawmjournal.com/articles/2013b/Mirelman_AAWM_Vol_2_2.pdf Tuning Procedures in Ancient Iraq]". ''Analytical Approaches to World Music'' 2, no. 2:43–56.}}
* {{wikicite|ref={{harvid|Mitchell|2008}}|reference=Mitchell, Barry (2008). "[http://theoryofmusic.wordpress.com/2008/01/16/an-explanation-for-the-emergence-of-jazz-1956/ An Explanation for the Emergence of Jazz (1956)]", ''Theory of Music'' (16 January):{{Page needed|date=July 2015}}.}}{{Unreliable source?|date=July 2015|reason=This is just a blog.}}
* {{wikicite|ref={{harvid|Moore|2001}}|reference=Moore, Allan F. (2001). "[https://www.jstor.org/stable/3526163 Categorical Conventions in Music Discourse: Style and Genre]". ''[[Music & Letters]]'' 82, no. 3 (August): 432–442.}}
* {{wikicite|ref={{harvid|Nattiez|1976}}|reference=[[Jean-Jacques Nattiez|Nattiez, Jean-Jacques]] (1976). ''Fondements d'une sémiologie de la musique''. Collection Esthétique. Paris: Union générale d'éditions. {{ISBN|978-2264000033}}.}}
* {{wikicite|ref={{harvid|Nattiez|1989}}|reference=Nattiez, Jean-Jacques(1989). ''Proust as Musician'', translated by Derrick Puffett. Cambridge and New York: Cambridge University Press. {{ISBN|978-0-521-36349-5|978-0-521-02802-8}}.}}
* {{wikicite|ref={{harvid|Nattiez|1990}}|reference=Nattiez, Jean-Jacques (1990). ''Music and Discourse: Toward a Semiology of Music'', translated by [[Carolyn Abbate]] of ''Musicologie generale et semiologie''. Princeton: Princeton University Press. {{ISBN|978-0-691-09136-5}} (cloth); {{ISBN|978-0-691-02714-2}} (pbk).}}
* {{OED|theory, ''n''.<sup>1</sup>|ref={{harvid|OED}}}}
* {{wikicite|ref={{harvid|Palisca and Bent|n.d.}}|reference=[[Claude V. Palisca|Palisca, Claude V.]], and [[Ian Bent|Ian D. Bent]]. n.d. "Theory, Theorists". ''[[Grove Music Online]]'', edited by Deane Root. Oxford University Press (accessed 17 December 2014).}}
* {{wikicite|ref={{harvid|Purwins|2005}}|reference=Purwins, Hendrik (2005). "[https://ccrma.stanford.edu/~purwins/purwinsPhD.pdf Profiles of Pitch Classes Circularity of Relative Pitch and Key: Experiments, Models, Computational Music Analysis, and Perspectives]". Doktor der Naturwissenschaften diss. Berlin: Technischen Universität Berlin.}}
* {{wikicite|ref={{harvid|Read|1969}}|reference=[[Gardner Read|Read, Gardner]] (1969). ''Music Notation: A Manual of Modern Practice'', second edition. Boston, Allyn and Bacon. Reprinted, London: Gollancz, 1974. {{ISBN|9780575017580}}. Reprinted, London: Gollancz, 1978. {{ISBN|978-0575025547}}. Reprinted, New York: Taplinger Publishing, 1979. {{ISBN|978-0800854591|978-0800854539}}.}}
* {{wikicite|ref={{harvid|Samson|n.d.}}|reference=[[Jim Samson|Samson, Jim]]. "[http://www.oxfordmusiconline.com/subscriber/article/grove/music/40599 Genre]". In ''[[Grove Music Online]]'', edited by Deane Root. Oxford Music Online. Accessed 4 March 2012}}
* {{wikicite|ref={{harvid|Schenker|1979}}|reference=[[Heinrich Schenker|Schenker, Heinrich]] (1979). ''Free Composition''. Translated and edited by [[Ernst Oster]]. New York and London, Longman.}}
* {{wikicite|ref={{harvid|Schoenberg|1983}}|reference=[[Arnold Schoenberg|Schoenberg, Arnold]] (1983). ''Structural Functions of Harmony'', revised edition with corrections, edited by [[Leonard Stein]]. London and Boston: Faber and Faber. {{ISBN|978-0-571-13000-9}}.}}
