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 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 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.[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,
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, considerations of musical notation, and techniques of tonal composition (harmony and counterpoint), among other topics.
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, Gǔdí, and Anasazi flute.
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 [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."
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
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").
The Samaveda and Yajurveda (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.
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 (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
- Anonymous (erroneously attributed to Euclid) Division of the Canon, Κατατομή κανόνος, 4th–3rd century BCE.
- Theon of Smyrna, On Mathematics Useful for the Understanding of Plato, Τωv κατά τό μαθηματικόν χρησίμων είς τήν Πλάτωνος άνάγνωσις, 115–140 CE.
- Nicomachus of Gerasa, Manual of Harmonics, Άρμονικόν έγχειρίδιον, 100–150 CE
- Cleonides, 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, Harmonic Elements, Άρμονικά στοιχεία, 375/360 – after 320 BCE.
- Aristoxenus, Rhythmic Elements, Ρυθμικά στοιχεία.
- Claudius Ptolemy, Harmonics, Άρμονικά, 127–148 CE.
- Porphyrius, On Ptolemy's Harmonics, Είς τά άρμονικά Πτολεμαίον ύπόμνημα, 232/3–c. 305 CE.
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:[n 3]
- Abū Yūsuf Ya'qūb al-Kindi († Bagdad, 873 CE), who uses the first twelve letters of the alphabet to describe the twelve frets on five strings of the oud, producing a chromatic scale of 25 degrees.
- [Yaḥyā ibn] al-Munajjim (Baghdad, 856–912), author of Risāla fī al-mūsīqī ("Treatise on music", MS GB-Lbl Oriental 2361) which describes a Pythagorean tuning of the oud and a system of eight modes perhaps inspired by Ishaq al-Mawsili (767–850).
- Abū n-Nașr Muḥammad al-Fārābi (Persia, 872? – Damas, 950 or 951 CE), author of Kitab al-Musiqa al-Kabir ("The Great Book of Music").
- 'Ali ibn al-Husayn ul-Isfahānī (897–967), known as Abu al-Faraj al-Isfahani, author of Kitāb al-Aghānī ("The Book of Songs").
- Abū 'Alī al-Ḥusayn ibn ʿAbd-Allāh ibn Sīnā, known as Avicenna (c. 980 – 1037), whose contribution to music theory consists mainly in Chapter 12 of the section on mathematics of his Kitab Al-Shifa ("The Book of Healing").
- 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 (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").
The Latin treatise De institutione musica by the Roman philosopher
During the thirteenth century, a new rhythm system called
Middle Eastern and Central Asian countries
- Bāqiyā Nāyinῑ (Uzbekistan, 17th century CE), Uzbek author and music theorist. Author of Zamzama e wahdat-i-mῡsῑqῑ ("The Chanting of Unity in Music").
- 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.
- 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 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.
Fundamentals of music
Music is composed of
Pitch is the lowness or highness of a
Specific frequencies are often assigned letter names. Today most orchestras assign
The difference in pitch between two notes is called an interval. The most basic interval is the unison, which is simply two notes of the same pitch. The octave interval is two pitches that are either double or half the frequency of one another. The unique characteristics of octaves gave rise to the concept of pitch class: pitches of the same letter name that occur in different octaves may be grouped into a single "class" by ignoring the difference in octave. For example, a high C and a low C are members of the same pitch class—the class that contains all C's. 
Musical tuning systems, or temperaments, determine the precise size of intervals. Tuning systems vary widely within and between world cultures. In Western culture, there have long been several competing tuning systems, all with different qualities. Internationally, the system known as equal temperament is most commonly used today because it is considered the most satisfactory compromise that allows instruments of fixed tuning (e.g. the piano) to sound acceptably in tune in all keys.
Scales and modes
Notes can be arranged in a variety of
The most commonly encountered scales are the seven-toned
In traditional Western notation, the scale used for a composition is usually indicated by a
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 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 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 polyrhythm.
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, Fred Lerdahl and Ray Jackendoff, Jonathan Kramer, and Justin London.
A melody is a group of musical sounds in agreeable succession or arrangement that typically moves 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
A chord, in music, is any harmonic set of three or more notes that is heard as if sounding simultaneously.: pp. 67, 359 : p. 63 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.: p. 15
The most frequently encountered chords are
A series of chords is called a
In music, harmony is the use of simultaneous
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
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.
In music, "
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 is the way the performer sounds notes. For example, staccato is the shortening of duration compared to the written note value, legato performs the notes in a smoothly joined sequence with no separation. Articulation is often described rather than quantified, therefore there is room to interpret how to execute precisely each articulation.
For example, staccato is often referred to as "separated" or "detached" rather than having a defined or numbered amount by which to reduce the notated duration. Violin players use a variety of techniques to perform different qualities of staccato. The manner in which a performer decides to execute a given articulation is usually based on the context of the piece or phrase, but many articulation symbols and verbal instructions depend on the instrument and musical period (e.g. viol, wind; classical, baroque; etc.).
There is a set of articulations that most instruments and voices perform in common. They are—from long to short: legato (smooth, connected); tenuto (pressed or played to full notated duration); marcato (accented and detached); staccato ("separated", "detached"); martelé (heavily accented or "hammered").[contradictory] Many of these can be combined to create certain "in-between" articulations. For example, portato is the combination of tenuto and staccato. Some instruments have unique methods by which to produce sounds, such as spiccato for bowed strings, where the bow bounces off the string.