|
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] |
Ben Johnston Notation
Benjamin Burwell Johnston Jr. (March 15, 1926 – July 21, 2019) was an American Contemporary classical music, contemporary music composer, known for his use of just intonation. He was called "one of the foremost composers of microtonal music" by Philip Bush and "one of the best non-famous composers this country has to offer" by John Rockwell. Biography Johnston was born in Macon, Georgia, and taught composition and theory at the University of Illinois at Urbana–Champaign from 1951 to 1986, before retiring to North Carolina. During his time teaching, he was in contact with Avant-garde music, avant-garde figures such as John Cage, La Monte Young, and Iannis Xenakis. Johnston's students included Stuart Saunders Smith, Neely Bruce, Thomas Albert (composer), Thomas Albert, Michael Pisaro, Manfred Stahnke, and Kyle Gann. He also considered his practice of just intonation to have influenced other composers, including Larry Polansky. In 1946 he married dance band singer Dorothy Haine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scripta Mathematica
''Scripta Mathematica'' was a quarterly journal published by Yeshiva University devoted to the Philosophy, history, and expository treatment of mathematics. It was said to be, at its time, "the only mathematical magazine in the world edited by specialists for laymen.". The journal was established in 1932 under the editorship of Jekuthiel Ginsburg, a professor of mathematics at Yeshiva University, and its first issue appeared in 1933 at a subscription price of three dollars per year. It ceased publication in 1973. Notable papers published in ''Scripta Mathematica'' included work by Nobelist Percy Williams Bridgman concerning the implications for physics of set-theoretic paradoxes, and Hermann Weyl's obituary of Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which .... Some ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Tone
Major most commonly refers to: * Major (rank), a military rank * Academic major, an academic discipline to which an undergraduate student formally commits * People named Major, including given names, surnames, nicknames * Major and minor in music, an interval, chord, scale, or key * Major sport competitions Major(s) or The Major may also refer to: Arts and entertainment Fictional characters * Old Major, a pig in ''Animal Farm'' * Major Major Major Major, in ''Catch-22'' * The Major (''Hellsing'') * Major (Cinderella), a horse in Disney's ''Cinderella'' * Major Gowen or the Major, in ''Fawlty Towers'' * Motoko Kusanagi or the Major, in ''Ghost in the Shell'' Film, television, theatre and print * '' The Major'', a 1963 BBC natural history documentary film * ''The Major'' (film), a 2013 Russian action film * ''Major'' (film), a 2022 Indian biopic * ''Major'' (manga), a sports manga and anime series by Takuya Mitsuda * ''The Major'' (play), an 1881 American musical comed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Major Third
In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two Whole step, whole steps. Along with the minor third, the major third is one of two commonly occurring thirds. It is described as ''major'' because it is the larger interval of the two: The major third spans four semitones, whereas the minor third only spans three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished third, Diminished and augmented thirds are shown on the musical staff the same number of lines and spaces apart, but contain a different number of semitones in pitch (two and five). Harmonic and non-harmonic thirds The major third may be derived from the harmonic series (music), harmonic series as the interval be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Octave
In music, an octave (: eighth) or perfect octave (sometimes called the Pythagorean interval, diapason) is an Interval (music), interval between two notes, one having twice the frequency of vibration of the other. 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". The interval between the first and second harmonics of the Harmonic series (music), harmonic series is an octave. In Western Musical notation, music notation, notes separated by an octave (or multiple octaves) have the same Musical note#Written notes, name and are of the same pitch class. To emphasize that it is one of the interval (music)#Perfect, perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other Interval quality, interval qualities are also possible, though rare. The octave above or below an indicated musical note, note is sometimes abbreviated ''8a'' o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Diminished Second
In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone.Bruce Benward and Marilyn Saker (2003). ''Music: In Theory and Practice, Vol. I'', p. 54. . Specific example of an d2 not given but general example of minor intervals described. In twelve-tone equal temperament, it is enharmonically equivalent to a perfect unison; therefore, it is the interval between notes on two adjacent staff positions, or having adjacent note letters, altered in such a way that they have no pitch difference in twelve-tone equal temperament. An example is the interval from a B to the C immediately above; another is the interval from a B to the C immediately above. In particular, it may be regarded as the "difference" between a diatonic and chromatic semitone. For instance, the interval from B to C is a diatonic semitone, the interval from B to B is a chromatic semitone, and their difference, the interval from B to C is a dimi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ditone
In music, a ditone (, from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also called a comma-redundant major third; the smallest is the interval with a ratio of 100:81, also called a comma-deficient major third. Pythagorean tuning The Pythagorean ditone is the major third in Pythagorean tuning, which has an interval ratio of 81:64, which is 407.82 cents. The Pythagorean ditone is evenly divisible by two major tones (9/8 or 203.91 cents) and is wider than a just major third (5/4, 386.31 cents) by a syntonic comma (81/80, 21.51 cents). Because it is a comma wider than a "perfect" major third of 5:4, it is called a "comma-redundant" interval. "The major third that appears commonly in the ythagoreansystem (C–E, D–F, etc.) is more properly known as the Pythagorean ditone and consists of two major and two minor semi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. 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". The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' (), ''8va bassa'' (, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing this mark above or below the staff. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive Musical note, notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the Tritone, diminished fifth spans six and the augmented fifth spans eight semitones. For example, the interval from C to G is a perfect fifth, as the note G lies seven semitones above C. The perfect fifth may be derived from the Harmonic series (music), harmonic series as the interval between the second and third harmonics. In a diatonic scale, the dominant (music), dominant note is a perfect fifth above the tonic (music), tonic note. The perfect fifth is more consonance and dissonance, consonant, or stable, than any other interval except the unison and the octave. It occu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Just Intonation
In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, 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 (music), harmonic series of an implied fundamental frequency, 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 (music), 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 fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pythagorean Limma
A semitone, also called a minor second, 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 (or half of a whole step), visually seen on a keyboard as the distance between two keys that are adjacent to each other. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
