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Music theory is the study of the practices and possibilities of
music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspe ...
. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "
rudiments In ''rudimental drumming'', a form of percussion music, a drum rudiment is one of a number of relatively small patterns which form the foundation for more extended and complex drumming patterns. The term "drum rudiment" is most closely assoc ...
", that are needed to understand music notation (key signatures, time signatures, and rhythmic notation); the second is learning scholars' views on music from 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." Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. Because of the ever-expanding conception of 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 From the time of Plato through the Middle Ages, the ''quadrivium'' (plural: quadrivia) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the ...
'' liberal arts university curriculum, that was common in medieval Europe, was an abstract system of proportions that was carefully studied at a distance from actual musical practice. 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. 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 instruments A musical instrument is a device created or adapted to make musical sounds. In principle, any object that produces sound can be considered a musical instrument—it is through purpose that the object becomes a musical instrument. A person who pl ...
, and other artifacts. For example, ancient instruments from 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 treatises and 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 Academic writing or scholarly writing is nonfiction produced as part of academic work, including reports on empirical Field research, fieldwork or research in facilities for the natural sciences or social sciences, monographs in which scholars a ...
cites earlier research. In modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, ''music theory'', is an act of contemplation of music, from the Greek word θεωρία, meaning a looking at, a viewing; a contemplation, speculation, theory; a sight, a spectacle. As such, it is often concerned with abstract musical aspects such as tuning and tonal systems, scales, consonance and dissonance, and rhythmic relationships. In addition, there is also a body of theory concerning practical aspects, such as the creation or the performance of music, orchestration, ornamentation, improvisation, and electronic sound production. A person who researches or teaches music theory is a music theorist. University study, typically to the MA or 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 textbooks, especially in the United States of America, often include elements of
musical acoustics Musical acoustics or music acoustics is a multidisciplinary field that combines knowledge from physics, psychophysics, organology (classification of the instruments), physiology, music theory, ethnomusicology, signal processing and instrument build ...
, considerations of musical notation, and techniques of tonal
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
( harmony and counterpoint), among other topics.


History


Prehistory

Preserved prehistoric instruments, artifacts, and later depictions of performance in artworks can give clues to the structure of pitch systems in prehistoric cultures. See for instance
Paleolithic flutes During regular archaeological excavations, several flutes that date to the European Upper Paleolithic were discovered in caves in the Swabian Alb region of Germany. Dated and tested independently by two laboratories, in England and Germany, th ...
, Gǔdí, and
Anasazi flute The Anasazi flute is the name of a prehistoric end-blown flute replicated today from findings at a massive cave in Prayer Rock Valley in Arizona, United States by an archaeological expedition led by Earl H. Morris in 1931. The team excavated 15 c ...
.


Antiquity


Mesopotamia

Several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts bout musicare 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."


China

Much of Chinese music history and theory remains unclear. 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. The
Lüshi chunqiu The ''Lüshi Chunqiu'', also known in English as ''Master Lü's Spring and Autumn Annals'', is an encyclopedic Chinese classic text compiled around 239 BC under the patronage of the Qin Dynasty Chancellor Lü Buwei. In the evaluation of Micha ...
from about 239 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 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''.
Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as the nature and functions of music. The ''Yueji'' ("Record of music", c1st and 2nd centuries BCE), for example, manifests 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 BCE) that music wasted human and material resources, and Laozi's claim that the greatest music had no sounds. ..Even the music of the ''qin'' zither, a genre closely affiliated with Confucian scholar-officials, includes many works with Daoist references, such as ''Tianfeng huanpei'' ("Heavenly Breeze and Sounds of Jade Pendants").


India

The Samaveda and
Yajurveda The ''Yajurveda'' ( sa, यजुर्वेद, ', from ' meaning "worship", and ''veda'' meaning "knowledge") is the Veda primarily of prose mantras for worship rituals.Michael Witzel (2003), "Vedas and Upaniṣads", in ''The Blackwell C ...
(c. 1200 – 1000 BCE) are among the earliest testimonies of Indian music, but they contain no theory properly speaking. The Natya Shastra, written between 200 BCE to 200 CE, discusses intervals (''Śrutis''), scales (''Grāmas''), consonances and dissonances, classes of melodic structure (''Mūrchanās'', modes?), melodic types (''Jātis''), instruments, etc.


Greece

Early preserved Greek writings on music theory include two types of works: * 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 Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His politi ...
(c. 570 – c. 495 BCE),
Philolaus Philolaus (; grc, Φιλόλαος, ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pyt ...
(c. 470 – c. 385 BCE), Archytas (428–347 BCE), and others. Works of the first type (technical manuals) include * Anonymous (erroneously attributed to
Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...
) ''Division of the Canon'', Κατατομή κανόνος, 4th–3rd century BCE. *
Theon of Smyrna Theon of Smyrna ( el, Θέων ὁ Σμυρναῖος ''Theon ho Smyrnaios'', ''gen.'' Θέωνος ''Theonos''; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. Hi ...
, ''On Mathematics Useful for the Understanding of Plato'', Τωv κατά τό μαθηματικόν χρησίμων είς τήν Πλάτωνος άνάγνωσις, 115–140 CE. *
Nicomachus of Gerasa Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'' in Greek. He was born in ...
, ''Manual of Harmonics'', Άρμονικόν έγχειρίδιον, 100–150 CE *
Cleonides Cleonides ( el, Κλεονείδης) is the author of a Greek treatise on music theory titled Εἰσαγωγὴ ἁρμονική ''Eisagōgē harmonikē'' (Introduction to Harmonics). The date of the treatise, based on internal evidence, can be e ...
, ''Introduction to Harmonics'', Είσαγωγή άρμονική, 2nd century CE. * Gaudentius, ''Harmonic Introduction'', Άρμονική είσαγωγή, 3d or 4th century CE. * Bacchius Geron, ''Introduction to the Art of Music'', Είσαγωγή τέχνης μουσικής, 4th century CE or later. * Alypius, ''Introduction to Music'', Είσαγωγή μουσική, 4th–5th century CE. More philosophical treatises of the second type include *
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
, ''Harmonic Elements'', Άρμονικά στοιχεία, 375/360 – after 320 BCE. *
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
, ''Rhythmic Elements'', Ρυθμικά στοιχεία. * Claudius
Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...
, ''Harmonics'', Άρμονικά, 127–148 CE. * Porphyrius, ''On Ptolemy's Harmonics'', Είς τά άρμονικά Πτολεμαίον ύπόμνημα, 232/3–c. 305 CE.


Post-classical


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.