* {{wikicite|ref={{harvid|Scholes|1977}}|reference=[[Percy Scholes|Scholes, Percy A.]] (1977). "Form". ''The Oxford Companion to Music'', tenth edition. Oxford and New York: Oxford University Press.}}
* {{wikicite|ref={{harvid|Service|2013}}|reference=Service, Jonathan (2013). "[http://www.hcs.harvard.edu/soundingchina/Service.html Chinese Music Theory]". ''Transmission/Transformation: Sounding China in Enlightenment Europe''. Cambridge: Harvard University Department of Music (web, accessed 17 December 2015).}}
* {{wikicite|ref={{harvid|Shiloah|1964}}|reference=Shiloah, Amnon (1964). [http://www.persee.fr/doc/ephe_0000-0001_1964_num_1_1_4883 La perfection des connaissances musicales: Traduction annotée du traité de musique arabe d'al-Ḥasan ibn Aḥmad ibn 'Ali al-Kātib] ''École pratique des hautes études. 4e section, Sciences historiques et philologiques, Annuaire 1964–1965'' 97, no. 1: 451–456.}}
* {{wikicite|ref={{harvid|Smith Brindle|1987}}|reference=[[Reginald Smith Brindle|Smith Brindle, Reginald]] (1987). ''The New Music: The Avant-Garde Since 1945'', second edition. Oxford and New York: Oxford University Press. {{ISBN|978-0-19-315471-1|978-0-19-315468-1}} (cloth & pbk).}}
* {{wikicite|ref={{harvid|Snarrenberg|1997}}|reference=Snarrenberg, Robert (1997). ''Schenker's Interpretive Practice''. Cambridge Studies in Music Theory and Analysis 11. Cambridge University Press. {{ISBN|0521497264}}.}}
* {{wikicite|ref={{harvid|Sorantin|1932}}|reference=Sorantin, Erich (1932). ''[https://books.google.com/books?id=B7dFAAAAMAAJ The Problem of Musical Expression: A Philosophical and Psychological Study]''. Nashville: Marshall and Bruce}}
* {{wikicite|ref={{harvid|Stefani|1973}}|reference=Stefani, Gino (1973). "Sémiotique en musicologie". ''Versus'' 5:20–42.}}
* {{wikicite|ref={{harvid|Stefani|1976}}|reference=Stefani, Gino (1976). ''Introduzione alla semiotica della musica''. Palermo: Sellerio editore. }}
* {{cite book|last=Stein|first=Leon|author-link=Leon Stein|year=1979|title=Structure and Style: The Study and Analysis of Musical Forms|place=Princeton, New Jersey|publisher=Summy-Birchard Music|isbn=978-0-87487-164-7}}
* {{cite book|last1=Stone|first1=Kurt|title=Music Notation in the Twentieth Century|date=1980|place=New York|publisher=W. W. Norton|isbn=978-0-393-95053-3}}
* {{wikicite|ref={{harvid|Tan, Peter, and Rom|2010}}|reference=Tan, Siu-Lan, Pfordresher Peter, and Harré Rom (2010). ''Psychology of Music: From Sound to Significance''. New York: Psychology Press. {{ISBN|978-1-84169-868-7}}.}}
* {{wikicite|ref={{harvid|Thompson|n.d.}}|reference=[[William Forde Thompson|Thompson, William Forde]] (n.d.). ''Music, Thought, and Feeling: Understanding the Psychology of Music'', second edition. New York: Oxford University Press. {{ISBN|0-19-537707-9}}.}}
* {{wikicite|ref={{harvid|Touma|1996}}|reference=[[Habib Hassan Touma|Touma, Habib Hassan]] (1996). ''The Music of the Arabs'', new expanded edition, translated by Laurie Schwartz. Portland, Oregon: Amadeus Press. {{ISBN|0-931340-88-8}}.}}
