Music theory is the study of theoretical frameworks for understanding the practices and possibilities ofmusic.The Oxford Companion to Music describes three interrelated uses of the term "music theory": The first is the "rudiments", that are needed to understandmusic notation (key signatures,time signatures, andrhythmic notation); the second is learning scholars' views on music fromantiquity to the present; the third is a sub-topic ofmusicology 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."[1]
Music theory is frequently concerned with describing how musicians and composers make music, includingtuning systems and composition methods among other topics. Because of the ever-expanding conception ofwhat 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 theQuadriviumliberal arts university curriculum, that was common inmedieval Europe, was an abstract system of proportions that was carefully studied at a distance from actual musical practice.[n 1] 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.[n 2]
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, and otherartifacts. For example, ancient instruments fromprehistoric 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 writtentreatises andmusic 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 asscholarly writing cites earlier research.
In modern academia, music theory is a subfield ofmusicology, the wider study of musical cultures and history.Guido Adler, however, in one of the texts that founded musicology in the late 19th century, wrote that "the science of music originated at the same time as the art of sounds",[3] where "the science of music" (Musikwissenschaft) obviously meant "music theory". Adler added that music only could exist when one began measuring pitches and comparing them to each other. He concluded that "all people for which one can speak of an art of sounds also have a science of sounds".[4] One must deduce that music theory exists in all musical cultures of the world.
Music theory is often concerned with abstract musical aspects such astuning and tonal systems,scales,consonance and dissonance, and rhythmic relationships. There is also a body of theory concerning practical aspects, such as the creation or the performance of music,orchestration,ornamentation, improvisation, andelectronic sound production.[5] A person who researches or teaches music theory is a music theorist. University study, typically to theMA orPhD 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 theorytextbooks, especially in the United States of America, often include elements ofmusical acoustics, considerations ofmusical notation, and techniques of tonalcomposition (harmony andcounterpoint), among other topics.
Several survivingSumerian andAkkadianclay tablets include musical information of a theoretical nature, mainly lists ofintervals andtunings.[6] 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 [about music] are united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years."[7]
Much of Chinese music history and theory remains unclear.[8]
Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, Five refers to the Pentatonic Scale (primarily uses a 5-note scale), And Eight refers to the eight categories of Chinese Music Instruments; classified by the material they are made from: (Metal, Stone, Silk, Bamboo, Gourd, Clay, Leather, and Wood). TheLüshi chunqiu from about 238 BCE recalls the legend ofLing Lun. On order of theYellow Emperor, Ling Lun collected twelvebamboo lengths with thick and even nodes. Blowing on one of these like a pipe, he found its sound agreeable and named ithuangzhong, the "Yellow Bell." He then heardphoenixes 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 thelülü or later theshierlü.[9]
Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as the nature and functions of music. TheYueji ("Record of music", c1st and 2nd centuries BCE), for example, manifestsConfucian 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 ofMozi (c. 468 – c. 376 BCE) that music wasted human and material resources, andLaozi's claim that the greatest music had no sounds. [...] Even the music of theqin zither, a genre closely affiliated with Confucian scholar-officials, includes many works withDaoist references, such asTianfeng huanpei ("Heavenly Breeze and Sounds of Jade Pendants").[8]
TheSamaveda andYajurveda (c. 1200 – 1000 BCE) are among the earliest testimonies of Indian music, but properly speaking, they contain no theory. TheNatya 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.[10]
Early preserved Greek writings on music theory include two types of works:[11]
Several names of theorists are known before these works, includingPythagoras (c. 570 ~c. 495 BCE),Philolaus (c. 470 ~ (c. 385 BCE),Archytas (428–347 BCE), and others.
Works of the first type (technical manuals) include
More philosophical treatises of the second type include
Thepipa instrument carried with it a theory of musical modes that subsequently led to the Sui and Tang theory of 84 musical modes.[8]
Medieval Arabic music theorists include:[n 3]
The Latin treatiseDe institutione musica by the Roman philosopherBoethius (written c. 500, translated asFundamentals of Music[2]) 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.[21] 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 theplainchant tradition.[22] At the end of the ninth century,Hucbald worked towards more precise pitch notation for theneumes used to record plainchant.