Arabic countries / Persian countries

Medieval Arabic music theorists include: * Abū Yūsuf Ya'qūb
al-Kindi Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...
(† Bagdad, 873 CE), who uses the first twelve letters of the alphabet to describe the twelve frets on five strings of the
oud , image=File:oud2.jpg , image_capt=Syrian oud made by Abdo Nahat in 1921 , background= , classification= * String instruments *Necked bowl lutes , hornbostel_sachs=321.321-6 , hornbostel_sachs_desc=Composite chordophone sounded with a plectrum , ...
, producing a chromatic scale of 25 degrees. * aḥyā ibnal- 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 , image=File:oud2.jpg , image_capt=Syrian oud made by Abdo Nahat in 1921 , background= , classification= * String instruments *Necked bowl lutes , hornbostel_sachs=321.321-6 , hornbostel_sachs_desc=Composite chordophone sounded with a plectrum , ...
and a system of eight modes perhaps inspired by
Ishaq al-Mawsili Ishaq al-Mawsili ( ar, إسحاق الموصلي; 767/772 – March 850) was an Arab musician of Persian origin active as a composer, singer, music theorist and writer on music. The leading musician of his time in the Abbasid Caliphate, he served ...
(767–850). * Abū n-Nașr Muḥammad al-Fārābi (Persia, 872? – Damas, 950 or 951 CE), author of ''
Kitab al-Musiqa al-Kabir ''Kitab al-Musiqa al-Kabir'' ( ar, كتاب الموسيقى الكبير, en, the Great Book of Music) is a treatise on music in east by the medieval philosopher al-Farabi (872-950/951). The work prescribes different aspects of music such as ma ...
'' ("The Great Book of Music"). * 'Ali ibn al-Husayn ul-Isfahānī (897–967), known as
Abu al-Faraj al-Isfahani Ali ibn al-Husayn al-Iṣfahānī ( ar, أبو الفرج الأصفهاني), also known as Abul-Faraj, (full form: Abū al-Faraj ʿAlī ibn al-Ḥusayn ibn Muḥammad ibn Aḥmad ibn al-Ḥaytham al-Umawī al-Iṣfahānī) (284–356 AH / 897 ...
, 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 ''The Book of Healing'' (; ; also known as ) is a scientific and philosophical encyclopedia written by Abu Ali ibn Sīna (aka Avicenna) from medieval Persia, near Bukhara in Maverounnahr. He most likely began to compose the book in 1014, comp ...
"). * 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). *
Safi al-Din al-Urmawi Safi al-Din al-Urmawi al-Baghdadi ( fa, صفی الدین اورموی) or Safi al-Din Abd al-Mu'min ibn Yusuf ibn al-Fakhir al-Urmawi al-Baghdadi (born c. 1216 AD in Urmia, died in 1294 AD in Baghdad) was a renowned musician and writer on the ...
(1216–1294 CE), author of the ''Kitabu al-Adwār'' ("Treatise of musical cycles") and ''ar-Risālah aš-Šarafiyyah'' ("Epistle to Šaraf"). * Mubārak Šāh, commentator of Safi al-Din's ''Kitāb al-Adwār'' (British Museum, Ms 823). * Anon. LXI, Anonymous commentary on Safi al-Din's ''Kitāb al-Adwār''. * Shams al-dῑn al-Saydᾱwῑ Al-Dhahabῑ (14th century CE (?)), music theorist. Author of ''Urjῡza fi'l-mῡsῑqᾱ'' ("A Didactic Poem on Music").


Europe

The Latin treatise ''De institutione musica'' by the Roman philosopher
Boethius Anicius Manlius Severinus Boethius, commonly known as Boethius (; Latin: ''Boetius''; 480 – 524 AD), was a Roman senator, consul, ''magister officiorum'', historian, and philosopher of the Early Middle Ages. He was a central figure in the tr ...
(written c. 500, translated as ''Fundamentals of Music'') 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. 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 Plainsong or plainchant (calque from the French ''plain-chant''; la, cantus planus) is a body of chants used in the liturgies of the Western Church. When referring to the term plainsong, it is those sacred pieces that are composed in Latin text ...
tradition. At the end of the ninth century,
Hucbald Hucbald ( – 20 June 930; also Hucbaldus or Hubaldus) was a Benedictine monk active as a music theorist, poet, composer, teacher, and hagiographer. He was long associated with Saint-Amand Abbey, so is often known as Hucbald of St Amand. Deeply i ...
worked towards more precise pitch notation for the
neume A neume (; sometimes spelled neum) is the basic element of Western and Eastern systems of musical notation prior to the invention of five-line staff notation. The earliest neumes were inflective marks that indicated the general shape but not nec ...
s used to record plainchant.
Guido d'Arezzo Guido of Arezzo ( it, Guido d'Arezzo; – after 1033) was an Italian music theorist and pedagogue of High medieval music. A Benedictine monk, he is regarded as the inventor—or by some, developer—of the modern staff notation that had a ma ...
' wrote in 1028 a letter to Michael of Pomposa, entitled ''Epistola de ignoto cantu'', in which he introduced the practice of using syllables to describe notes and intervals. This was the source of the hexachordal
solmization Solmization is a system of attributing a distinct syllable to each note of a musical scale. Various forms of solmization are in use and have been used throughout the world, but solfège is the most common convention in countries of Western cultur ...
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. During the thirteenth century, a new rhythm system called
mensural notation Mensural notation is the musical notation system used for European vocal polyphonic music from the later part of the 13th century until about 1600. The term "mensural" refers to the ability of this system to describe precisely measured rhythmi ...
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 Franco of Cologne (; also Franco of Paris) was a German music theorist and possibly a composer. He was one of the most influential theorists of the Late Middle Ages, and was the first to propose an idea which was to transform musical notation pe ...
(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

* Bᾱqiyᾱ Nᾱyinῑ (Uzbekistan, 17th century CE), Uzbek author and music theorist. Author of ''Zamzama e wahdat-i-mῡsῑqῑ'' ("The Chanting of Unity in Music"). * Baron Francois Rodolphe d'Erlanger (Tunis, Tunisia, 1910–1932 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.


Europe

* Renaissance * Baroque * 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. **
Sacred harp Sacred Harp singing is a tradition of sacred choral music that originated in New England and was later perpetuated and carried on in the American South. The name is derived from ''The Sacred Harp'', a ubiquitous and historically important tune ...
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.


Contemporary


Fundamentals of music

Music is composed of
aural Hearing, or auditory perception, is the ability to perceive sounds through an organ, such as an ear, by detecting vibrations as periodic changes in the pressure of a surrounding medium. The academic field concerned with hearing is audito ...
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.