* {{cite book|last=van der Merwe|first=Peter|author-link=Peter van der Merwe (musicologist)|year=1989|title=Origins of the Popular Style: The Antecedents of Twentieth-Century Popular Music|publisher=Clarendon Press |location=Oxford |isbn=978-0-19-316121-4 |url-access=registration |url=https://archive.org/details/originsofpopular0000vand }}
* {{wikicite|ref={{harvid|Whittall|2008}}|reference=[[Arnold Whittall|Whittall, Arnold]] (2008). ''The Cambridge Introduction to Serialism''. Cambridge Introductions to Music. New York: Cambridge University Press. {{ISBN|978-0-521-86341-4|978-0-521-68200-8}} (cloth & pbk).}}
* {{wikicite|ref={{harvid|Wohl|2005}}|reference=Wohl, Gennady. (2005). "[http://sonantometry.blogspot.com/2007_05_01_archive.html Algebra of Tonal Functions]", translated by Mykhaylo Khramov. Sonantometry Blogspot (16 June; accessed 31 July 2015).}}{{Unreliable source?|date=July 2015|reason=This appears to be a self-published web blog.}}
* {{wikicite|ref={{harvid|Wong|2011}}|reference=Wong, Janice (2011). "[http://mastersofmedia.hum.uva.nl/2011/04/26/visualising-music-the-problems-with-genre-classification/ Visualising Music: The Problems with Genre Classification]". Masters of Media blog site (accessed 11 August 2015).}}{{Unreliable source?|date=July 2015|reason=This appears to be a self-published web blog.}}
* {{wikicite|ref={{harvid|Wright|2001a}}|reference=Wright, Owen (2001a). "Munajjim, al- [Yaḥyā ibn]". ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan. Reprinted in ''[[Grove Music Online]]'', Oxford Music Online. {{subscription required}}.}}
* {{wikicite|ref={{harvid|Wright|2001b}}|reference=Wright, Owen (2001b). "[http://www.oxfordmusiconline.com/subscriber/article/grove/music/01139pg1 Arab Music, §1: Art Music, 2. The Early Period (to 900 CE), (iv) Early Theory]". ''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan. Reprinted in ''Grove Music Online'', Oxford Music Online. {{subscription required}}.}}
* {{wikicite|ref={{harvid|Wulstan|1968}}|reference=Wulstan, David (1968). "The Tuning of the Babylonian Harp". ''Iraq'' 30: 215–28.}}
* {{cite book|last=Yeston|first=Maury|author-link=Maury Yeston|title=The Stratification of Musical Rhythm|date=1976|publisher=Yale University Press|location=New Haven}}
{{refend}}

==Further reading==
{{div col|colwidth=45em}}
* {{cite book |authorlink1=Willi Apel |last1=Apel |first1=Willi |first2=Ralph T. |last2=Daniel |year=1960 |title=The Harvard Brief Dictionary of Music |location=New York |publisher=Simon & Schuster Inc. |isbn=0-671-73747-3}}
* [[Aristoxenus]] (1902). ''Aristoxenou Harmonika stoicheia: The Harmonics of Aristoxenus'', Greek text edited with an English translation and notes by Henry Marcam. Oxford: The Clarendon Press.
* {{cite journal | last1=Bakkegard | first1=B. M. | last2=Morris | first2=E. A. | title=Seventh Century Flutes from Arizona | journal=Ethnomusicology | volume=5 | issue=3 | date=1961 | doi=10.2307/924518 | page=184| jstor=924518 }}
* Bakshi, Haresh (2005). ''101 Raga-s for the 21st Century and Beyond: A Music Lover's Guide to Hindustani Music''. Victoria, British Columbia: Trafford. {{ISBN|978-1412046770|978-1412231350}} (ebook).
