musical theory

Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to 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. But this medieval discipline became the basis for tuning systems in later centuries and is generally included in modern scholarship on the history of music theory.

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

In modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, ''music theory'', is an act of contemplation of music, from the Greek word θεωρία, meaning a looking at, a viewing; a contemplation, speculation, theory; a sight, a spectacle. As such, it is often concerned with abstract musical aspects such as tuning and tonal systems, scales, consonance and dissonance, and rhythmic relationships. In addition, there is also a body of theory concerning practical aspects, such as the creation or the performance of music, orchestration, ornamentation, improvisation, and electronic sound production. A person who researches or teaches music theory is a music theorist. University study, typically to the MA or PhD level, is required to teach as a tenure-track music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by western music notation. Comparative, descriptive, statistical, and other methods are also used. Music theory textbooks, especially in the United States of America, often include elements of musical acoustics, considerations of musical notation, and techniques of tonal composition (harmony and counterpoint), among other topics.

History

Prehistory

Preserved prehistoric instruments, artifacts, and later depictions of performance in artworks can give clues to the structure of pitch systems in prehistoric cultures. See for instance Paleolithic flutes, Gǔdí, and Anasazi flute.

Antiquity

Mesopotamia

Several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these texts dates from before 1500 BCE, a millennium earlier than surviving evidence from any other culture of comparable musical thought. Further, "All the Mesopotamian texts bout musicare united by the use of a terminology for music that, according to the approximate dating of the texts, was in use for over 1,000 years."

China

Much of Chinese music history and theory remains unclear.

Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed. The Lüshi chunqiu from about 239 BCE recalls the legend of Ling Lun. On order of the Yellow Emperor, Ling Lun collected twelve bamboo lengths with thick and even nodes. Blowing on one of these like a pipe, he found its sound agreeable and named it ''huangzhong'', the "Yellow Bell." He then heard phoenixes singing. The male and female phoenix each sang six tones. Ling Lun cut his bamboo pipes to match the pitches of the phoenixes, producing twelve pitch pipes in two sets: six from the male phoenix and six from the female: these were called the ''lülü'' or later the ''shierlü''.

Apart from technical and structural aspects, ancient Chinese music theory also discusses topics such as the nature and functions of music. The ''Yueji'' ("Record of music", c1st and 2nd centuries BCE), for example, manifests Confucian moral theories of understanding music in its social context. Studied and implemented by Confucian scholar-officials .. these theories helped form a musical Confucianism that overshadowed but did not erase rival approaches. These include the assertion of Mozi (c. 468 – c. 376 BCE) that music wasted human and material resources, and Laozi's claim that the greatest music had no sounds. ..Even the music of the ''qin'' zither, a genre closely affiliated with Confucian scholar-officials, includes many works with Daoist references, such as ''Tianfeng huanpei'' ("Heavenly Breeze and Sounds of Jade Pendants").

India

The Samaveda and Yajurveda (c. 1200 – 1000 BCE) are among the earliest testimonies of Indian music, but they contain no theory properly speaking. The Natya Shastra, written between 200 BCE to 200 CE, discusses intervals (''Śrutis''), scales (''Grāmas''), consonances and dissonances, classes of melodic structure (''Mūrchanās'', modes?), melodic types (''Jātis''), instruments, etc.

Greece

Early preserved Greek writings on music theory include two types of works:
* technical manuals describing the Greek musical system including notation, scales, consonance and dissonance, rhythm, and types of musical compositions
* treatises on the way in which music reveals universal patterns of order leading to the highest levels of knowledge and understanding.
Several names of theorists are known before these works, including Pythagoras (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.

Post-classical

China

The pipa instrument carried with it a theory of musical modes that subsequently led to the Sui and Tang theory of 84 musical modes.

Arabic countries / Persian countries

Medieval Arabic music theorists include:
* Abū Yūsuf Ya'qūb al-Kindi († 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.
* aḥyā ibnal- Munajjim (Baghdad, 856–912), author of ''Risāla fī al-mūsīqī'' ("Treatise on music", MS GB-Lbl Oriental 2361) which describes a Pythagorean tuning of the oud 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").