Pitch

Pitch is the lowness or highness of a 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. Specific frequencies are often assigned letter names. Today most orchestras assign
concert A Concert pitch is the pitch (music), pitch reference to which a group of musical instruments are musical tuning, tuned for a performance. Concert pitch may vary from musical ensemble, ensemble to ensemble, and has varied widely over music history. ...
(the A above middle C on the piano) to the frequency of 440 Hz. This assignment is somewhat arbitrary; for example, in 1859 France, the same A was tuned to 435 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. The most basic interval is the
unison In music, unison is two or more musical parts that sound either the same pitch or pitches separated by intervals of one or more octaves, usually at the same time. ''Rhythmic unison'' is another term for homorhythm. Definition Unison or per ...
, 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 In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
: 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. Musical tuning systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. In
Western culture Leonardo da Vinci's ''Vitruvian Man''. Based on the correlations of ideal Body proportions">human proportions with geometry described by the ancient Roman architect Vitruvius in Book III of his treatise ''De architectura''. image:Plato Pio-Cle ...
, 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

Notes can be arranged in a variety of scales and
modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
. Western music theory generally divides the octave into a series of twelve pitches, called a
chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce th ...
, within which the interval between adjacent tones is called a half step, or
semitone A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent no ...
. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales. The most commonly encountered scales are the seven-toned major, the
harmonic minor In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
, the
melodic minor In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which al ...
, and the
natural minor In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which als ...
. Other examples of scales are the
octatonic scale An octatonic scale is any eight- note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetric ...
and the
pentatonic A pentatonic scale is a musical scale (music), scale with five Musical note, notes per octave, in contrast to the heptatonic scale, which has seven notes per octave (such as the major scale and minor scale). Pentatonic scales were developed ...
or five-tone scale, which is common in
folk music Folk music is a music genre that includes traditional folk music and the contemporary genre that evolved from the former during the 20th-century folk revival. Some types of folk music may be called world music. Traditional folk music has b ...
and
blues Blues is a music genre and musical form which originated in the Deep South of the United States around the 1860s. Blues incorporated spirituals, work songs, field hollers, shouts, chants, and rhymed simple narrative ballads from the Afr ...
. Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classical Ottoman,
Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples ** Persian language, an Iranian language of the ...
,
Indian Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asia ...
and
Arabic Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
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. In traditional Western notation, the scale used for a composition is usually indicated by a
key signature In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the clef a ...
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
transposed In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix by producing another matrix, often denoted by (among other notations). The tr ...
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 In Western music theory, a major second (sometimes also called whole tone or a whole step) is a second spanning two semitones (). A second is a musical interval encompassing two adjacent staff positions (see Interval number for more det ...
. 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 Range may refer to: Geography * Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra) ** Mountain range, a group of mountains bordered by lowlands * Range, a term used to i ...
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. The interrelationship of the keys most commonly used in Western tonal music is conveniently shown by the
circle of fifths In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of ...
. 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 The doctrine of the affections, also known as the ''doctrine of affects'', ''doctrine of the passions'', ''theory of the affects'', or by the German term Affektenlehre (after the German ''Affekt''; plural ''Affekte'') was a theory in the aesthe ...
, 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

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. 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 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.


Rhythm

Rhythm is produced by the sequential arrangement of sounds and silences in time.
Meter The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
measures music in regular pulse groupings, called measures or bars. The
time signature The time signature (also known as meter signature, metre signature, or measure signature) is a notational convention used in Western musical notation to specify how many beats (pulses) are contained in each measure (bar), and which note value ...
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. Syncopated rhythms contradict those conventions by accenting unexpected parts of the beat. Playing simultaneous rhythms in more than one time signature is called
polyrhythm Polyrhythm is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. The rhythmic layers may be the basis of an entire piece of music ( cross-rhyt ...
. 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 Maury Yeston (born October 23, 1945) is an American composer, lyricist and music theorist. He is known as the initiator of new Broadway musicals and writing their music and lyrics, as well as a classical orchestral and ballet composer, Yale Uni ...
,
Fred Lerdahl Alfred Whitford (Fred) Lerdahl (born March 10, 1943, in Madison, Wisconsin) is the Fritz Reiner Professor Emeritus of Musical Composition at Columbia University, and a composer and music theorist best known for his work on musical grammar and co ...
and
Ray Jackendoff Ray Jackendoff (born January 23, 1945) is an American linguist. He is professor of philosophy, Seth Merrin Chair in the Humanities and, with Daniel Dennett, co-director of the Center for Cognitive Studies at Tufts University. He has always st ...
, Jonathan Kramer, and Justin London.


Melody

A melody is a series of tones ''perceived as an entity'', sounding in succession that typically move toward a climax of tension then resolve to a state of rest. 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
scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number w ...
or
modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
. 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.


Chord

A chord, in music, is any harmonic set of three or more
note Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened version ...
s that is heard as if sounding
simultaneously Simultaneity may refer to: * Relativity of simultaneity, a concept in special relativity. * Simultaneity (music), more than one complete musical texture occurring at the same time, rather than in succession * Simultaneity, a concept in Endogene ...
. These need not actually be played together: arpeggios and broken chords may, for many practical and theoretical purposes, constitute chords. Chords and sequences of chords are frequently used in modern Western, West African, and Oceanian music, whereas they are absent from the music of many other parts of the world. The most frequently encountered chords are triads, so called because they consist of three distinct notes: further notes may be added to give
seventh chord A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a mi ...
s, extended chords, or
added tone chord An added tone chord, or added note chord, is a non- tertian chord composed of a triad and an extra "added" note. Any tone that is not a seventh factor is commonly categorized as an added tone. It can be outside the tertian sequence of ascendin ...
s. The most common chords are the '' major'' and '' minor triads'' and then the '' augmented'' and '' diminished triads''. The descriptions ''major'', ''minor'', ''augmented'', and ''diminished'' are sometimes referred to collectively as chordal ''quality''. Chords are also commonly classed by their
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
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
inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...
, the order in which the notes are stacked. A series of chords is called a
chord progression In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice ...
. Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishing
key Key or The Key may refer to: Common meanings * Key (cryptography), a piece of information that controls the operation of a cryptography algorithm * Key (lock), device used to control access to places or facilities restricted by a lock * Key (map ...
in common-practice harmony. To describe this, chords are numbered, using
Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
(upward from the key-note), per their diatonic function. Common ways of notating or representing chords in western music other than conventional
staff notation In Western musical notation, the staff (US and UK)"staff" in the Collins ...
include
Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
,
figured bass Figured bass is musical notation in which numerals and symbols appear above or below (or next to) a bass note. The numerals and symbols (often accidentals) indicate intervals, chords, and non-chord tones that a musician playing piano, harpsi ...
(much used in the
Baroque era The Baroque (, ; ) is a style of architecture, music, dance, painting, sculpture, poetry, and other arts that flourished in Europe from the early 17th century until the 1750s. In the territories of the Spanish and Portuguese empires including th ...
),
chord letter Musicians use various kinds of chord names and symbols in different contexts to represent Chord (music), musical chords. In most List of popular music genres, genres of popular music, including jazz, pop music, pop, and rock music, rock, a chord ...
s (sometimes used in modern musicology), and various systems of
chord chart A chord chart (or chart) is a form of musical notation that describes the basic harmonic and rhythmic information for a song or tune. It is the most common form of notation used by professional session musicians playing jazz or popular music. ...
s typically found in the
lead sheet A lead sheet or fake sheet is a form of musical notation that specifies the essential elements of a popular song: the melody, lyrics and harmony. The melody is written in modern Western music notation, the lyric is written as text below the st ...
s used in
popular music Popular music is music with wide appeal that is typically distributed to large audiences through the music industry. These forms and styles can be enjoyed and performed by people with little or no musical training.Popular Music. (2015). ''Fu ...
to lay out the sequence of chords so that the musician may play accompaniment chords or improvise a solo.