* Baur, John (2014). ''Practical Music Theory''. Dubuque: Kendall-Hunt Publishing Company. {{ISBN|978-1-4652-1790-5}}
* Benade, Arthur H. (1960). ''Horns, Strings, and Harmony''. Science Study Series S 11. Garden City, New York: Doubleday
* [[Ian Bent|Bent, Ian D.]], and [[Anthony Pople]] (2001). "Analysis." ''[[The New Grove Dictionary of Music and Musicians]]'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]]. London: Macmillan.
* Benward, Bruce, Barbara Garvey Jackson, and Bruce R. Jackson. (2000). ''Practical Beginning Theory: A Fundamentals Worktext'', 8th edition, Boston: McGraw-Hill. {{ISBN|0-697-34397-9}}. [First edition 1963]
* Benward, Bruce, and Marilyn Nadine Saker (2009). ''Music in Theory and Practice'', eighth edition, vol. 2. Boston: McGraw-Hill. {{ISBN|978-0-07-310188-0}}.
* Billmeier, Uschi (1999). ''Mamady Keïta: A Life for the Djembé – Traditional Rhythms of the Malinké'', fourth edition. Kirchhasel-Uhlstädt: Arun-Verlag. {{ISBN|978-3-935581-52-3}}.
* [[Benjamin Boretz|Boretz, Benjamin]] (1995). ''Meta-Variations: Studies in the Foundations of Musical Thought''. Red Hook, New York: Open Space.
* Both, Arnd Adje (2009). "Music Archaeology: Some Methodological and Theoretical Considerations". ''[[Yearbook for Traditional Music]]'' 41:1–11. {{JSTOR|25735475}}
* [[Albert Bregman|Bregman, Albert]] (1994). ''Auditory Scene Analysis: The Perceptual Organization of Sound''. Cambridge: MIT Press. {{ISBN|0-262-52195-4}}.
* [[Mark Brill|Brill, Mark]] (2012). "Music of the Ancient Maya: New Venues of Research". Paper presented at AMS-SW Conference Fall 2012. Texas State University{{Full citation needed|date=December 2014|reason=This appears to be published in a 'conference proceedings' of some sort, but the publication details need filling in.}}
* Brown, James Murray (1967). ''A Handbook of Musical Knowledge'', 2 vols. London: Trinity College of Music.
* {{Cite web |last=Cavanagh |first=Lynn |year=1999 |url=http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf |title=A Brief History of the Establishment of International Standard Pitch A=440 Hertz |url-status=dead |archive-url=https://web.archive.org/web/20090325223741/http://www.wam.hr/Arhiva/US/Cavanagh_440Hz.pdf |archive-date=25 March 2009 |ref=none}} (Accessed 1 May 2010)
* {{cite book |last1=Charry |first1=Eric |location=Chicago |title=Mande Music: Traditional and Modern Music of the Maninka and Mandinka of Western Africa |date=2000 |publisher=University of Chicago Press |isbn=978-0-226-10161-3 |ref=none}}
* Cheong, Kong F. (2012). "A Description of the Ceramic Musical Instruments Excavated from the North Group of Pacbitun, Belize". In ''Pacbitun Regional Archaeological Project, Report on the 2011 Field Season'', edited by Terry G. Powis, 15–29. Belmopan, Belize: Institute of Archaeology.
* Chernoff, John (1981). ''African Rhythm and African Sensibility: Aesthetics and Social Action in African Musical Idioms''. Chicago: University of Chicago Press. {{ISBN|978-0-226-10345-7}}.
* Civil, Miguel (2010). "The Lexical Texts in the Schøyen Collection". ''Cornell University Studies in Assyriology and Sumerology'' 12:203–214.
* [[Confucius]] (1999). ''The Analects of Confucius'', edited by [[Roger T. Ames]] and Henry Rosemont Jr.{{clarify|date=December 2014|reason=Surely this is in English—who translated it?}} Ballantine Books. {{ISBN|0345434072}}.