Guido d'Arezzo wrote a letter to Michael of Pomposa in 1028, entitledEpistola de ignoto cantu,[23] in which he introduced the practice of using syllables to describe notes and intervals. This was the source of the hexachordalsolmization 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.[21]
During the thirteenth century, a new rhythm system calledmensural notation grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatiseArs cantus mensurabilis ("The art of measured chant") byFranco of Cologne (c. 1280). Mensural notation used different note shapes to specify different durations, allowing scribes to capture rhythms which varied instead of repeating the same fixed pattern; it is a proportional notation, in the sense that each note value is equal to two or three times the shorter value, or half or a third of the longer value. This same notation, transformed through various extensions and improvements during the Renaissance, forms the basis for rhythmic notation inEuropean classical music today.
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.[20]
Music is composed ofaural 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.[27]
Pitch is the lowness or highness of atone, for example the difference betweenmiddle 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.[28]
Specific frequencies are often assigned letter names. Today most orchestras assignconcert A (the A abovemiddle 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, inhistorically 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 aninterval. The most basic interval is theunison, which is simply two notes of the same pitch. Theoctave 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 ofpitch class: pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring the difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's.[29]
Musical tuning systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. InWestern culture, there have long been several competing tuning systems, all with different qualities. Internationally, the system known asequal 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.
Notes can be arranged in a variety ofscales andmodes. Western music theory generally divides the octave into a series of twelve pitches, called achromatic scale, within which the interval between adjacent tones is called asemitone, or half step. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales.[30]
The most commonly encountered scales are the seven-tonedmajor, theharmonic minor, themelodic minor, and thenatural minor. Other examples of scales are theoctatonic scale and thepentatonic or five-tone scale, which is common infolk music andblues. Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classicalOttoman,Persian,Indian andArabic 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.[30]
In traditional Western notation, the scale used for a composition is usually indicated by akey signature at the beginning to designate the pitches that make up that scale. As the music progresses, the pitches used may change and introduce a different scale. Music can betransposed 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 awhole tone. Since the interval relationships remain unchanged, transposition may be unnoticed by a listener, however other qualities may change noticeably because transposition changes the relationship of the overall pitchrange 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.[31]
The interrelationship of the keys most commonly used in Western tonal music is conveniently shown by thecircle of fifths. Unique key signatures are also sometimes devised for a particular composition. During the Baroque period, emotional associations with specific keys, known as thedoctrine of the affections, were an important topic in music theory, but the unique tonal colorings of keys that gave rise to that doctrine were largely erased with the adoption of equal temperament. However, many musicians continue to feel that certain keys are more appropriate to certain emotions than others.Indian classical music theory continues to strongly associate keys with emotional states, times of day, and other extra-musical concepts and notably, does not employ equal temperament.
Consonance and dissonance 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.[32]
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 theCommon 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.[32]
Rhythm is produced by the sequential arrangement of sounds and silences in time.Meter measures music in regular pulse groupings, calledmeasures or bars. Thetime signature or meter signature specifies how many beats are in a measure, and which value of written note is counted or felt as a single beat.
Through increased stress, or variations in duration or articulation, particular tones may be accented. There are conventions in most musical traditions for regular and hierarchical accentuation of beats to reinforce a given meter.Syncopated rhythms contradict those conventions by accenting unexpected parts of the beat.[33] Playing simultaneous rhythms in more than one time signature is calledpolyrhythm.[34]
In recent years, rhythm and meter have become an important area of research among music scholars. The most highly cited of these recent scholars areMaury Yeston,[35]Fred Lerdahl andRay Jackendoff,[36]Jonathan Kramer,[37] and Justin London.[38]
Amelody is a group of musical sounds in agreeable succession or arrangement.[40] 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 asscales ormodes. 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.[41]
A chord, in music, is anyharmonic set of three or morenotes that is heard as if soundingsimultaneously.[42]: pp. 67, 359 [43]: p. 63 These need not actually be played together:arpeggios and broken chords may, for many practical and theoretical purposes, constitute chords. Chords andsequences of chords are frequently used in modern Western, West African,[44] and Oceanian[45] music, whereas they are absent from the music of many other parts of the world.[46]: p. 15
The most frequently encountered chords aretriads, so called because they consist of three distinct notes: further notes may be added to giveseventh chords,extended chords, oradded tone chords. The mostcommon chords are themajor andminortriads and then theaugmented anddiminishedtriads. The descriptionsmajor,minor,augmented, anddiminished are sometimes referred to collectively as chordalquality. Chords are also commonly classed by theirroot note—so, for instance, the chordC major may be described as a triad of major quality built on the noteC. Chords may also be classified byinversion, the order in which the notes are stacked.