Harmony

In music, harmony is the use of simultaneous pitches ( tones,
notes Note, notes, or NOTE may refer to: Music and entertainment * Musical note, a pitched sound (or a symbol for a sound) in music * ''Notes'' (album), a 1987 album by Paul Bley and Paul Motian * ''Notes'', a common (yet unofficial) shortened versio ...
), or
chords Chord may refer to: * Chord (music), an aggregate of musical pitches sounded simultaneously ** Guitar chord a chord played on a guitar, which has a particular tuning * Chord (geometry), a line segment joining two points on a curve * Chord ( ...
. The study of harmony involves chords and their construction and
chord progression In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice ...
s and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from
melodic line A melody (from Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combinat ...
, or the "horizontal" aspect. Counterpoint, which refers to the interweaving of melodic lines, and
polyphony Polyphony ( ) is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, h ...
, which refers to the relationship of separate independent voices, is thus sometimes distinguished from harmony. In
popular Popularity or social status is the quality of being well liked, admired or well known to a particular group. Popular may also refer to: In sociology * Popular culture * Popular fiction * Popular music * Popular science * Populace, the total ...
and
jazz harmony Jazz harmony is the theory and practice of how chords are used in jazz music. Jazz bears certain similarities to other practices in the tradition of Western harmony, such as many chord progressions, and the incorporation of the major and min ...
, chords are named by their
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the su ...
plus various terms and characters indicating their qualities. For example, a
lead sheet A lead sheet or fake sheet is a form of musical notation that specifies the essential elements of a popular song: the melody, lyrics and harmony. The melody is written in modern Western music notation, the lyric is written as text below the st ...
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 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 In European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid-Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evoluti ...
a dissonant chord (chord with tension) "resolves" to a consonant chord.
Harmonization In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads". A harmonized scale can be created by using each note of a musical scale as a root ...
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.


Timbre

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," but can be accurately described and analyzed by Fourier analysis and other methods because it results from the combination of all sound frequencies, attack and release envelopes, and other qualities that a tone comprises.
Timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...
is principally determined by two things: (1) the relative balance of
overtones An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic) In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental i ...
produced by a given instrument due its construction (e.g. shape, material), and (2) the
envelope An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card. Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a sh ...
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. 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.


Dynamics

In music, " dynamics" normally refers to variations of intensity or volume, as may be measured by physicists and audio engineers in decibels or
phon The phon is a logarithmic unit of loudness level for tones and complex sounds. Loudness is measured in sone which is a linear unit. Human sensitivity to sound is variable across different frequencies; therefore, although two different tones may ...
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 " hairpins" when indicated with diverging or converging lines as shown in the graphic above.


Articulation

Articulation is the way the performer sounds notes. For example, '' staccato'' is the shortening of duration compared to the written note value, ''
legato In music performance and notation, legato (; Italian for "tied together"; French ''lié''; German ''gebunden'') indicates that musical notes are played or sung smoothly and connected. That is, the player makes a transition from note to note wit ...
'' 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 In musical notation, ''tenuto'' ( Italian, past participle of ''tenere'', "to hold"), denoted as a horizontal bar adjacent to a note, is a direction for the performer to hold or sustain a note for its full length. Its precise interpretation can ...
'' (pressed or played to full notated duration); ''
marcato Marcato (short form: Marc.; Italian for ''marked'') is a musical instruction indicating a note, chord, or passage is to be played louder or more forcefully than the surrounding music. The instruction may involve the word ''marcato'' itself writt ...
'' (accented and detached); ''staccato'' ("separated", "detached"); '' martelé'' (heavily accented or "hammered"). Many of these can be combined to create certain "in-between" articulations. For example, ''
portato Portato (; Italian past participle of ''portare'', "to carry"), also mezzo-staccato, French notes portées, in music denotes a smooth, pulsing articulation and is often notated by adding dots under slur markings. Portato is also known as arti ...
'' is the combination of ''tenuto'' and ''staccato''. Some instruments have unique methods by which to produce sounds, such as '' spicatto'' for bowed strings, where the bow bounces off the string.


Texture

In music, texture is how the
melodic A melody (from Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combinat ...
,
rhythm Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular re ...
ic, and harmonic materials are combined in a
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
, thus determining the overall quality of the sound in a piece. Texture is often described in regard to the density, or thickness, and
range Range may refer to: Geography * Range (geographic), a chain of hills or mountains; a somewhat linear, complex mountainous or hilly area (cordillera, sierra) ** Mountain range, a group of mountains bordered by lowlands * Range, a term used to i ...
, 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 In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...
of the instruments or voices playing these parts and the harmony,
tempo In musical terminology, tempo ( Italian, 'time'; plural ''tempos'', or ''tempi'' from the Italian plural) is the speed or pace of a given piece. In classical music, tempo is typically indicated with an instruction at the start of a piece (ofte ...
, and rhythms used. 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. Common types included
monophonic Monaural or monophonic sound reproduction (often shortened to mono) is sound intended to be heard as if it were emanating from one position. This contrasts with stereophonic sound or ''stereo'', which uses two separate audio channels to reproduc ...
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
homophonic In music, homophony (;, Greek: ὁμόφωνος, ''homóphōnos'', from ὁμός, ''homós'', "same" and φωνή, ''phōnē'', "sound, tone") is a texture in which a primary part is supported by one or more additional strands that flesh ...
texture (chords accompanying a melody).


