|
Schisma On C
In music, the schisma (also spelled ''skhisma'') is the interval between a Pythagorean comma (531441:524288) and a syntonic comma (81:80) and equals or 32805:32768 = 1.00113, which is 1.9537 cents (). It may also be defined as: * the difference between 8 justly tuned perfect fifths plus a justly tuned major third and 5 octaves; * the difference between major limma and Pythagorean limma; * the difference between the syntonic comma and the diaschisma. ''Schisma'' is a Greek word meaning a split (see schism) whose musical sense was introduced by Boethius at the beginning of the 6th century in the 3rd book of his 'De institutione musica'. Boethius was also the first to define diaschisma. Andreas Werckmeister defined the ''grad'' as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth (3/2) and the equally tempered fifth of 700 cents (2). This value, 1.955 cents, may be approximated by the ratio 886:885. This interval is also s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schisma
In music, the schisma (also spelled ''skhisma'') is the interval between a Pythagorean comma (531441:524288) and a syntonic comma (81:80) and equals or 32805:32768 = 1.00113, which is 1.9537 cents (). It may also be defined as: * the difference between 8 justly tuned perfect fifths plus a justly tuned major third and 5 octaves; * the difference between major limma and Pythagorean limma; * the difference between the syntonic comma and the diaschisma. ''Schisma'' is a Greek word meaning a split (see schism) whose musical sense was introduced by Boethius at the beginning of the 6th century in the 3rd book of his 'De institutione musica'. Boethius was also the first to define diaschisma. Andreas Werckmeister defined the ''grad'' as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth (3/2) and the equally tempered fifth of 700 cents (2). This value, 1.955 cents, may be approximated by the ratio 886:885. This interval is also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schism
A schism ( , , or, less commonly, ) is a division between people, usually belonging to an organization, movement, or religious denomination. The word is most frequently applied to a split in what had previously been a single religious body, such as the Great East–West Schism or the Western Schism. It is also used of a split within a non-religious organization or movement or, more broadly, of a separation between two or more people, be it brothers, friends, lovers, etc. A schismatic is a person who creates or incites schism in an organization or who is a member of a splinter group. Schismatic as an adjective means pertaining to a schism or schisms, or to those ideas, policies, etc. that are thought to lead towards or promote schism. In religion, the charge of schism is distinguished from that of heresy, since the offence of schism concerns not differences of belief or doctrine but promotion of, or the state of division, especially among groups with differing pastoral jurisdict ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twelfth Root Of Two
The twelfth root of two or \sqrt 2/math> (or equivalently 2^) is an algebraic irrational number, approximately equal to 1.0594631. It is most important in Western music theory, where it represents the frequency ratio ( musical interval) of a semitone () in twelve-tone equal temperament. This number was proposed for the first time in relationship to musical tuning in the sixteenth and seventeenth centuries. It allows measurement and comparison of different intervals (frequency ratios) as consisting of different numbers of a single interval, the equal tempered semitone (for example, a minor third is 3 semitones, a major third is 4 semitones, and perfect fifth is 7 semitones). A semitone itself is divided into 100 cents (1 cent = \sqrt 2002^). Numerical value The twelfth root of two to 20 significant figures is . Fraction approximations in increasing order of accuracy are , , and . , its numerical value has been computed to at least twenty billion decimal digits. The equal-tem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Dahlhaus
Carl Dahlhaus (10 June 1928 – 13 March 1989) was a German musicologist who was among the leading postwar musicologists of the mid to late 20th-century. A prolific scholar, he had broad interests though his research focused on 19th- and 20th-century classical music, both areas in which he made significant advancements. However, he remains best known in the English-speaking world for his writings on Wagner. Dahlhaus wrote on many other composers, including Josquin, Gesualdo, Bach and Schoenberg. He spent the bulk of his career as head of the Berlin Institute of Technology's musicology department, which he raised to an international standard. Dahlhaus pioneered the development of numerous musicological fields, particularly the aesthetics of music, which he raised to a central status. Active as a historian, analyst, editor and organizer, he was massively influential and his work has since incited considerable discussion and debate. Life and career Dahlhaus was born in Hanover ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schismatic Temperament
