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Schisma
In music, the schisma (also spelled ''skhisma'') is the interval between the syntonic comma (81:80) and the Pythagorean comma which is slightly larger. It equals or ≈ 1.00113, which corresponds to 1.9537 cents (). It may also be defined as: * the difference (in cents) between 8 justly tuned perfect fifths plus a justly tuned major third and 5 octaves; * the ratio of major limma to the Pythagorean limma; * the ratio of the syntonic comma and the diaschisma. ''Schisma'' is a Greek word meaning a split or crack (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 the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Schisma On C
In music, the schisma (also spelled ''skhisma'') is the interval between the syntonic comma (81:80) and the Pythagorean comma which is slightly larger. It equals or ≈ 1.00113, which corresponds to 1.9537 cents (). It may also be defined as: * the difference (in cents) between 8 justly tuned perfect fifths plus a justly tuned major third and 5 octaves; * the ratio of major limma to the Pythagorean limma; * the ratio of the syntonic comma and the diaschisma. ''Schisma'' is a Greek word meaning a split or crack (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 the 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 cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
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] [Amazon] |
Pythagorean Comma
In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B, or D and C. It is equal to the frequency ratio = ≈ 1.01364, or about 23.46 cents, roughly a quarter of a semitone (in between 75:74 and 74:73). The comma that musical temperaments often "temper" is the Pythagorean comma. The Pythagorean comma can be also defined as the difference between a Pythagorean apotome and a Pythagorean limma (i.e., between a chromatic and a diatonic semitone, as determined in Pythagorean tuning); the difference between 12 just perfect fifths and seven octaves; or the difference between three Pythagorean ditones and one octave. (This is why the Pythagorean comma is also called a ''ditonic comma''.) The diminished second, in Pythagorean tuning, is defined as the difference between limma and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 include , , , , and . The equal-tempered chromatic scale A musical interval is a ratio of frequencies and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Bach
Johann Sebastian Bach (German: �joːhan zeˈbasti̯an baχ ( – 28 July 1750) was a German composer and musician of the late Baroque period. He is known for his prolific output across a variety of instruments and forms, including the orchestral ''Brandenburg Concertos''; solo instrumental works such as the cello suites and sonatas and partitas for solo violin; keyboard works such as the '' Goldberg Variations'' and '' The Well-Tempered Clavier''; organ works such as the ' and the Toccata and Fugue in D minor; and choral works such as the '' St Matthew Passion'' and the Mass in B minor. Since the 19th-century Bach Revival, he has been widely regarded as one of the greatest composers in the history of Western music. The Bach family had already produced several composers when Johann Sebastian was born as the last child of a city musician, Johann Ambrosius Bach, Johann Ambrosius, in Eisenach. After being orphaned at age 10, he lived for five years with his eldes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 studied the organ with Johann Peter Kellner and Heinrich Nicolaus Gerber, and starting in 1738 he studied with the violinist Meil in Sondershausen, but most significant is the time he spent from 1739 until 1741 (with breaks) studying performance and composition with Johann Sebastian Bach."Johann Philipp Kirnberger (Composer, Music Theorist, Violin, Copyist, Bach's Pupil)" Bach Cantatas website 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 |
Equal Temperament
An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencies of any adjacent pair of notes is the same. This system yields Pitch (music), pitch steps perceived as equal in size, due to the logarithmic changes in pitch frequency. In classical music and Western music in general, the most common tuning system since the 18th century has been 12 equal temperament (also known as ''12 tone equal temperament'', ' or ', informally abbreviated as ''12 equal''), which divides the octave into 12 parts, all of which are equal on a logarithmic scale, with a ratio equal to the twelfth root of two, 12th root of 2, (\sqrt[12] ≈ 1.05946). That resulting smallest interval, the width of an octave, is called a semitone or half step. In Western world, Western countries the term ''equal temperamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rational Intonation
In music, just intonation or pure intonation is a tuning system in which the space between notes' frequencies (called intervals) is a whole number ratio. Intervals spaced in this way are said to be pure, and are called just intervals. 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, bowed instruments such as violins, violas, cellos, and double basses are tuned using pure fifths or fourths. In contrast, keyboard 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 el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Perfect Fourth
A fourth is a interval (music), 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 fourth, Diminished and Tritone, 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 (music), 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 cent (music), cents (), while in equal temperam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
