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Semicomma
The semicomma,Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxix. . also Fokker's comma (after 31-TET pioneer Adriaan Fokker), is type of small musical interval, or comma, in microtonal music Microtonality is the use in music of microtones — intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal interv ... equivalent to 2109375:2097152, or . This is a ratio of approximately 1:1.0058283805847168, or about 10.06 cents (). It is derived from the difference in pitch between three 75:64 just augmented seconds () and one 8:5 just minor sixth () begun on the same root ((3 × 274.58) − (1 × 813.69) = 823.74 − 813.69 = 10.05 cents). It can also be viewed as the amount by which three tritaves exceed seven minor sixths. See also * Septimal kleisma * Septimal semicomma References 5-limit tuning and intervals Commas (music ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comma (music)
In music theory, a comma is a very small interval (music), interval, the difference resulting from Musical tuning, tuning one note (music), note two different ways. Traditionally, there are two most common commata; the syntonic comma (80:81), "the difference between a just intonation, just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma (524288:531441, approximately 73:74), "the difference between twelve 5ths and seven octaves". The word ''comma'' used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning system, and another F tuned using the D-based quarter-comma meantone tuning system. Pitches separated by either comma are considered the same note because conventional notation does not distinguish Pythagorean intervals from 5-limit intervals. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. ... [...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, to check intonation, or to compare the sizes of comparable intervals in different tuning systems. For humans, a single 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, \sqrt 200/math>, at Robert Holford Macdowell Bosanquet's suggestion. Making extensive measurements of musical instruments from around the world, Ellis used cents to report and compare the scales employed, and further described and utilized the system in his 1875 edition of Hermann von Helmholtz's ''On the Sensations of Tone''. It has become the standard me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
31-TET
In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the musical temperament, tempered scale derived by dividing the octave into 31 equally-proportioned steps (equal frequency ratios). Each step represents a frequency ratio of , or 38.71 cent (music), cents (). is a very good approximation of quarter-comma meantone temperament. More generally, it is a regular diatonic tuning in which the tempered perfect fifth is equal to 696.77 cents, as shown in Figure 1. On an isomorphic keyboard, the fingering of music composed in is precisely the same as it is in any other syntonic tuning (such as so long as the notes are spelled properly—that is, with no assumption of Enharmonic, enharmonicity. History and use Division of the octave into 31 steps arose naturally out of Renaissance music theory; the lesser diesis – the ratio of an octave to three major thirds, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adriaan Fokker
Adriaan Daniël Fokker (; 17 August 1887 – 24 September 1972) was a Dutch physicist. He worked in the fields of special relativity and statistical mechanics. He was the inventor of the Fokker organ, a 31 equal temperament, 31-tone equal-tempered (31-TET) organ. Life and work Adriaan Daniël Fokker was born on 17 August 1887 in Buitenzorg, Dutch East Indies (now Bogor, Indonesia), the son of Anthony Herman Gerard Fokker, president of the branch of the Netherlands Trading Society in Batavia, Dutch East Indies, and Susanna Alida der Kinderen. He was a cousin of the Aeronautics, aeronautical engineer Anthony Fokker. Fokker studied mining engineering at the Delft University of Technology and physics at the Leiden University, University of Leiden with Hendrik Lorentz, where he earned his doctorate in 1913. He continued his studies with Albert Einstein, Ernest Rutherford and William Henry Bragg, William Bragg. In his 1913 thesis, he derived the Fokker–Planck equation along with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (music)
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 fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microtonal Music
Microtonality is the use in music of microtones — intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in equal temperament. Terminology Microtone ''Microtonal music'' can refer to any music containing microtones. The words "microtone" and "microtonal" were coined before 1912 by Maud MacCarthy Mann in order to avoid the misnomer " quarter tone" when speaking of the srutis of Indian music. Prior to this time the term "quarter tone" was used, confusingly, not only for an interval actually half the size of a semitone, but also for all intervals (considerably) smaller than a semitone. It may have been even slightly earlier, perhaps as early as 1895, that the Mexican composer Julián Carrillo, writing in Spanish or Frenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Kleisma
In music, the ratio 225/224 is called the septimal kleisma (). It is a minute comma type interval of approximately 7.7 cents. Factoring it into primes gives 2−5 32 52 7−1, which can be rewritten 2−1 (5/4)2 (9/7). That says that it is the amount that two major thirds of 5/4 and a septimal major third, or supermajor third, of 9/7 exceeds the octave. The septimal kleisma can also be viewed as the difference between the diatonic semitone A semitone, also called a minor second, half step, or a half tone, is the smallest interval (music), musical interval commonly used in Western tonal music, and it is considered the most Consonance and dissonance#Dissonance, dissonant when sounde ... (16:15) and the septimal diatonic semitone (15:14). References 7-limit tuning and intervals Commas (music) 0225:0224 {{music-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Semicomma
In music, the septimal semicomma, a seven- limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (). It is also called the ''small septimal comma''Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxvi. . and the ''starling comma'' after its use in starling temperament. Factored into primes it is: 2*3^2*5^*7 Or as simple just intervals: (6/5)^3*(7/6)*(2/1)^ Thus it is the difference between three minor thirds of 6/5 plus a septimal minor third of 7/6 and an octave (2/1). This comma is important to certain tuning systems, such as septimal meantone temperament. A diminished seventh chord consisting of three minor thirds and a subminor third making up an octave is possible in such systems. This characteristic feature of these tuning systems is known as the ''septimal semicomma diminished seventh chord''. In equal temperament It is tempered out in 19 equal temperament and 31 equal temperament, but not in 22 equal temperament, 34 equa ... [...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 conson ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