A series of chords is called achord progression. Although any chord may in principle be followed by any other chord, certain patterns of chords have been accepted as establishingkey incommon-practice harmony. To describe this, chords are numbered, usingRoman numerals (upward from the key-note),[47] per theirdiatonic function. Common ways ofnotating or representing chords[48] in western music other than conventionalstaff notation includeRoman numerals,figured bass (much used in theBaroque era),chord letters (sometimes used in modernmusicology), and various systems ofchord charts typically found in thelead sheets used inpopular music to lay out the sequence of chords so that the musician may play accompaniment chords or improvise a solo.
In music, harmony is the use of simultaneouspitches (tones,notes), orchords.[46]: p. 15 The study of harmony involves chords and their construction andchord progressions and the principles of connection that govern them.[49] Harmony is often said to refer to the "vertical" aspect of music, as distinguished frommelodic line, or the "horizontal" aspect.[50]Counterpoint, which refers to the interweaving of melodic lines, andpolyphony, which refers to the relationship of separate independent voices, is thus sometimes distinguished from harmony.[51]
Inpopular andjazz harmony, chords are named by theirroot plus various terms and characters indicating their qualities. For example, alead sheet may indicate chords such as C major, D minor, and G dominant seventh. In many types of music, notably Baroque, Romantic, modern, and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relativelydissonant 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 classicalcommon practice period a dissonant chord (chord with tension) "resolves" to a consonant chord.Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and "relaxed" moments.[52][unreliable source?]
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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,"[53] but can be accurately described and analyzed byFourier analysis and other methods[54] because it results from the combination of all soundfrequencies, attack and release envelopes, and other qualities that a tone comprises.
Timbre is principally determined by two things: (1) the relative balance ofovertones produced by a given instrument due its construction (e.g. shape, material), and (2) theenvelope of the sound (including changes in the overtone structure over time). Timbre varies widely between different instruments, voices, and to lesser degree, between instruments of the same type due to variations in their construction, and significantly, the performer's technique. The timbre of most instruments can be changed by employing different techniques while playing. For example, the timbre of a trumpet changes when a mute is inserted into the bell, the player changes their embouchure, or volume.[citation needed]
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 worddolce (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 likemarcato (^) and dynamic indications (pp) can also indicate changes in timbre.[55]
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In music, "dynamics" normally refers to variations of intensity or volume, as may be measured by physicists and audio engineers indecibels orphons. 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 likeforte (f) for loud andpiano (p) for soft. These two basic notations are modified by indications includingmezzo piano (mp) for moderately soft (literally "half soft") andmezzo forte (mf) for moderately loud,sforzando orsforzato (sfz) for a surging or "pushed" attack, orfortepiano (fp) for a loud attack with a sudden decrease to a soft level. The full span of these markings usually range from a nearly inaudiblepianissississimo (pppp) to a loud-as-possiblefortissississimo (ffff).
Greater extremes ofpppppp andfffff and nuances such asp+ orpiù 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 ordecrescendo), often called "hairpins" when indicated with diverging or converging lines as shown in the graphic above.
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Articulation is the way the performer sounds notes. For example,staccato is the shortening of duration compared to the written note value,legato performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation.
For example,staccato is often referred to as "separated" or "detached" rather than having a defined or numbered amount by which to reduce the notated duration. Violin players use a variety of techniques to perform different qualities ofstaccato. The manner in which a performer decides to execute a given articulation is usually based on the context of the piece or phrase, but many articulation symbols and verbal instructions depend on the instrument and musical period (e.g. viol, wind; classical, baroque; etc.).