Form or structure

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. In the tenth edition of ''
The Oxford Companion to Music ''The Oxford Companion to Music'' is a music reference book in the Book series, series of Oxford Companions produced by the Oxford University Press. It was originally conceived and written by Percy Scholes and published in 1938. Since then, it ...
'',
Percy Scholes Percy Alfred Scholes PhD OBE (24 July 1877 – 31 July 1958) (pronounced ''skolz'') was an English musician, journalist and prolific writer, whose best-known achievement was his compilation of the first edition of ''The Oxford Companion to Music'' ...
defines musical form as "a series of strategies designed to find a successful mean between the opposite extremes of unrelieved repetition and unrelieved alteration." According to Richard Middleton, musical form is "the shape or structure of the work." He describes it through difference: the distance moved from a 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, unity and variety, and contrast and connection.


Expression

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, 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. 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 Emotions are mental states brought on by neurophysiology, neurophysiological changes, variously associated with thoughts, feelings, behavioral responses, and a degree of pleasure or suffering, displeasure. There is currently no scientific ...
, ideally causing a sympathetic emotional response in its listeners. 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 A national anthem is a patriotic musical composition symbolizing and evoking eulogies of the history and traditions of a country or nation. The majority of national anthems are marches or hymns in style. American, Central Asian, and Europea ...
), but can rarely be completely separated from its context. The components of musical expression continue to be the subject of extensive and unresolved dispute.


Notation

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.In the 2000s, computer
file formats A file format is a standard way that information is encoded for storage in a computer file. It specifies how bits are used to encode information in a digital storage medium. File formats may be either proprietary or free. Some file formats ...
have become important as well. Spoken language and 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 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 A chord chart (or chart) is a form of musical notation that describes the basic harmonic and rhythmic information for a song or tune. It is the most common form of notation used by professional session musicians playing jazz or popular music. ...
indicating the song's
chord progression In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice ...
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

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 Ian David Bent (born 1 January 1938) is a British-born music scholar. He is now Professor Emeritus, after retiring from Full Professor of Music, at Columbia University and Honorary Professor in the History of Music Theory at the University of Cambr ...
, "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 In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire ...
onwards."
Adolf Bernhard Marx Friedrich Heinrich Adolf Bernhard Marx . B. Marx(15 May 1795, Halle – 17 May 1866, Berlin) was a German music theorist, critic, and musicologist. Life Marx was the son of a Jewish doctor in Halle who, though a member of the congregation, was ...
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 nalysisis to decompose, to mutilate the spirit of a work". Schenkerian analysis is a method of musical analysis of tonal music based on the theories of
Heinrich Schenker Heinrich Schenker (19 June 1868 – 14 January 1935) was a Galician-born Austrian music theorist whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis, was most fully ex ...
(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 Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is ca ...
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 techniques of elaboration. The most fundamental concept of Schenker's theory of tonality may be that of ''tonal space''. 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 In Schenkerian analysis, the fundamental structure (german: Ursatz) describes the structure of a tonal work as it occurs at the most remote (or "background") level and in the most abstract form. A basic elaboration of the tonic triad, it consist ...
(''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. 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. 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 David Benjamin Lewin (July 2, 1933 – May 5, 2003) was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation", he did his most influential theoretical work on the development ...
in the 1980s, and formally introduced in his 1987 work, ''Generalized Musical Intervals and Transformations''. The theory, which models musical transformations as elements of a mathematical group, can be used to analyze both tonal and
atonal music Atonality in its broadest sense is music that lacks a tonal center, or key. ''Atonality'', in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a ...
. The goal of transformational theory is to change the focus from musical objects—such as the "C
major chord In music theory Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the " rudiments", that are needed to understan ...
" 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 operation." (Symbolically, one might write "Dominant(C major) = G major.") While traditional
musical set theory Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed th ...
focuses on the makeup of musical objects, transformational theory focuses on the
intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ...
or types of musical motion that can occur. According to Lewin's description of this change in emphasis, " he transformationalattitude 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?'"


Music perception and cognition

Music psychology or the psychology of music may be regarded as a branch of both
psychology Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries betwe ...
and musicology. It aims to explain and understand musical behavior and
experience Experience refers to conscious events in general, more specifically to perceptions, or to the practical knowledge and familiarity that is produced by these conscious processes. Understood as a conscious event in the widest sense, experience involv ...
, including the processes through which music is perceived, created, responded to, and incorporated into everyday life. Modern music psychology is primarily empirical; its knowledge tends to advance on the basis of interpretations of data collected by systematic observation of and interaction with human participants. Music psychology is a field of research with practical relevance for many areas, including music performance,
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
,
education Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty ...
, criticism, and
therapy A therapy or medical treatment (often abbreviated tx, Tx, or Tx) is the attempted remediation of a health problem, usually following a medical diagnosis. As a rule, each therapy has indications and contraindications. There are many different ...
, as well as investigations of human
aptitude An aptitude is a component of a competence to do a certain kind of work at a certain level. Outstanding aptitude can be considered "talent". Aptitude is inborn potential to perform certain kinds of activities, whether physical or mental, and ...
, skill,
intelligence Intelligence has been defined in many ways: the capacity for abstraction, logic, understanding, self-awareness, learning, emotional knowledge, reasoning, planning, creativity, critical thinking, and problem-solving. More generally, it can be des ...
, creativity, and
social behavior Social behavior is behavior among two or more organisms within the same species, and encompasses any behavior in which one member affects the other. This is due to an interaction among those members. Social behavior can be seen as similar to an ...
. 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 Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous system ...
and
computational modelling Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...
of musical structures such as melody, harmony,
tonality Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is ca ...
,
rhythm Rhythm (from Greek , ''rhythmos'', "any regular recurring motion, symmetry") generally means a " movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions". This general meaning of regular re ...
,
meter The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
, and
form Form is the shape, visual appearance, or configuration of an object. In a wider sense, the form is the way something happens. Form also refers to: *Form (document), a document (printed or electronic) with spaces in which to write or enter data ...
. Research in
music history Music history, sometimes called historical musicology, is a highly diverse subfield of the broader discipline of musicology that studies music from a historical point of view. In theory, "music history" could refer to the study of the history o ...
can benefit from systematic study of the history of
musical syntax When analysing the regularities and structure of music as well as the processing of music in the brain, certain findings lead to the question of whether music is based on a syntax that could be compared with linguistic syntax. To get closer to th ...
, or from psychological analyses of composers and compositions in relation to perceptual, affective, and social responses to their music. Ethnomusicology can benefit from psychological approaches to the study of music cognition in different cultures.