* Conrad, Nicholas J., Maria Malina, and Susanne C. Münzel (2009). "New Flutes Document the Earliest Musical Tradition in Southwestern Germany". ''[[Nature (journal)|Nature]]'' 460, no. 7256 (6 August): 737–740.
* [[Robert P. Crease|Crease, Robert P.]] (2011). ''World in the Balance: The Historic Quest for an Absolute System of Measurement''. New York, London: W. W. Norton.
* {{cite journal | last=Crickmore | first=Leon | title=A Musicological Interpretation of the Akkadan Term Siḫpu | journal=Journal of Cuneiform Studies | volume=64 | issue=1 | date=2012 | issn=0022-0256 | doi=10.5615/jcunestud.64.0057 | pages=57–64}}
* Chase, Wayne (2006). ''How Music REALLY Works!'', second edition. Vancouver, Canada: Roedy Black Publishing. {{ISBN|1-897311-55-9}} (book).
* [[Francesco d'Errico|d'Errico, Francesco]], [[Christopher Henshilwood]], Graeme Lawson, Marian Vanhaeren, Anne-Marie Tillier, Marie Soressi, Frederique Bresson, Bruno Maureille, April Nowell, Joseba Lakarra, Lucinda Backwell, Michele Julien (2003). "[http://www.eva.mpg.de/evolution/staff/soressi/pdf/Derrico-and-al2003_JWP.pdf Archaeological Evidence for the Emergence of Language, Symbolism, and Music – An Alternative Multidisciplinary Perspective]". ''Journal of World Prehistory'' 17, no. 1 (March): 1–70.
* Despopoulos, Agamemnon, and Stefan Silbernagl (2003). ''Color Atlas of Physiology'', fifth edition. New York and Stuttgart: Thieme. {{ISBN|3-13-545005-8}}.
* {{cite journal |last1=Dietrich |first1=Manfried |author1link=:de:Manfried Dietrich |first2=Oswald |last2=Loretz |author2-link=:de:Oswald Loretz |title=Kollationen zum Musiktext aus Ugarit |journal=Ugarit-Forschungen |date=1975 |volume=7 |pages=521–22 |ref=none}}
* Dunbar, Brian (2010). ''Practical Music Theory: A Guide to Music as Art, Language, and Life''. Rochester, MN: Factum Musicae. {{ISBN|978-0578062471}}.
* {{cite web |last1=Gross |first1=Clint |date=n.d. |title=Anasazi Flutes from the Broken Flute Cave |url=http://www.flutopedia.com/flute_types_north_america.htm |website=Flutopedia |publisher=Clint Gross |access-date=4 December 2014 |ref=none}}
* {{cite journal | last1=Solis | first1=R. S. | last2=Haas | first2=J. | last3=Creamer | first3=W. | title=Dating Caral, a preceramic site in the Supe Valley on the central coast of Peru | journal=Science | volume=292 | issue=5517 | date=2001-04-27 | issn=0036-8075 | pmid=11326098 | doi=10.1126/science.1059519 | pages=723–726| bibcode=2001Sci...292..723S }}
* Harnsberger, Lindsey C. (1997). "Articulation". ''Essential Dictionary of Music: Definitions, Composers, Theory, Instrument and Vocal Ranges'', second edition. The Essential Dictionary Series. Los Angeles: Alfred Publishing. {{ISBN|0-88284-728-7}}.