There is a set of articulations that most instruments and voices perform in common. They are—from long to short:legato (smooth, connected);tenuto (pressed or played to full notated duration);marcato (accented and detached);staccato ("separated", "detached");martelé (heavily accented or "hammered").[contradictory] Many of these can be combined to create certain "in-between" articulations. For example,portato is the combination oftenuto andstaccato. Some instruments have unique methods by which to produce sounds, such asspiccato for bowed strings, where the bow bounces off the string.
In music, texture is how themelodic,rhythmic, andharmonic materials are combined in acomposition, thus determining the overall quality of the sound in a piece. Texture is often described in regard to the density, or thickness, andrange, 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, thetimbre of the instruments or voices playing these parts and the harmony,tempo, and rhythms used.[57] 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.[58][incomplete short citation]
Common types includedmonophonic 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 andhomophonic texture (chords accompanying a melody).[citation needed]
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.[60] In the tenth edition ofThe Oxford Companion to Music,Percy Scholes defines musical form as "a series of strategies designed to find a successful mean between the opposite extremes of unrelieved repetition and unrelieved alteration."[61] According toRichard Middleton, musical form is "the shape or structure of the work." He describes it through difference: the distance moved from arepeat; the latter being the smallest difference. Difference is quantitative and qualitative:how far, andof what type, different. In many cases, form depends on statement andrestatement, unity and variety, andcontrast and connection.[62]
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.[clarification needed] 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 recognizableemotion, ideally causing asympathetic emotional response in its listeners.[63] 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., anational anthem), but can rarely be completely separated from its context.[citation needed]
The components of musical expression continue to be the subject of extensive and unresolved dispute.[64][65][66][67][68][69]
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.[70] In the 2000s, computerfile formats have become important as well.[71] Spoken language andhand 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 astaff 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 handwrittenchord chart indicating the song'schord progression using chord names (e.g., C major, D minor, G7, etc.). All of the chord voicings, rhythms and accompaniment figures are improvised by the band members.
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.
Musical analysis is the attempt to answer the questionhow 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 toIan Bent, "analysis, as a pursuit in its own right, came to be established only in the late 19th century; its emergence as an approach and method can be traced back to the 1750s. However, it existed as a scholarly tool, albeit an auxiliary one, from theMiddle Ages onwards."[72][incomplete short citation]Adolf Bernhard Marx was influential in formalising concepts about composition and music understanding towards the second half of the 19th century. The principle of analysis has been variously criticized, especially by composers, such asEdgard Varèse's claim that, "to explain by means of [analysis] is to decompose, to mutilate the spirit of a work".[73]
Schenkerian analysis is a method of musical analysis of tonal music based on the theories ofHeinrich Schenker (1868–1935). The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work and to help reading the score according to that structure. The theory's basic tenets can be viewed as a way of definingtonality 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 varioustechniques of elaboration. The most fundamental concept of Schenker's theory of tonality may be that oftonal space.[74] The intervals between the notes of the tonic triad form atonal 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 thefundamental structure (Ursatz) to reach the score, the practice of Schenkerian analysis more often is reductive, starting from the score and showing how it can be reduced to its fundamental structure. The graph of theUrsatz is arrhythmic, as is a strict-counterpoint cantus firmus exercise.[75] 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 issubjective. There is no mechanical procedure involved and the analysis reflects the musical intuitions of the analyst.[76] The analysis represents a way of hearing (and reading) a piece of music.