A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 (1.9537 cents) to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament. Construction In Pythagorean tuning all notes are tuned as a number of perfect fifths (701.96 cents ). The major third above C, E, is considered four fifths above C. This causes the Pythagorean major third, E (407.82 cents ), to differ from the just major third, E (386.31 cents ): the Pythagorean third is sharper than the just third by 21.51 cents (a syntonic comma ). C — G — D — A — E Ellis's "skhismic temperament". instead uses the note eight fifths ''below'' C, F (384.36 cents ), the Pythagorean diminished fourth or schismatic major third. Though spelled "incorrectly" for a major third, this note is only 1.95 cents (a schisma) flat of E, and thus more in tune than the Pythagorean major third. As Ellis puts it, "the Fifths should be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bach
Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard works such as the ''Goldberg Variations'' and ''The Well-Tempered Clavier''; organ works such as the '' Schubler Chorales'' and the Toccata and Fugue in D minor; and vocal music such as the ''St Matthew Passion'' and the Mass in B minor. Since the 19th-century Bach revival he has been generally regarded as one of the greatest composers in the history of Western music. The Bach family already counted several composers when Johann Sebastian was born as the last child of a city musician in Eisenach. After being orphaned at the age of 10, he lived for five years with his eldest brother Johann Christoph, after which he continued his musical education in Lüneburg. From 1703 he was back in Thuringia, working as a musician for Protestant c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johann Kirnberger
Johann Philipp Kirnberger (also ''Kernberg''; 24 April 1721, Saalfeld – 27 July 1783, Berlin) was a musician, composer (primarily of fugues), and music theorist. He was a student of Johann Sebastian Bach. According to Ingeborg Allihn, Kirnberger played a significant role in the intellectual and cultural exchange between Germany and Poland in the mid-18th century (Allihn 1995, 209). Between 1741 and 1751 Kirnberger lived and worked in Poland for powerful magnates including Lubomirski, Poninski, and Rzewuski before ending up at the Benedictine Cloister in Lviv (then part of Poland). He spent much time collecting Polish national dances and compiled them in his treatise Die Charaktere der Taenze (Allihn 1995, 211). Kirnberger became a violinist at the court of Frederick II of Prussia in 1751. He was the music director to the Prussian Princess Anna Amalia from 1758 until his death. Kirnberger greatly admired Johann Sebastian Bach, deeming him "the greatest of all composers." Kirnb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equal Temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency. In classical music and Western music in general, the most common tuning system since the 18th century has been twelve-tone equal temperament (also known as 12 equal temperament, 12-TET or 12-ET; informally abbreviated to twelve equal), 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 ( ≈ 1.05946). That resulting smallest interval, the width of an octave, is called a semitone or half step. In Western countries the term ''equal temperament'', without qualification, generally means 12-TET. In modern times, 12-TET is usually tuned relative to a standard pitch of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Intonation
In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios (such as 3:2 or 4:3) of frequencies. An interval tuned in this way is said to be pure, and is called a just interval. Just intervals (and chords created by combining them) consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes G3 and C4 (labelled 3 and 4) are tuned as members of the harmonic series of the lowest C, their frequencies will be 3 and 4 times the fundamental frequency. The interval ratio between C4 and G3 is therefore 4:3, a just fourth. In Western musical practice, instruments are rarely tuned using only pure intervals—the desire for different keys to have identical intervals in Western music makes this impractical. Some instruments of fixed pitch, such as electric pianos, are commonly tuned using equal temperament, in which all intervals other than octaves consist of irrational-number frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fourth
A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones (four and six, respectively). The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term ''perfect'' identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor. A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cents (), while in equal temperament a perfect fourth is equal to five semitones, or 500 cents (see additive s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andreas Werckmeister
Andreas Werckmeister (November 30, 1645 – October 26, 1706) was a German organist, music theorist, and composer of the Baroque era. He was amongst the earliest advocates of equal temperament, and through this advocacy was highly influential to the harmonic basis underlying almost all of subsequent Western music. Life Born in Benneckenstein, Werckmeister attended schools in Nordhausen and Quedlinburg. He received his musical training from his uncles Heinrich Christian Werckmeister and Heinrich Victor Werckmeister. In 1664 he became an organist in Hasselfelde; ten years later in Elbingerode; and in 1696 of the Martinskirche in Halberstadt. Musical compositions Of his compositions only a booklet remains: pieces for violin with basso continuo, with the title ''Musikalische Privatlust'' (1689). Also some organ works remain: Canzon in a-minor, Canzona in d-minor, Praeludium ex G, Canzonetta in D-major. Theoretical works Werckmeister is best known today as a theorist, in particular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
