Music theory

Music theory is the study of the practices and possibilities of music. It generally derives from observation of how musicians and composers make music, but includes hypothetical speculation. Most commonly, the term describes the academic study and analysis of fundamental elements of music such as pitch, rhythm, harmony, and form, but also refers to descriptions, concepts, or beliefs related to music. Because of the ever-expanding conception of what constitutes music (see Definition of music), a more inclusive definition could be that music theory is the consideration of any sonic phenomena, including silence, as it relates to music.

Music theory is a subfield of musicology, which is itself a subfield within the overarching field of the arts and humanities. Etymologically, music theory is an act of contemplation of music, from the Greek θεωρία, a looking at, viewing, contemplation, speculation, theory, also a sight, a spectacle.^[1] As such, it is often concerned with abstract musical aspects such as tuning and tonal systems, scales, consonance and dissonance, and rhythmic relationships, but there is also a body of theory concerning such practical aspects as the creation or the performance of music, orchestration, ornamentation, improvisation, and electronic sound production.^[2] A person working in music theory is a music theorist. Methods of analysis include mathematics, graphic analysis, and, especially, analysis enabled by Western music notation. Comparative, descriptive, statistical, and other methods are also used.

The development, preservation, and transmission of music theory may be found in oral and practical music-making traditions, musical instruments, and other artifacts. For example, ancient instruments from Mesopotamia, China,^[3] and 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 (see History of music and Musical instrument). In ancient and living cultures around the world, the deep and long roots of music theory are clearly visible in instruments, oral traditions, and current music making. Many cultures, at least as far back as ancient Mesopotamia, Pharoanic Egypt, and ancient China have also considered music theory in more formal ways such as written treatises and music notation.

History of music theory

The beginnings of music theory can be observed in extremely ancient instruments, artifacts, and later, depictions of performance in artworks.

As early as the Paleolithic, it appears people considered elements of music in some way. For instance, a bone flute with carefully placed finger holes found in Hohle Fels in Germany and dated c.35,000 BCE,^[4] may be a prehistoric example of the manufacture of an instrument to produce a preconceived set of pitches. For further discussion of Upper Paleolithic flutes, see d'Errico, et al. 2003, 39–48.

Similar bone flutes (gǔdí, 贾湖骨笛) from Neolithic Jiahu, China dated c. 7,000 BCE^[5] reveal their makers progressively added more holes to expand their scales, structured pitch intervals closer to each other to adjust tuning, and could play increasingly expressive and varied music.^[6] "Tonal analysis of the flutes revealed that the seven holes [in some of the flutes] correspond to a tone scale remarkably similar to Western eight-pitch scales."^[7][8] These instruments^[9] indicate their makers became familiar with acoustics and developed theories of music comparable to those of later times. Audio recordings of two of these flutes by Brookhaven National Laboratory are available here.

In North America, similar flutes from the Anasazi Indian culture were found in Arizona and dated c. 600–750 CE, but again, suggest an older tradition. These instruments typically have six finger holes ranging one and a half octaves.^[10] As with all these ancient flutes, it is likely an error to imagine the Anasazi flutes were limited to only as many tones as they have holes. Changes in embouchure, overblowing, and cross-fingering are common techniques on modern flutes like these that produce a much larger range of notes within an octave and in octaves above the fundamental octave.^[11]

The earliest known examples of written music theory are inscribed on clay tablets found in Iraq and Syria, some of which contain lists of intervals and other details^[12][13] from which "...musicologists have been able to produce credible reconstructions of the Mesopotamian tonal and tuning systems."^[14] Tablets from Ugarit contain what are known as the Hurrian songs or Hurrian Hymns dated c. 1,400 BCE. An interpretation of the only substantially complete Hurrian Hymn, h.6, may be heard here. The system of phonetic notation in Sumer and Babylonia is based on a music terminology that gives individual names to nine musical strings or "notes", and to fourteen basic terms describing intervals of the fourth and fifth that were used in tuning string instruments (according to seven heptatonic diatonic scales), and terms for thirds and sixths that appear to have been used to fine tune (or temper in some way) the seven notes generated for each scale.^{[15][16][17][18][19]}