Transformational theory is a branch of music theory developed byDavid Lewin in the 1980s, and formally introduced in his 1987 work,Generalized Musical Intervals and Transformations. The theory, which modelsmusical transformations as elements of amathematical group, can be used to analyze bothtonal andatonal music. The goal of transformational theory is to change the focus from musical objects—such as the "Cmajor chord" or "G major chord"—to relations between objects. Thus, instead of saying that a C major chord is followed by G major, a transformational theorist might say that the first chord has been "transformed" into the second by the "Dominant operation." (Symbolically, one might write "Dominant(C major) = G major.") While traditionalmusical set theory focuses on the makeup of musical objects, transformational theory focuses on theintervals or types of musical motion that can occur. According to Lewin's description of this change in emphasis, "[The transformational] attitude does not ask for some observed measure of extension between reified 'points'; rather it asks: 'If I amat s and wish to get to t, what characteristicgesture should I perform in order to arrive there?'"[77]
Music psychology or the psychology of music may be regarded as a branch of bothpsychology andmusicology. It aims to explain and understand musicalbehavior andexperience, including the processes through which music is perceived, created, responded to, and incorporated into everyday life.[78][79] Modern music psychology is primarilyempirical; its knowledge tends to advance on the basis of interpretations of data collected by systematicobservation of and interaction withhuman participants. Music psychology is a field of research with practical relevance for many areas, including musicperformance,composition,education,criticism, andtherapy, as well as investigations of humanaptitude, skill,intelligence, creativity, andsocial behavior.
Music psychology can shed light on non-psychological aspects ofmusicology and musical practice. For example, it contributes to music theory through investigations of theperception andcomputational modelling of musical structures such asmelody,harmony,tonality,rhythm,meter, andform. Research inmusic history can benefit from systematic study of the history ofmusical syntax, or from psychological analyses of composers and compositions in relation to perceptual, affective, and social responses to their music.
A music genre is a conventional category that identifies some pieces of music as belonging to a shared tradition or set of conventions.[80] It is to be distinguished frommusical form andmusical style, although in practice these terms are sometimes used interchangeably.[81][failed verification]
Music can be divided into differentgenres 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 termgenreitself. In his bookForm in Tonal Music, Douglass M. Green distinguishes between genre andform. He listsmadrigal,motet,canzona,ricercar, and dance as examples of genres from theRenaissance period. To further clarify the meaning ofgenre, 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 theAgnus Dei from his Mass, K. 317 are quite different in genre but happen to be similar in form."[82] Some, likePeter van der Merwe, treat the termsgenre andstyle as the same, saying thatgenre should be defined as pieces of music that came from the same style or "basic musical language."[83]
Others, such as Allan F. Moore, state thatgenre andstyle are two separate terms, and that secondary characteristics such as subject matter can also differentiate between genres.[84] A music genre or subgenre may also be defined by themusical techniques, 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".[85]
Musical technique is the ability ofinstrumental and vocal musicians to exert optimal control of their instruments orvocal cords to produce precise musical effects. Improving technique generally entails practicing exercises that improve muscular sensitivity and agility. To improve technique, musicians often practice fundamental patterns of notes such as thenatural,minor,major, andchromatic scales,minor andmajor triads,dominant anddiminished sevenths, formula patterns andarpeggios. For example,triads andsevenths teach how to play chords with accuracy and speed.Scales teach how to move quickly and gracefully from one note to another (usually by step). Arpeggios teach how to playbroken chords over larger intervals. Many of these components of music are found in compositions, for example, a scale is a very common element of classical and romantic era compositions.[citation needed]
Heinrich Schenker argued that musical technique's "most striking and distinctive characteristic" isrepetition.[86] Works known asétudes (meaning "study") are also frequently used for the improvement of technique.
Music theorists sometimes use mathematics to understand music, and although music has noaxiomatic 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".[87] The attempt to structure and communicate new ways of composing and hearing music has led to musical applications ofset theory,abstract algebra andnumber theory. Some composers have incorporated thegolden ratio andFibonacci numbers into their work.[88][89] 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,[90] thePythagoreans (in particularPhilolaus andArchytas)[91] of ancient Greece were the first researchers known to have investigated the expression ofmusical scales in terms of numericalratios.