Genre and technique

A music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions. It is to be distinguished from '' musical form'' and ''musical style'', although in practice these terms are sometimes used interchangeably. Music can be divided into different
genres Genre () is any form or type of communication in any mode (written, spoken, digital, artistic, etc.) with socially-agreed-upon conventions developed over time. In popular usage, it normally describes a category of literature, music, or other for ...
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
form Form is the shape, visual appearance, or configuration of an object. In a wider sense, the form is the way something happens. Form also refers to: *Form (document), a document (printed or electronic) with spaces in which to write or enter data ...
. He lists
madrigal A madrigal is a form of secular vocal music most typical of the Renaissance music, Renaissance (15th–16th c.) and early Baroque music, Baroque (1600–1750) periods, although revisited by some later European composers. The Polyphony, polyphoni ...
, motet,
canzona The canzona is an Italian musical form derived from the Franco-Flemish and Parisian chansons, and during Giovanni Gabrieli's lifetime was frequently spelled canzona, though both earlier and later the singular was spelled either canzon or canzone ...
,
ricercar A ricercar ( , ) or ricercare ( , ) is a type of late Renaissance and mostly early Baroque instrumental composition. The term ''ricercar'' derives from the Italian verb which means 'to search out; to seek'; many ricercars serve a preludial funct ...
, and dance as examples of genres from the
Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...
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." Some, like 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." 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. A music genre or subgenre may also be defined by the
musical technique Musical technique is the ability of instrumental and vocal musicians to exert optimal control of their instruments or vocal cords in order to produce the precise musical effects they desire. Improving one's technique generally entails practicin ...
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". Musical technique is the ability of
instrumental An instrumental is a recording normally without any vocals, although it might include some inarticulate vocals, such as shouted backup vocals in a big band setting. Through semantic widening, a broader sense of the word song may refer to instru ...
and vocal musicians to exert optimal control of their instruments or
vocal cords In humans, vocal cords, also known as vocal folds or voice reeds, are folds of throat tissues that are key in creating sounds through vocalization. The size of vocal cords affects the pitch of voice. Open when breathing and vibrating for speec ...
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 Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...
, minor, major, and
chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce th ...
s, minor and
major triad In music theory, a major chord is a chord that has a root, a major third, and a perfect fifth. When a chord comprises only these three notes, it is called a major triad. For example, the major triad built on C, called a C major triad, has pitch ...
s, dominant and
diminished seventh In classical music from Western culture, a diminished seventh () is an interval produced by narrowing a minor seventh by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an d7 ...
s, formula patterns and arpeggios. For example, triads and sevenths teach how to play chords with accuracy and speed.
Scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number w ...
teach how to move quickly and gracefully from one note to another (usually by step). Arpeggios teach how to play
broken chord A broken chord is a chord broken into a sequence of notes. A broken chord may repeat some of the notes from the chord and span one or more octaves. An arpeggio () is a type of broken chord, in which the notes that compose a chord are played ...
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.
Heinrich Schenker Heinrich Schenker (19 June 1868 – 14 January 1935) was a Galician-born Austrian music theorist whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis, was most fully ex ...
argued that musical technique's "most striking and distinctive characteristic" is
repetition Repetition may refer to: * Repetition (rhetorical device), repeating a word within a short space of words *Repetition (bodybuilding), a single cycle of lifting and lowering a weight in strength training *Working title for the 1985 slasher film '' ...
. Works known as
étude An étude (; ) or study is an instrumental musical composition, usually short, designed to provide practice material for perfecting a particular musical skill. The tradition of writing études emerged in the early 19th century with the rapid ...
s (meaning "study") are also frequently used for the improvement of technique.


Mathematics

Music theorists sometimes use mathematics to understand music, and although music has no
axiomatic An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or ...
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". The attempt to structure and communicate new ways of composing and hearing music has led to musical applications of
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
,
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...
and
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mat ...
. Some composers have incorporated the
golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, where the Greek letter phi ( ...
and
Fibonacci numbers In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
into their work. 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, the
Pythagoreans Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...
(in particular
Philolaus Philolaus (; grc, Φιλόλαος, ''Philólaos''; ) was a Greek Pythagorean and pre-Socratic philosopher. He was born in a Greek colony in Italy and migrated to Greece. Philolaus has been called one of three most prominent figures in the Pyt ...
and Archytas) of ancient Greece were the first researchers known to have investigated the expression of
musical scale In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Often, especially in the ...
s in terms of numerical
ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
s. In the modern era, musical
set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
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 and
inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...
, one can discover deep structures in the music. Operations such as transposition and inversion are called
isometries In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' mea ...
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 In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...
with 12 elements. It is possible to describe just intonation in terms of a free abelian group.


Serial composition and set theory

In music theory, serialism is a method or technique of
composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography *Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include v ...
that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's
twelve-tone technique The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law o ...
, though his contemporaries were also working to establish serialism as one example of
post-tonal Atonality in its broadest sense is music that lacks a tonal center, or key. ''Atonality'', in this sense, usually describes compositions written from about the early 20th-century to the present day, where a hierarchy of harmonies focusing on a ...
thinking. Twelve-tone technique orders the twelve notes of the
chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce th ...
, forming a
row Row or ROW may refer to: Exercise *Rowing, or a form of aquatic movement using oars *Row (weight-lifting), a form of weight-lifting exercise Math *Row vector, a 1 × ''n'' matrix in linear algebra. *Row (database), a single, implicitly structured ...
or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and
variations Variation or Variations may refer to: Science and mathematics * Variation (astronomy), any perturbation of the mean motion or orbit of a planet or satellite, particularly of the moon * Genetic variation, the difference in DNA among individua ...
. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "
parameters A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
"), such as
duration Duration may refer to: * The amount of time elapsed between two events * Duration (music) – an amount of time or a particular time interval, often cited as one of the fundamental aspects of music * Duration (philosophy) – a theory of time and ...
, dynamics, and
timbre In music, timbre ( ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musica ...
. The idea of serialism is also applied in various ways in the visual arts, design, and architecture; "Integral serialism" or "total serialism" is the use of series for aspects such as duration, dynamics, and register as well as pitch. 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". Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by
Howard Hanson Howard Harold Hanson (October 28, 1896 – February 26, 1981)''The New York Times'' – Obituaries. Harold C. Schonberg. February 28, 1981 p. 1011/ref> was an American composer, conductor, educator, music theorist, and champion of American class ...
(1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as
Allen Forte Allen, Allen's or Allens may refer to: Buildings * Allen Arena, an indoor arena at Lipscomb University in Nashville, Tennessee * Allen Center, a skyscraper complex in downtown Houston, Texas * Allen Fieldhouse, an indoor sports arena on the Univ ...
(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. 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,
inversion Inversion or inversions may refer to: Arts * , a French gay magazine (1924/1925) * ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas * Inversion (music), a term with various meanings in music theory and musical set theory * ...
, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.


