Music theory From Wikipedia, the free encyclopedia 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. Contents 1 History of music theory 2 Fundamentals of music 2.1 Pitch 2.2 Scales and modes 2.3 Consonance and dissonance 2.4 Rhythm 2.5 Melody 2.6 Chord 2.7 Harmony 2.8 Timbre 2.8.1 Dynamics 2.8.2 Articulation 2.9 Texture 2.10 Form or structure 2.11 Analysis 2.12 Music perception and cognition 2.13 Expression 2.14 Performance and style 2.15 Mathematics 2.16 Serial composition and set theory 2.17 Musical semiotics 3 Music subjects 3.1 Notation 4 See also 5 Notes 6 Sources 7 Further reading 8 External links 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 Ancient Egyptian musicians playing lutes in an Jiahu, China dated c. 7,000 BCE[5] reveal their makers ensemble. 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 (http://www.bnl.gov/bnlweb/pubaf/pr/1999/bnlpr092299.html). 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 (https://www.youtube.com/watch?v=ygoCqxjMcEQ). 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.