In the modern era, musicalset theory uses the language of mathematical set theory in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such astransposition andinversion, one can discover deep structures in the music. Operations such as transposition and inversion are calledisometries 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 anabelian group with 12 elements. It is possible to describejust intonation in terms of afree abelian group.[92]
In music theory, serialism is a method or technique ofcomposition that uses a series of values to manipulate differentmusical elements. Serialism began primarily withArnold Schoenberg'stwelve-tone technique, though his contemporaries were also working to establish serialism as one example ofpost-tonal thinking. Twelve-tone technique orders the twelve notes of thechromatic scale, forming arow or series and providing a unifying basis for a composition'smelody,harmony, structural progressions, andvariations. Other types of serialism also work withsets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "parameters"), such asduration,dynamics, andtimbre. The idea of serialism is also applied in various ways in the visual arts, design, and architecture[93]
"Integral serialism" or "total serialism" is the use of series for aspects such as duration, dynamics, and register as well as pitch.[94] 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".[95]
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated byHoward Hanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such asAllen Forte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.[citation needed]
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 astransposition,inversion, andcomplementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.[citation needed]
Music semiology (semiotics) is the study of signs as they pertain to music on a variety of levels. FollowingRoman Jakobson,Kofi Agawu adopts the idea of musical semiosis being introversive or extroversive—that is, musical signs within a text and without.[citation needed] "Topics", or various musical conventions (such as horn calls, dance forms, and styles), have been treated suggestively by Agawu, among others.[citation needed] The notion ofgesture is beginning to play a large role in musico-semiotic enquiry.[citation needed]
Writers on music semiology include Kofi Agawu (on topical theory,[citation needed]Heinrich Schenker,[104][105] Robert Hatten (on topic, gesture)[citation needed],Raymond Monelle (on topic, musical meaning)[citation needed],Jean-Jacques Nattiez (on introversive taxonomic analysis and ethnomusicological applications)[citation needed],Anthony Newcomb (on narrativity)[citation needed], andEero Tarasti[citation needed].
Roland Barthes, himself a semiotician and skilled amateur pianist, wrote about music inImage-Music-Text,[full citation needed]The Responsibilities of Form,[full citation needed] andEiffel Tower,[full citation needed] though he did not consider music to be a semiotic system[citation needed].
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 ofPhilip Tagg (Ten Little Tunes,[full citation needed]Fernando the Flute,[full citation needed]Music's Meanings[full citation needed]) 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 ofLeonard B. Meyer inStyle and Music[full citation needed] theorizes the relationship between ideologies and musical structures and the phenomena of style change, and focuses on romanticism as a case study.
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.[106] A growing number of scholars began promoting the idea that music theory should be taught by theorists, rather than composers, performers or music historians.[106] This led to the founding of theSociety for Music Theory in the United States in 1977. In Europe, the FrenchSociété d'Analyse musicale was founded in 1985. It called the First European Conference of Music Analysis for 1989, which resulted in the foundation of theSociété belge d'Analyse musicale in Belgium and theGruppo analisi e teoria musicale in Italy the same year, theSociety for Music Analysis in the UK in 1991, theVereniging voor Muziektheorie in the Netherlands in 1999 and theGesellschaft für Musiktheorie in Germany in 2000.[107] They were later followed by the Russian Society for Music Theory in 2013, the Polish Society for Music Analysis in 2015 and theSociedad de Análisis y Teoría Musical in Spain in 2020, and others are in construction. These societies coordinate the publication of music theory scholarship and support the professional development of music theory researchers. They formed in 2018 a network of European societies for Theory and/or Analysis of Music, theEuroT&AM
As part of their initial training, music theorists will typically complete aB.Mus or aB.A. in music (or a related field) and in many cases an M.A. in music theory. Some individuals apply directly from a bachelor's degree to a PhD, and in these cases, they may not receive an M.A. In the 2010s, given the increasingly interdisciplinary nature of university graduate programs, some applicants for music theory PhD programs may have academic training both in music and outside of music (e.g., a student may apply with a B.Mus. and a Masters in Music Composition or Philosophy of Music).
Most music theorists work as instructors, lecturers or professors in colleges, universities orconservatories. 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" 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 assessional lecturers. 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 asMusic appreciation or Introduction to Music Theory), conducting research in this area of expertise, publishing research articles in peer-reviewed journals, authoring book chapters, books or textbooks, traveling to conferences to present papers and learn about research in the field, and, if the program includes a graduate school, supervising M.A. and PhD students and giving them guidance on the preparation of their theses and dissertations. Some music theory professors may take on senior administrative positions in their institution, such asDean or Chair of the School of Music.
Syncopation is achieved by accenting a weak instead of a strong beat, by putting rests on strong beats, by holding on over strong beats, and by introducing a sudden change of time‐signature.
The superposition of different rhythms or metres.
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