Musical semiotics

Music semiology (
semiotics Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something ...
) is the study of signs as they pertain to music on a variety of levels. Following
Roman Jakobson Roman Osipovich Jakobson (russian: Рома́н О́сипович Якобсо́н; October 11, 1896Kucera, Henry. 1983. "Roman Jakobson." ''Language: Journal of the Linguistic Society of America'' 59(4): 871–883. – July 18,Kofi Agawu adopts the idea of musical semiosis being introversive or extroversive—that is, musical signs within a text and without. "Topics," or various musical conventions (such as horn calls, dance forms, and styles), have been treated suggestively by Agawu, among others. The notion of gesture is beginning to play a large role in musico-semiotic enquiry. :"There are strong arguments that music inhabits a semiological realm which, on both
ontogenetic Ontogeny (also ontogenesis) is the origination and development of an organism (both physical and psychological, e.g., moral development), usually from the time of fertilization of the egg to adult. The term can also be used to refer to the st ...
and
phylogenetic In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups o ...
levels, has developmental priority over verbal language." Writers on music semiology include Kofi Agawu (on topical theory,
Heinrich Schenker Heinrich Schenker (19 June 1868 – 14 January 1935) was a Galician-born Austrian music theorist whose writings have had a profound influence on subsequent musical analysis. His approach, now termed Schenkerian analysis, was most fully ex ...
, Robert Hatten (on topic, gesture),
Raymond Monelle Raymond Monelle (19 August 1937 in Bristol, England – 12 March 2010 in Edinburgh, Scotland). was a music theory, music theorist, teacher, music critic, composer and jazz pianist. Monelle wrote three books, dozens of articles on music, and ...
(on topic, musical meaning),
Jean-Jacques Nattiez Jean-Jacques Nattiez (; born December 30, 1945 in Amiens, France) is a musical semiologist or semiotician and professor of musicology at the Université de Montréal. He studied semiology with Georges Mounin and Jean Molino and music semiolog ...
(on introversive taxonomic analysis and ethnomusicological applications),
Anthony Newcomb Anthony Newcomb (August 6, 1941 - November 18, 2018) was an American musicologist. He was born in New York City and studied at the University of California, Berkeley where he graduated with a Bachelor of Arts in 1962. He then studied with Gustav Le ...
(on narrativity), and
Eero Tarasti Eero Aarne Pekka Tarasti (born 27 September 1948 in Helsinki), is a Finnish musicologist and semiologist, currently serving as Professor Emeritus of Musicology at the University of Helsinki. He received his Ph.D. degree at the University of Hel ...
(generally considered the founder of musical semiotics).
Roland Barthes Roland Gérard Barthes (; ; 12 November 1915 – 26 March 1980) was a French literary theorist, essayist, philosopher, critic, and semiotician. His work engaged in the analysis of a variety of sign systems, mainly derived from Western popula ...
, himself a semiotician and skilled amateur pianist, wrote about music in ''Image-Music-Text,'' ''The Responsibilities of Form,'' and ''Eiffel Tower,'' though he did not consider music to be a semiotic system. 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'', ''Fernando the Flute'', ''Music's Meanings'') 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'' 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

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. A growing number of scholars began promoting the idea that music theory should be taught by theorists, rather than composers, performers or music historians. This led to the founding of the
Society for Music Theory The Society for Music Theory (SMT) is an American organization devoted to the promotion of music theory as a scholarly and pedagogical discipline. It currently has a membership of over 1200, primarily in the United States. In the 1970s, few schoo ...
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. 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. As part of their initial training, music theorists will typically complete a
B.Mus Bachelor of Music (BM or BMus) is an academic degree awarded by a college, university, or conservatory upon completion of a program of study in music. In the United States, it is a professional degree, and the majority of work consists of prescr ...
or a
B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...
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 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. 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 "All but dissertation" (ABD) is a term identifying a stage in the process of obtaining a research doctorate, most commonly used in the United States. In typical usage of the term, the ABD graduate student has completed the required preparatory ...
" 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 Sessional lecturer or sessional instructor are contract faculty who hold full- or part-time teaching positions and may perform administrative duties but have no research responsibilities. Sessionals hold short-term contracts, typically running ...
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 Music appreciation is a division of musicology that is designed to teach students how to understand and describe the contexts and creative processes involved in music composition. The concept of music appreciation is often taught as a subset o ...
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 Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * ...
or Chair of the School of Music.


See also

* List of music theorists *
Music psychology 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 behaviour and experience, including the processes through which music is perceived, created, ...
* Musicology *
Theory of painting The idea of founding a theory of painting after the model of music theory was suggested by Goethe in 1807 and gained much regard among the avant-garde artists of the 1920s, the Weimar culture period, like Paul Klee. From Goethe to Klee Goethe famo ...


