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Equal Tempered
An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In other words, there are equal ratios of the frequencies of any adjacent pair, and, since pitch is perceived roughly as the logarithm of frequency,[2] equal perceived "distance" from every note to its nearest neighbor. In equal temperament tunings, the generating interval is often found by dividing some larger desired interval, often the octave (ratio 2:1), into a number of smaller equal steps (equal frequency ratios between successive notes). In classical music and Western music in general, the most common tuning system for the past few hundred years has been and remains twelve-tone equal temperament (also known as 12 equal temperament, 12-TET, or 12-ET), which divides the octave into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the 12th root of 2 (12√2 ≈ 1.05946)
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Octave
In music, an octave (Latin: octavus: eighth) or perfect octave is the interval between one musical pitch and another with half or double its frequency. It is defined by ANSI[2] as the unit of frequency level when the base of the logarithm is two. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems".[3] The most important musical scales are typically written using eight notes, and the interval between the first and last notes is an octave. For example, the C major scale is typically written C D E F G A B C, the initial and final Cs being an octave apart
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Galileo Galilei
Galileo Galilei
Galileo Galilei
(Italian: [ɡaliˈlɛːo ɡaliˈlɛi]; 15 February 1564[3] – 8 January 1642) was an Italian polymath. Galileo is a central figure in the transition from natural philosophy to modern science and in the transformation of the scientific Renaissance into a scientific revolution. Galileo's championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system.[4] He met with opposition from astronomers,
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Southern And Northern Dynasties
The Northern and Southern dynasties
Southern dynasties
(Chinese: 南北朝; pinyin: Nán-Běi Cháo) was a period in the history of China that lasted from 420 to 589, following the tumultuous era of the Sixteen Kingdoms
Sixteen Kingdoms
and the Wu Hu states. It is sometimes considered as the latter part of a longer period known as the Six Dynasties
Six Dynasties
(220 to 589).[1] Though an age of civil war and political chaos, it was also a time of flourishing arts and culture, advancement in technology, and the spread of Mahayana
Mahayana
Buddhism
Buddhism
and Daoism. The period saw large-scale migration of Han Chinese
Han Chinese
to the lands south of the Yangtze
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Music Of China
Music of China
China
refers to the music of the Chinese people, which may be the music of the Han Chinese
Han Chinese
as well as other ethnic minorities within mainland China. It also includes music produced by people of Chinese origin in some territories outside mainland China
China
using traditional Chinese instruments or in the Chinese language. It covers a highly diverse range of music from the traditional to the modern. Different types of music have been recorded in historical Chinese documents from the early periods of Chinese civilization which, together with archaeological artifacts discovered, provided evidence of a well-developed musical culture as early as the Zhou Dynasty
Zhou Dynasty
(1122 BC – 256 BC). These further developed into various forms of music through succeeding dynasties, producing the rich heritage of music that is part of the Chinese cultural landscape today
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Ming Dynasty
The Ming dynasty
Ming dynasty
(/mɪŋ/)[2] was the ruling dynasty of China
China
– then known as the Great Ming Empire
Empire
– for 276 years (1368–1644) following the collapse of the Mongol-led Yuan dynasty. The Ming, described by Edwin O. Reischauer, John K. Fairbank and Albert M. Craig as "one of the greatest eras of orderly government and social stability in human history",[3] was the last imperial dynasty in China ruled by ethnic Han Chinese
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Matteo Ricci
Matteo Ricci, S.J. (Italian pronunciation: [matˈtɛːo ˈrittʃi]; Latin: Mattheus Riccius Maceratensis; 6 October 1552 – 11 May 1610), was an Italian Jesuit
Jesuit
priest and one of the founding figures of the Jesuit
Jesuit
China
China
missions. His 1602 map of the world in Chinese characters
Chinese characters
introduced the findings of European exploration to East Asia. He is considered a Servant of God in Roman Catholicism. Ricci arrived at the Portuguese settlement of Macau
Macau
in 1582 where he began his missionary work in China. He became the first European to enter the Forbidden City
Forbidden City
of Beijing
Beijing
in 1601 when invited by the Wanli Emperor, who sought his selected services in matters such as court astronomy and calendrical science
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Jesuit
The Society of Jesus
Society of Jesus
(SJ – from Latin: Societas Iesu) is a scholarly religious congregation of the Catholic Church
Catholic Church
which originated in sixteenth-century Spain. The members are called Jesuits.[2] The society is engaged in evangelization and apostolic ministry in 112 nations on six continents. Jesuits
Jesuits
work in education (founding schools, colleges, universities, and seminaries), intellectual research, and cultural pursuits. Jesuits
Jesuits
also give retreats, minister in hospitals and parishes, sponsor direct social ministries, and promote ecumenical dialogue. Ignatius of Loyola, a Basque nobleman from the Pyrenees