Over time, many cultures began to record their theories of music in writing by describing practices and theory that was previously developed and passed along through oral tradition. In cultures where no written examples exist, oral traditions indicate a long history of theoretical consideration, often with unique concepts of use, performance, tuning and intervals, and other fundamental elements of music. The Vedas, the sacred texts of India (c. 1,000–500 BCE) contain theoretical discussion of music in the Sama Veda and Yajur-Veda. The Natya Shastra,^[20] written between 200 BCE to 200 CE and attributed to Bharata Muni, discusses classes of melodic structure, intervals, consonance and dissonance, performance, and other theoretical aspects such a "shruti," defined as the least perceivable difference between two pitches.^[21]

The music of pre-Columbian Mesoamerica is known through the many instruments discovered. Thirty-two condor-bone flutes and thirty-seven cornet-like instruments made of deer and llama bones have been recovered from a site at Caral, Peru dating to c. 2,100 BCE.^[22][23][24] Flute No. 15 produces five distinct fundamental tones. A Mayan marimba-like instrument (c. 350 CE), made from five turtle shells of decreasing sizes suspended on a wooden frame, has been discovered in Belize.^[25]

Later artwork depicts ensemble and solo performance. Taken together, this evidence does not in itself demonstrate anything about music theory in Mesoamerica from at least 2,000 BCE, though "...it is widely accepted that finds and depictions of ancient musical instruments are not only markers of musical traditions in space and time. … The information obtained from the archaeological record can be deepened considerably when ancient scripts, historical treaties, and other written sources concerning music are related. Such documents offer notes on performance practices and their sociocultural contexts. For some cultures, hints concerning ancient music theory and musical aesthetics may also be found."^[26]

Music theory in ancient Africa can also be seen in instruments .^[27] The Mbira, a wood or bamboo-tined instrument similar to a Kalimba, appeared on the west coast of Africa about 3,000 years ago, and metal-tined lamellophones appeared in the Zambezi River valley around 1,300 years ago.^[28] In the 20th century, these instruments produce a number of tones, ranging to 32 separate pitches, and demonstrate a great variety of tunings—tunings "so dissimilar as to offer no apparent common foundation", something that might have been expected at least by 1932.^[29] The djembé, a common type of drum, likely originated from earlier, extremely ancient drums.^[30] Djembé ensembles create complex polyrhythmic patterns,^[31] but produce a variety of pitches depending on size and playing technique, usually producing at least three separate tones.^[32] African music theory is also preserved in oral and cultural traditions that are one example of the great variety of concepts of fundamental aspects of music around the world.^[33]

In China, a variety of wind, string, percussion instruments, and written descriptions and drawings of them from the Shang Dynasty (c.16th to 11th century BCE), show sophisticated form and design.^[34] During the Zhou Dynasty (c. 1046–256 BC), a formal system of court and ceremonial music later termed "yayue" was established. As early as the 7th century BCE, a system of pitch generation was described based on a ratio of 2:3 and a pentatonic scale was derived from the cycle of fifths,^[35] the beginnings of which appear in 7,000 year-old Jiahu bone flutes. In the tomb of the Marquis Yi of Zeng (5th century BCE), among many other instruments, a set of bronze chime bells were found that sound five complete seven note octaves in the key of C Major and include twelve semitones.^[36] The Analects of Confucius, believed to have been written c. 475 to 221 BC, discuss the aesthetics of what Confucius considered the most benevolent form and use of music, in contrast to popular music of his time—an example of early music criticism and consideration of aesthetics.^[37][38]

Around the time of Confucius, the ancient Greeks, notably Pythagoras (c. 530 BCE), Aristotle (c. 350 BCE),^[39] Aristoxenus (c. 335 BCE),^[40] and later Ptolemy (c. 120 CE),^[41] speculated and experimented with ideas that became the basis of music theory in Middle Eastern and Western cultures during the Middle Ages as can be seen, for example, in the writing of Boethius in 5th century Rome^[42] and Yunus al-Katibin 7th century Medina.^[43] Middle Eastern and Western theory diverged in different directions from ancient Greek theory and created what are now two distinctly different bodies of theory and styles of music.