* {{cite book | last=Hewitt | first=Michael | title=Music Theory for Computer Musicians | publisher=Course Technology Ptr | publication-place=Boston, MA | date=2008 | isbn=978-1-59863-503-4 | oclc=185033110}}
* {{cite book |last=Houtsma |first=Adrianus JM. |chapter=Pitch perception| editor-last=Moore | editor-first=B.C.J. | title=Hearing | publisher=Elsevier Science | series=Handbook of Perception and Cognition |edition=Second| year=1995 | isbn=978-0-08-053386-5 | chapter-url=https://books.google.com/books?id=OywDx9pxCMYC&pg=PA267  | pages=267–295}}
* Huang, Xiang-peng (黄翔鹏) (1989). "Wuyang Jiahu gudi de ceyin yanjiu (舞阳贾湖骨笛的测音研究)" [Pitch Measurement Studies of Bone Flutes from Jiahu of Wuyang County]. ''Wenwu'' (文物) [Cultural Relics], no.&nbsp;1:15–17. Reprinted in 黄翔鹏文存 [Collected Essays of Huang Xiang-Peng], 2 vols, edited by Zhongguo Yishu Yanjiuyuan Yinyue Yanjiusuo (中国艺术研究院音乐研究所), 557–560. Ji'nan, China: Shandong Wenyi Chubanshe, 2007. {{ISBN|978-7-5329-2669-5}}.
* Hung, Eric (2012). "[http://www.muscan.org/en/news/job-postings/184-job-western-university-music-theory Western University, Don Wright Faculty of Music: Tenure-Track Appointment in Music Theory]". Toronto: MusCan.
* {{cite journal | last1=Jackendoff | first1=Ray |authorlink1=Ray Jackendoff| last2=Lerdahl | first2=Fred |authorlink2=Fred Lerdahl| title=Generative Music Theory and Its Relation to Psychology | journal=Journal of Music Theory | publisher=[Duke University Press, Yale University Department of Music] | volume=25 | issue=1 | year=1981 | issn=0022-2909 | jstor=843466 | pages=45–90 | url=http://www.jstor.org/stable/843466 }}
* Josephs, Jess L. (1967). ''The Physics of Musical Sound''. Princeton, Toronto, and London: D. Van Nostrand Company.
* [[Stefan Kostka|Kostka, Stefan]], and Dorothy Payne (2004). ''Tonal Harmony'', fifth edition. New York: McGraw-Hill.
* [[Gerhard Kubik|Kubik, Gerhard]] (1998). ''Kalimba—Nsansi—Mbira. Lamellophone in Afrika''. Berlin: Museum fur Volkerkunde. {{ISBN|3886094391}}.
* [[Emmanuel Laroche|Laroche, Emmanuel]] (1955). ''Le palais royal d' Ugarit 3: Textes accadiens et hourrites des archives est, ouest et centrales''. Paris: C. Klincksieck
* Lawn, Richard J., and Jeffrey L. Hellmer (1996). ''Jazz Theory and Practice''. [n.p.]: Alfred Publishing Co. {{ISBN|0-88284-722-8}}.
* Lee, Yuan-Yuan, and Sin-Yan Shen (1999). ''Chinese Musical Instruments''. Chinese Music Monograph Series. Chicago: Chinese Music Society of North America Press. {{ISBN|1880464039}}.
* [[Fred Lerdahl|Lerdahl, Fred]] (2001). ''Tonal Pitch Space''. Oxford: Oxford University Press.
* Lloyd, Llewellyn S., and Hugh Boyle (1978). ''Intervals, Scales and Temperaments''. New York: St. Martin's Press. {{ISBN|0-312-42533-3}}.
* Lu, Liancheng (2005). "The Eastern Zhou and the Growth of Regionalism". In ''The Formation of Chinese Civilization'', edited by [[Sarah Allan]], 203–248. New Haven and London: Yale University Press. {{ISBN|978-0-300-09382-7}}.
* [[Alfred Mann (musicologist)|Mann, Alfred]], J. Kenneth Wilson, and Peter Urquhart. n.d. "Canon (i)." ''[[Grove Music Online]]''. Oxford Music Online (Accessed 2 January 2011) {{subscription required}}.
* {{cite book |last=Mazzola |first=Guerino |title=Gruppen und Kategorien in der Musik: Entwurf einer mathematischen Musiktheorie |url=https://books.google.com/books?id=ktPuAAAAMAAJ |access-date=26 February 2012 |year=1985 |publisher=Heldermann |isbn=978-3-88538-210-2 |ref=none}}
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{{div col end}}

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