Pyrenees
area of northern Spain, founded the society after discerning his spiritual vocation while recovering from a wound sustained in the Battle of Pamplona
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J. Murray Barbour
James Murray Barbour
James Murray Barbour
(1897-1970) is an American acoustician, musicologist, and composer best known for his work Tuning and Temperament: A Historical Survey (1951, 2d ed. 1953). As the opening of the work describes, it is based upon his unpublished dissertation from 1932, his interest having been sparked by musicologist Curt Sachs having shown him Marin Mersenne's Harmonie Universelle.[1] Murray Barbour taught at Ithaca College, New York, 1932-1939, and Michigan State College (later University), 1939-1964. Murray Barbour adapted the Strähle construction
Strähle construction
for use in approximating equal temperaments. He is also the author of"Synthetic Musical Scales", The American Mathematical Monthly, Vol. 36, No. 3, (Mar., 1929), pp. 155-160. Trumpets, Horns and Music (1964). Michigan State University. "A Geometrical approximation to the Roots of Numbers", American Mathematical Monthly, vol. 64, 1957
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Hermann Von Helmholtz
Hermann Ludwig Ferdinand von Helmholtz (August 31, 1821 – September 8, 1894) was a German physician and physicist who made significant contributions in several scientific fields
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Victor-Charles Mahillon
Victor-Charles Mahillon
Victor-Charles Mahillon
(March 10, 1841 in Brussels
Brussels
– June 17, 1924 in Saint-Jean-Cap-Ferrat, France) was a Belgian musician, instrument builder and writer on musical topics. He was the founder and first curator of the Musée instrumental du Conservatoire Royal de Musique, known today as the Musical Instrument Museum. He built, collected, and described more than 1500 musical instruments.[1]Contents1 Biography1.1 Early life & family 1.2 Brussels
Brussels
Royal Music Conservatory2 Honours 3 Works 4 References 5 External linksBiography[edit]Horn by MahillonAida trumpets by MahillonEarly life & family[edit] Born in a family of instrument makers and music publishers, son of Charles Mahillon (1813-1887), and brother of Joseph-Jean Mahillon (1848-1923, Adolphe Désiré Mahillon (1851-1906) and Ferdinand-Charles-Eugène Mahillon (1855-1948)
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Aristoxenus
Aristoxenus
Aristoxenus
of Tarentum (Greek: Ἀριστόξενος ὁ Ταραντίνος; b. c. 375, fl. 335 BCE) was a Greek Peripatetic philosopher, and a pupil of Aristotle. Most of his writings, which dealt with philosophy, ethics and music, have been lost, but one musical treatise, Elements of Harmony (Greek: Ἁρμονικῶν στοιχείων; Latin: Elementa harmonica), survives incomplete, as well as some fragments concerning rhythm and meter
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Vincenzo Galilei
Vincenzo Galilei
Vincenzo Galilei
(c. 1520 – 2 July 1591) was an Italian lutenist, composer, and music theorist, and the father of the famous astronomer and physicist Galileo Galilei
Galileo Galilei
and of the lute virtuoso and composer Michelagnolo Galilei. He was a seminal figure in the musical life of the late Renaissance
Renaissance
and contributed significantly to the musical revolution which demarcates the beginning of the Baroque era. Vincenzo, in his study of pitch and string tension, produced perhaps the first non-linear mathematical description of a natural phenomenon known to history.[1] It was an extension of a Pythagorean tradition but went beyond it
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Fronimo Dialogo
The Fronimo Dialogo di Vincentio Galilei (Vincenzo Galilei) is an instructional book on playing, composing and intabulating vocal music for the lute. The first edition was printed by Girolamo Scotto in Venice
Venice
with the full title FRONIMO DIALOGO / DI VINCENTIO GALILEI FIORENTINO, / NEL QUALE SI CONTENGONO LE VERE, / et necessarie regole del Intavolare la Musica nel Liuto. While the title page bears the date 1568, the final page confusingly bears the date 1569. Apparently, although the manuscript was completed by Galilei in the Autumn of 1568, the official letter of privilege allowing the publication of the book was received only in December, and the printing actually took place in 1569. In addition, still in 1569, Girolamo Scotto broke the book into two parts, selling a collection of 30 musical selections from near the end of the book and the Dialogo separately
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Simon Stevin
Simon Stevin
Simon Stevin
(Dutch: [ˈsimɔn ˈsteːvɪn]; 1548–1620), sometimes called Stevinus, was a Flemish / Dutch mathematician, physicist and military engineer. He was active in a great many areas of science and engineering, both theoretical and practical
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Ricercar
A ricercar (Italian pronunciation: [ritʃɛr'kare], also spelled ricercare, recercar, recercare) is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many ricercars serve a preludial function to "search out" the key or mode of a following piece. A ricercar may explore the permutations of a given motif, and in that regard may follow the piece used as illustration. For example, " Ricercar
Ricercar
sopra Benedictus" might develop motifs from a motet titled "Benedictus". The term is also used to designate an etude or study that explores a technical device in playing an instrument, or singing. In its most common contemporary usage, it refers to an early kind of fugue, particularly one of a serious character in which the subject uses long note values
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