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.^[44][45]

Major contributors to the field include the ancient Greeks: Archytas, Aristotle, ristoxenus, Eratosthenes, Plato, Pythagoras, and later Ptolemy. The Middle Ages of Europe had Boethius, Franco of Cologne, Guido of Arezzo, Hucbald of Saint-Amand, Jacob of Liège, and Jean de Muris. Later in Europe, Zarlino, Rameau, Werckmeister, and Fux helped further musical knowledge. More recently, Riemann, Schenker, Boulanger, and Schoenberg contributed (see List of music theorists). Musical theorists in India include Bharata Muni, Vishnu Narayan Bhatkhande, Purandara Dasa, and Sharngadeva. The Middle East had Ibn Misjah, Ibrahim al-Mawsili. and his son Ishaq, Yunus al-Katib, Ibn Sina (known in Europe as Avicenna). China had Confucius, Yong Menzhoue, and Cao Rou.

Fundamentals of music

Music is composed of aural phenomena, and "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.^[46]

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 we rarely hear a single frequency or pure pitch. In music, tones, even those sounded by solo instruments or voices, are usually a complex combination of frequencies, and therefore a mix of pitches. Accordingly, theorists often describe pitch as a subjective sensation.^[47]

Most people appear to possess relative pitch, which means they perceive each note relative to some reference pitch, or as some interval from the previous pitch. Significantly fewer people demonstrate absolute pitch (or perfect pitch), the ability to identify pitches without comparison to another pitch. Human perception of pitch can be comprehensively fooled to create auditory illusions. Despite these perceptual oddities, perceived pitch is nearly always closely connected with the fundamental frequency of a note, with a lesser connection to sound pressure level, harmonic content (complexity) of the sound, and to the immediately preceding history of notes heard.^[48] In general, the higher the frequency of vibration, the higher the perceived pitch. The lower the frequency, the lower the pitch.^[49] However, even for tones of equal intensity, perceived pitch and measured frequency do not stand in a simple linear relationship.^[50]

Intensity (loudness) can change perception of pitch. Below about 1000 Hz, perceived pitch gets lower as intensity increases. Between 1000 and 2000 Hz, pitch remains fairly constant. Above 2000 Hz, pitch rises with intensity.^[51] This is due to the ear's natural sensitivity to higher pitched sound, as well as the ear's particular sensitivity to sound around the 2000–5000 Hz interval,^[52] the frequency range most of the human voice occupies.^[53]

The difference in frequency between two pitches is called an interval. The most basic interval is the unison, which is simply two notes of the same pitch, followed by the slightly more complex octave: pitches that are either double or half the frequency of the other. The unique characteristics of octaves gave rise to the concept of what is called pitch class, an important aspect of music theory. 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. The concept of pitch class greatly aids aspects of analysis and composition.^[54]

Although pitch can be identified by specific frequency, the letter names assigned to pitches are somewhat arbitrary. For example, today most orchestras assign Concert A (the A above middle C on the piano) to the specific frequency of 440 Hz, rather than, for instance, 435HZ as it was in France in 1859. In England, that A varied between 439 and 452. These differences can have a noticeable effect on the timbre of instruments and other phenomena. Many cultures do not attempt to standardize pitch, often considering that it should be allowed to vary depending on genre, style, mood, etc. In historically informed performance of older music, tuning is often set to match the tuning used in the period when it was written. A frequency of 440 Hz was recommended as the standard pitch for Concert A in 1939, and in 1955 the International Organization for Standardization affirmed the choice.^[55] A440 is now widely, though not exclusively, the standard for music around the world.

Pitch is also an important consideration in tuning systems, or temperament, used to determine the intervallic distance between tones, as within a scale. Tuning systems vary widely within and between world cultures. In Western culture, there have long been several competing tuning systems, all with different qualities. Internationally, the system known as equal temperament is most commonly used today because it is considered the most satisfactory compromise that allows instruments of fixed tuning (e.g. the piano) to sound acceptably in tune in all keys.