Notes


References


Sources

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


Further reading

* Anon. (2011)
Job: Adjunct/Affiliate in Music Theory
Philadelphia: St Josephs University. * Anon. (2014).
Full-time, Tenure-track Position in Music Theory, at the Rank of Assistant Professor, Beginning Fall 2014
. Buffalo: University at Buffalo Department of Music. * Anon. (2015).
College of William and Mary: Assistant Professor of Music, Theory and Composition (Tenure Eligible)
. Job Listings, MTO (accessed 10 August 2015). * Apel, Willi, and Ralph T. Daniel (1960). ''The Harvard Brief Dictionary of Music''. New York: Simon & Schuster Inc. *
Aristoxenus Aristoxenus of Tarentum ( el, Ἀριστόξενος ὁ Ταραντῖνος; born 375, fl. 335 BC) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been ...
(1902). ''Aristoxenou Harmonika stoicheia: The Harmonics of Aristoxenus'', Greek text edited with an English translation and notes by Henry Marcam. Oxford: The Clarendon Press. * Bakkegard, B. M., and Elizabeth Ann Morris (1961). "Seventh Century Flutes from Arizona". '' Ethnomusicology'' 5, no. 3 (September): 184–186. . * Bakshi, Haresh (2005). ''101 Raga-s for the 21st Century and Beyond: A Music Lover's Guide to Hindustani Music''. Victoria, British Columbia: Trafford. (ebook). * Barnes, Latham (1984). ''The Complete Works of Aristotle''. Princeton: Princeton University Press. . * Baur, John (2014). ''Practical Music Theory''. Dubuque: Kendall-Hunt Publishing Company. * Benade, Arthur H. (1960). ''Horns, Strings, and Harmony''. Science Study Series S 11. Garden City, New York: Doubleday * Bent, Ian D., and Anthony Pople (2001). "Analysis." ''
The New Grove Dictionary of Music and Musicians ''The New Grove Dictionary of Music and Musicians'' is an encyclopedic dictionary of music and musicians. Along with the German-language ''Die Musik in Geschichte und Gegenwart'', it is one of the largest reference works on the history and theo ...
'', second edition, edited by Stanley Sadie and 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. . irst edition 1963* Benward, Bruce, and Marilyn Nadine Saker (2009). ''Music in Theory and Practice'', eighth edition, vol. 2. Boston: McGraw-Hill. . * Billmeier, Uschi (1999). ''Mamady Keïta: A Life for the Djembé – Traditional Rhythms of the Malinké'', fourth edition. Kirchhasel-Uhlstädt: Arun-Verlag. . * 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 The ''Yearbook for Traditional Music'' is a peer-reviewed academic journal covering research on folk music and dance. It is published by the International Council for Traditional Music, once a year in December. The editor-in-chief is Kati Szego. ...
'' 41:1–11. * Bregman, Albert (1994). ''Auditory Scene Analysis: The Perceptual Organization of Sound''. Cambridge: MIT Press. . * Brill, Mark (2012). "Music of the Ancient Maya: New Venues of Research". Paper presented at AMS-SW Conference Fall 2012. Texas State University * Brown, James Murray (1967). ''A Handbook of Musical Knowledge'', 2 vols. London: Trinity College of Music. * (Accessed 1 May 2010) * * 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. . * Civil, Miguel (2010). "The Lexical Texts in the Schøyen Collection". ''Cornell University Studies in Assyriology and Sumerology'' 12:203–214. *
Confucius Confucius ( ; zh, s=, p=Kǒng Fūzǐ, "Master Kǒng"; or commonly zh, s=, p=Kǒngzǐ, labels=no; – ) was a Chinese philosopher and politician of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. C ...
(1999). ''The Analects of Confucius'', edited by Roger T. Ames and Henry Rosemont Jr. Ballantine Books. . * Conrad, Nicholas J., Maria Malina, and Susanne C. Münzel (2009). "New Flutes Document the Earliest Musical Tradition in Southwestern Germany". ''
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'' 460, no. 7256 (6 August): 737–740. * Crease, Robert P. (2011). ''World in the Balance: The Historic Quest for an Absolute System of Measurement''. New York, London: W. W. Norton. * Crickmore, Leon (2012). "A Musicological Interpretation of the Akkadian Term Sihpu". ''
Journal of Cuneiform Studies The ''Journal of Cuneiform Studies'' was founded in 1947 by the Baghdad School of the American Schools of Oriental Research. The journal presents articles about ancient Mesopotamian language and history in English, French and German. Extern ...
'' 64:57–64. * Chase, Wayne (2006). ''How Music REALLY Works!'', second edition. Vancouver, Canada: Roedy Black Publishing. (book). * 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).
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. . * * Dunbar, Brian (2010). ''Practical Music Theory: A Guide to Music as Art, Language, and Life''. Rochester, MN: Factum Musicae. . * * Haas, Shady R., and J. W. Creamer (2001).
Dating Caral, a Pre-ceramic Site in the Supe Valley on the Central Coast of Peru
. ''
Science Science is a systematic endeavor that Scientific method, builds and organizes knowledge in the form of Testability, testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earli ...
'' 292: 723–726. . * 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. . * Hewitt, Michael (2008). ''Music Theory for Computer Musicians''. United States: Cengage Learning. . * Houtsma, Adrianus J. M. (1995).
Pitch Perception
. In ''Hearing'', Handbook of Perception and Cognition Volume 2, second edition, edited by Brian C. J. Moore, 267–295. San Diego and London. Academic Press. . * Huang, Xiang-peng (黄翔鹏) (1989). "Wuyang Jiahu gudi de ceyin yanjiu (舞阳贾湖骨笛的测音研究)" itch Measurement Studies of Bone Flutes from Jiahu of Wuyang County ''Wenwu'' (文物) ultural Relics no. 1:15–17. Reprinted in 黄翔鹏文存 ollected 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. . * Hung, Eric (2012).
Western University, Don Wright Faculty of Music: Tenure-Track Appointment in Music Theory
. Toronto: MusCan. * Jackendoff, Ray and
Fred Lerdahl Alfred Whitford (Fred) Lerdahl (born March 10, 1943, in Madison, Wisconsin) is the Fritz Reiner Professor Emeritus of Musical Composition at Columbia University, and a composer and music theorist best known for his work on musical grammar and co ...
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Journal of Music Theory The ''Journal of Music Theory'' is a peer-reviewed academic journal specializing in music theory and analysis. It was established by David Kraehenbuehl (Yale University) in 1957. According to its website, " e ''Journal of Music Theory'' fosters ...
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Kostka, Stefan Stefan M. Kostka (born 1939) is an American music theorist, author, and Professor Emeritus of music theory at the University of Texas at Austin. Education Kostka graduated from the University of Colorado with a Bachelor's Degree, and then receiv ...
, and Dorothy Payne (2004). ''Tonal Harmony'', fifth edition. New York: McGraw-Hill. * Kubik, Gerhard (1998). ''Kalimba—Nsansi—Mbira. Lamellophone in Afrika''. Berlin: Museum fur Volkerkunde. . * 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''. .p. Alfred Publishing Co. . * Lee, Yuan-Yuan, and Sin-Yan Shen (1999). ''Chinese Musical Instruments''. Chinese Music Monograph Series. Chicago: Chinese Music Society of North America Press. . * 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. . * Lu, Liancheng (2005). "The Eastern Zhou and the Growth of Regionalism". In ''The Formation of Chinese Civilization'', edited by
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Journal of the Acoustical Society of America The ''Journal of the Acoustical Society of America'' is a monthly peer-reviewed scientific journal covering all aspects of acoustics. It is published by the Acoustical Society of America and the editor-in-chief is James F. Lynch (Woods Hole Oceanog ...
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Music & Letters ''Music & Letters'' is an academic journal published quarterly by Oxford University Press with a focus on musicology. The journal sponsors the Music & Letters Trust, twice-yearly cash awards of variable amounts to support research in the music fie ...
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he relation of Jiahu bone flutes and turtle shell shakers to the origin of Chinese music He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' ...
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External links


Music theory resources
* Dillen, Oscar van
Outline of basic music theory
(2011)
Why A Little Bit of Theory Matters
* * * {{DEFAULTSORT:Music Theory Music history Musicology