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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 a ... [...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 p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diaschisma
The diaschisma (or diacisma) is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds (in just intonation). It can be represented by the ratio 2048:2025 and is about 19.5 cents. The use of the name diaschisma for this interval is due to Helmholtz; earlier Rameau had called that interval a "diminished comma" or comma minor. A diaschisma is the difference between a schisma and a syntonic comma, as well as the difference between the greater chromatic semitone (135:128 = 92.18 cents) and the just minor second (16:15 = 111.73 cents). (1897). Columbian cyclopedia, Volume 9', np. Garretson, Cox & Company. pre-ISBN. Medieval theorists Boethius and Tinctoris described the diaschisma as one-half of the Pythagorean minor second, or 256/243, which would make the other half either 25/24 (70.67 cents) or about 45 cents. The diaschisma may be approximated by 89/88, 19.56 cents. Tempering out the diaschisma, in the modern me ... [...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 jurisdi ... [...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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Musical Interval
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic frequ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
5-limit Tuning And Intervals
Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as . Powers of 2 represent intervallic movements by octaves. Powers of 3 represent movements by intervals of perfect fifths (plus one octave, which can be removed by multiplying by 1/2, i.e., 2−1). Powers of 5 represent intervals of major thirds (plus two octaves, removable by multiplying by 1/4, i.e., 2−2). Thus, 5-limit tunings are constructed entirely from stacking of three basic purely-tuned intervals (octaves, thirds and fifths). Since the perception of consonance seems related to low numbers in the harmonic series, and 5-limit tuning relies on the three lowest primes, 5-limit tuning should be capable of producing very consonan ... [...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 pit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cent (music)
The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each. Typically, cents are used to express small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is too small to be perceived between successive notes. Cents, as described by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose to base his measures on the hundredth part of a semitone, , at Robert Holford Macdowell Bosanquet's suggestion. He made extensive measurements of musical instruments from around the world, using cents extensively to report and compare the scales employed, and further described and employed the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard method of representin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Limma
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale. For example, C is adjacent to C; the interval between them is a semitone. In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a whole tone or major second is 2 semitones wide, a major third 4 semitones, and a perfect fifth 7 semitones. In music theory, a distinction is made between a diatonic semitone, or minor second (an interval encompassing two different staff positions, e.g. from C to D) and a chromatic semitone or augmented unison (an interval between two notes at the same staff position, e.g. from C to C). These are enharmonically equivalent when twelve-tone equal temperament is used, but are not the same thing in meantone te ... [...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." Kirn ... [...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 frequenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