Europe

The Latin treatise ''De institutione musica'' by the Roman philosopher Boethius (written c. 500, translated as ''Fundamentals of Music'') was a touchstone for other writings on music in medieval Europe. Boethius represented Classical authority on music during the Middle Ages, as the Greek writings on which he based his work were not read or translated by later Europeans until the 15th century. This treatise carefully maintains distance from the actual practice of music, focusing mostly on the mathematical proportions involved in tuning systems and on the moral character of particular modes. Several centuries later, treatises began to appear which dealt with the actual composition of pieces of music in the plainchant tradition. At the end of the ninth century, Hucbald worked towards more precise pitch notation for the neumes used to record plainchant.

Guido d'Arezzo' wrote in 1028 a letter to Michael of Pomposa, entitled ''Epistola de ignoto cantu'', in which he introduced the practice of using syllables to describe notes and intervals. This was the source of the hexachordal solmization that was to be used until the end of the Middle Ages. Guido also wrote about emotional qualities of the modes, the phrase structure of plainchant, the temporal meaning of the neumes, etc.; his chapters on polyphony "come closer to describing and illustrating real music than any previous account" in the Western tradition.

During the thirteenth century, a new rhythm system called mensural notation grew out of an earlier, more limited method of notating rhythms in terms of fixed repetitive patterns, the so-called rhythmic modes, which were developed in France around 1200. An early form of mensural notation was first described and codified in the treatise ''Ars cantus mensurabilis'' ("The art of measured chant") by Franco of Cologne (c. 1280). Mensural notation used different note shapes to specify different durations, allowing scribes to capture rhythms which varied instead of repeating the same fixed pattern; it is a proportional notation, in the sense that each note value is equal to two or three times the shorter value, or half or a third of the longer value. This same notation, transformed through various extensions and improvements during the Renaissance, forms the basis for rhythmic notation in European classical music today.

Modern

Middle Eastern and Central Asian countries

* Bᾱqiyᾱ Nᾱyinῑ (Uzbekistan, 17th century CE), Uzbek author and music theorist. Author of ''Zamzama e wahdat-i-mῡsῑqῑ'' ("The Chanting of Unity in Music").
* Baron Francois Rodolphe d'Erlanger (Tunis, Tunisia, 1910–1932 CE), French musicologist. Author of ''La musique arabe'' and ''Ta'rῑkh al-mῡsῑqᾱ al-arabiyya wa-usῡluha wa-tatawwurᾱtuha'' ("A History of Arabian Music, its principles and its Development")
D'Erlanger divulges that the Arabic music scale is derived from the Greek music scale, and that Arabic music is connected to certain features of Arabic culture, such as astrology.

Europe

* Renaissance

* Baroque

* 1750–1900
** As Western musical influence spread throughout the world in the 1800s, musicians adopted Western theory as an international standard—but other theoretical traditions in both textual and oral traditions remain in use. For example, the long and rich musical traditions unique to ancient and current cultures of Africa are primarily oral, but describe specific forms, genres, performance practices, tunings, and other aspects of music theory.
** Sacred harp music uses a different kind of scale and theory in practice. The music focuses on the solfege "fa, sol, la" on the music scale. Sacred Harp also employs a different notation involving "shape notes", or notes that are shaped to correspond to a certain solfege syllable on the music scale. Sacred Harp music and its music theory originated with Reverend Thomas Symmes in 1720, where he developed a system for "singing by note" to help his church members with note accuracy.

Contemporary

Fundamentals of music

Music is composed of aural phenomena; "music theory" considers how those phenomena apply in music. Music theory considers melody, rhythm, counterpoint, harmony, form, tonal systems, scales, tuning, intervals, consonance, dissonance, durational proportions, the acoustics of pitch systems, composition, performance, orchestration, ornamentation, improvisation, electronic sound production, etc.

Pitch

Pitch is the lowness or highness of a tone, for example the difference between middle C and a higher C. The frequency of the sound waves producing a pitch can be measured precisely, but the perception of pitch is more complex because single notes from natural sources are usually a complex mix of many frequencies. Accordingly, theorists often describe pitch as a subjective sensation rather than an objective measurement of sound.

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

The difference in pitch between two notes is called an interval. The most basic interval is the unison, 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 scales and modes. Western music theory generally divides the octave into a series of twelve pitches, called a chromatic scale, within which the interval between adjacent tones is called a half step, or semitone. Selecting tones from this set of 12 and arranging them in patterns of semitones and whole tones creates other scales.

The most commonly encountered scales are the seven-toned major, the harmonic minor, the melodic minor