Scales and modes

Notes can be arranged in a variety of scales and modes. Western music theory generally divides the octave into a series of twelve tones, called a chromatic scale, within which the interval between adjacent tones is called a half step or semitone. In equal temperament each semitone is equidistant from the next, but other tuning systems are also used. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales.^[56]

The most commonly encountered scales are the seven-toned major, the harmonic minor, the melodic minor, and the natural minor. Other examples of scales are the octatonic scale and the pentatonic or five-tone scale, which is common in folk music and blues. Non-Western cultures often use scales that do not correspond with an equally divided twelve-tone division of the octave. For example, classical Ottoman, Persian, Indian and Arabic musical systems often make use of multiples of quarter tones (half the size of a semitone, as the name indicates), for instance in 'neutral' seconds (three quarter tones) or 'neutral' thirds (seven quarter tones) – they do not normally use the quarter tone itself as a direct interval.^[56]

In traditional Western notation, the scale used for a composition is usually indicated by a key signature at the beginning to designate the pitches that make up that scale. As the music progresses, the pitches used may change and introduce a different scale. Music can be transposed from one scale to another for various purposes, often to accommodate the range of a vocalist. Such transposition raises or lowers the overall pitch range, but preserves the intervallic relationships of the original scale. For example, transposition from the key of C major to D major raises all pitches of the scale of C major equally by a whole tone. Since the interval relationships remain unchanged, transposition may be unnoticed by a listener, however other qualities may change noticeably because transposition changes the relationship of the overall pitch range 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.^[57]

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

Consonance and dissonance

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 greater or lesser degree.^[58]

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.^[58]

Dissonance is an essential element of music and used in most every culture and genre, not only for effect, but as a fundamental structural element to create motion and tension. J.S. Bach’s music depends in great part on the effect of dissonance. The art of melody writing depends heavily upon the selection of consonant and dissonant tones.

Rhythm

Rhythm is produced by the sequential arrangement of sounds and silences in time. Meter measures music in regular pulse groupings, called measures or bars. The time signature or meter signature specifies how many beats are in a measure, and which value of written note is counted or felt as a single beat.

Through increased stress, or variations in duration or articulation, particular tones may be accented. There are conventions in most musical traditions for regular and hierarchical accentuation of beats to reinforce a given meter. Syncopated rhythms contradict those conventions by accenting unexpected parts of the beat. Playing simultaneous rhythms in more than one time signature is called polymeter. See also polyrhythm.

In recent years, rhythm and meter have become an important area of research among music scholars. Recent work in these areas includes books by Bengt-Olov Palmqvist, Fred Lerdahl and Ray Jackendoff, and Jonathan Kramer.

Melody

A melody is a series of tones 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 or modes. Melody may consist, to increasing degree, of the figure, motive, semi-phrase, antecedent and consequent phrase, and period or sentence. The period may be considered the complete melody, however some examples combine two periods, or use other combinations of constituents to create larger form melodies.^[59]

Chord

Harmony

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,"^[60] but can be accurately described and analyzed by Fourier analysis and other methods^[61] because it results from the combination of all sound frequencies, attack and release envelopes, and other qualities that comprise a tone.

Timbre is principally determined by two things: (1) the relative balance of overtones produced by a given instrument due its construction (e.g. shape, material), and (2) the envelope 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 phons. 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 (decrescendo), often called "hairpins" when indicated with diverging or converging lines as shown in the graphic above.

Articulation

Articulation is the manner in which the performer sounds notes. For example, staccato is the shortening of duration compared to the written note value, legato performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation.

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

There are a set of articulations that most all instruments and voices perform in common. They are, in order of 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"). Many of these can be combined to create certain "in-between" articulations. For example, portato is the combination of tenuto and staccato. Some instruments have unique methods by which to produce sounds, such as spicatto for bowed strings, where the bow bounces off the string.

Form or structure

Analysis

Music perception and cognition

Expression

Performance and style

Mathematics

Serial composition and set theory

Musical semiotics

Music subjects

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. Computer file formats have become important as well.^[62] 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 are often used to indicate tempo, technique, and other aspects.

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.^[63]

See also

• Pitch (psychophysics)
• AP Music Theory
• Theory of painting
• Musicology
• List of music theorists

Notes

Sources

Further reading

External links

Wikibooks has more on the topic of: Music theory

• Dillen, Oscar van, Outline of basic music theory (2011)
• http://www.musictheoryhelp.co.uk
• https://www.khanacademy.org/humanities/music/music-basics-notes-rhythm-music
• http://www.musictheoryis.com

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