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Rothenberg Propriety
In diatonic set theory, Rothenberg propriety is an important concept, lack of contradiction and ambiguity, in the general theory of musical scales which was introduced by David Rothenberg in a seminal series of papers in 1978. The concept was independently discovered in a more restricted context by Gerald Balzano, who termed it ''coherence''. "Rothenberg calls a scale 'strictly proper' if it possesses a generic ordering, 'proper' if it admits ambiguities but no contradictions, and 'improper' if it admits contradictions." A scale is strictly proper if all two step intervals are larger than any one step interval, all three step intervals are larger than any two step interval and so on. For instance with the diatonic scale, the one step intervals are the semitone (1) and tone (2), the two step intervals are the minor (3) and major (4) third, the three step intervals are the fourth (5) and tritone (6), the four step intervals are the fifth (7) and tritone (6), the five step interv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rothenberg Propriety Diatonic Scale
Rothenberg is a village and a former municipality in the Odenwaldkreis (district) in Hesse, Germany. Since January 2018, it is part of the new town Oberzent. Geography Location Rothenberg lies at elevations between 200 and 500 m in the southern Odenwald in the ''Geo-Naturpark Bergstraße-Odenwald'', 7 km north of Hirschhorn on the Neckar. The main centre lies in the south of the municipal area as a high settlement in a clearing 430 m high on the ridge of the otherwise wooded Hirschhorner Höhe (heights). The municipal area stretches northwestwards along the Finkenbach. Many tourists visit Billy Rothenberg because of the wonderful natural setting and because of so many possibilities for sports such as swimming, riding bikes, riding horses, hiking, gliding (with a flex-wing or with a glider). Neighbouring communities Rothenberg borders in the north on the town of Beerfelden (Odenwaldkreis), in the east on the town of Eberbach (Rhein-Neckar-Kreis in Baden-Württember ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Otonal
''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,.... Definition An otonality is a collection of pitches which can be expressed in ratios, expressing their relationship to the fixed tone, that have equal denominators and consecutive numerators. For example, , , and (just major chord) form an otonality because they can be written as , , . This in turn can be written as an extended ratio 4:5:6. Every otonality is therefore composed of members of a harmonic series. Similarly, the ratios of a utonality share the same numerator and have consecutive denominators. , , , and () form a utonality, sometimes written as , or as . Every utonality is therefore composed of members of a subharmonic series. This term is used extensively by Harry Partch in ''Genesis of a Music''. An otonality corresponds to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval Class
In musical set theory, an interval class (often abbreviated: ic), also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'" (; ), is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 ≡ 7 (mod 12). See modular arithmetic for more on modulo 12. The largest interval class is 6 since any greater interval ''n'' may be reduced to 12 − ''n''. Use of interval classes The concept of interval class accounts for octave, enharmonic, and inversional equivalency. Consider, for instance, the following passage: (To hear a MIDI realization, click the following: In the example above, all four labeled pitch-pairs, or dyads, share a common "intervallic color." In atonal theory, this sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diminished Fifth
Diminished may refer to: *Diminution In Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of ... in music * "Diminished" (R.E.M. song), from the 1998 album ''Up'' {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augmented Fourth
Augment or augmentation may refer to: Language *Augment (Indo-European), a syllable added to the beginning of the word in certain Indo-European languages *Augment (Bantu languages), a morpheme that is prefixed to the noun class prefix of nouns in certain Bantu languages *Augment, a name sometimes given to the verbal ''ō-'' prefix in Nahuatl grammar Technology *Augmentation (obstetrics), the process by which the first and/or second stages of an already established labour is accelerated or potentiated by deliberate and artificial means *Augmentation (pharmacology), the combination of two or more drugs to achieve better treatment results *Augmented reality, a live view of a physical, real-world environment whose elements are ''augmented'' by computer-generated sensory input *Augmented cognition, a research field that aims at creating revolutionary human-computer interactions *Augment (Tymshare), a hypertext system derived from Douglas Engelbart's oN-Line System, renamed "Augment" b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tritone
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. Narrowly defined, each of these whole tones must be a step in the scale, so by this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. More broadly, a tritone is also commonly defined as any interval with a width of three whole tones (spanning six semitones in the chromatic scale), regardless of scale degrees. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augmented fourth) and B–F (from B to the F abo ... [...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] |
Pitch Class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set : = . Although there is no formal upper or lower limit to this sequence, only a few of these pitches are audible to humans. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called "octave equivalence". Psychologists refer to the quality of a pitch as its "chroma". A ''chroma'' is an attribute of pitches (as opposed to ''tone height''), just like hue is an attribute of color. A ''pitch class'' is a set of all pit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. 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'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by placing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasiperiodic Function
In mathematics, a quasiperiodic function is a function (mathematics), function that has a certain similarity to a periodic function. A function f is quasiperiodic with quasiperiod \omega if f(z + \omega) = g(z,f(z)), where g is a "''simpler''" function than f. What it means to be "''simpler''" is vague. A simple case (sometimes called arithmetic quasiperiodic) is if the function obeys the equation: : f(z + \omega) = f(z) + C Another case (sometimes called geometric quasiperiodic) is if the function obeys the equation: : f(z + \omega) = C f(z) An example of this is the theta function, Jacobi theta function, where :\vartheta(z+\tau;\tau) = e^{-2\pi iz - \pi i\tau}\vartheta(z;\tau), shows that for fixed \tau it has quasiperiod \tau; it also is periodic with period one. Another example is provided by the Weierstrass sigma function, which is quasiperiodic in two independent quasiperiods, the periods of the corresponding Weierstrass elliptic functions, Weierstrass ''℘'' funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hirajōshi Scale
''Hirajōshi'' scale, or is a tuning scale adapted from shamisen music by Yatsuhashi Kengyō for tuning of the ''koto''. "The ''hirajoshi'', ''kumoijoshi'', and ''kokinjoshi'' 'scales' are Western derivations of the koto tunings of the same names. These scales have been used by rock and jazz guitarists in search of 'new' sounds."Speed, Burgess (2008). ''Japan: Your Passport to a New World of Music'', p.15. . Burrows gives C-E-F-G-B. Sachs, as well as Slonimsky, give C-D-F-G-B. Speed and Kostka & PayneKostka & Payne (1995). ''Tonal Harmony'', p.484. Third Edition. . give C-D-E-G-A. Note that all are hemitonic pentatonic scales (five note scales with one or more semitones) and are different modes of the same pattern of intervals, 2-1-4-1-4 semitones. Peter Sculthorpe's Earth Cry uses the Hirajoshi mode as a tonal centre of the work. The five modes of ''hirajoshi'' can also be derived as subsets of the Ionian, Phrygian, Lydian, Aeolian, and Locrian modes. Synonymous sca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
