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Gamma Scale
The γ (gamma) scale is a non-octave repeating musical scale invented by Wendy Carlos while preparing ''Beauty in the Beast'' (1986) though it does not appear on the album. It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into 20 equal parts (3:2≈35.1 cents), by splitting the neutral third into two equal parts, or ten equal parts of approximately 35.1 cents each () for 34.188 steps per octave.Carlos, Wendy (1989–96)"Three Asymmetric Divisions of the Octave" ''WendyCarlos.com''. The scale step may also precisely be derived from using 20:11 (B, 1035 cents, ) to approximate the interval , which equals 6:5 (E, 315.64 cents, ). Thus the step is approximately 35.099 cents and there are 34.1895 per octave.Benson, Dave (2006). ''Music: A Mathematical Offering'', p.232-233. . "Carlos has 34.188 γ-scale degrees to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Third On C
Neutral or neutrality may refer to: Mathematics and natural science Biology * Neutral organisms, in ecology, those that obey the unified neutral theory of biodiversity Chemistry and physics * Neutralization (chemistry), a chemical reaction in which an acid and a base react quantitatively with each other * Neutral solution, a chemical solution which is neither acidic nor basic * Neutral particle, a particle without electrical charge Mathematics * Neutral element or identity element, in mathematics, a special element with respect to a binary operation, such that if the operation is applied to any element in a set, that element is unchanged * Neutral vector, a multivariate random variable that exhibits a particular type of statistical independence ( Dirichlet distribution) Philosophy * Neutrality (philosophy), the absence of declared or intentional bias * Neutrality (psychoanalysis) * Neutral level, the physical or material traces of esthesic and poietic processes identified ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Step
In Schenkerian theory, a scale-step (german: Stufe) is a triad (based on one of the diatonic scale degrees) that is perceived as an organizing force for a passage of music (in accordance with the principle of composing-out). In ''Harmony'', Schenker gives the following example and asserts that A scale-step triad is designated by an uppercase Roman numeral representing the scale degree of the root, much as in traditional "harmonic analysis" (see chord progression). Thus, in the above example (which is in G major), the G major triad that Schenker claims we perceive through the first two measures would be labelled "I". However, unlike traditional harmonic analyses, Schenker's theory is not concerned with the mere labelling of such chords, but rather with discerning hierarchical relationships among tones. For Schenker, the chords occurring in a passage need not be of equal import. As he explains: Furthermore, in terms of Schenker's mature theory, the question of whether a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equal Temperaments
Equal(s) may refer to: Mathematics * Equality (mathematics). * Equals sign (=), a mathematical symbol used to indicate equality. Arts and entertainment * ''Equals'' (film), a 2015 American science fiction film * ''Equals'' (game), a board game * The Equals, a British pop group formed in 1965 * "Equal", a 2016 song by Chrisette Michele from ''Milestone'' * "Equal", a 2022 song by Odesza featuring Låpsley from '' The Last Goodbye'' * "Equals", a 2009 song by Set Your Goals from '' This Will Be the Death of Us'' * ''Equal'' (TV series), a 2020 American docuseries on HBO * ''='' (album), a 2021 album by Ed Sheeran * "=", a 2022 song by J-Hope from ''Jack in the Box'' Other uses * Equal (sweetener), a brand of artificial sweetener. * EQUAL Community Initiative, an initiative within the European Social Fund of the European Union. See also * Equality (other) Equality may refer to: Society * Political equality, in which all members of a society are of equal standing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Chord
An octatonic scale is any eight-note musical scale. However, the term most often refers to the symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory (in contrast to jazz theory), this symmetrical scale is commonly called the ''octatonic scale'' (or the ''octatonic collection''), although there are a total of 42 enharmonically non-equivalent, transpositionally non-equivalent eight-note sets. The earliest systematic treatment of the octatonic scale was in Edmond de Polignac's unpublished treatise "Étude sur les successions alternantes de tons et demi-tons (Et sur la gamme dite majeure-mineure)" (''Study of the Succession of Alternating Whole Tones and Semitones (and of the so-called Major-Minor Scale)'') from c. 1879, which preceded Vito Frazzi's ''Scale alternate per pianoforte'' of 1930 by a full half-century. Nomenclature In Saint Petersburg at the turn of the 20th century, this scale had become so familiar in the circle of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohlen–Pierce Scale
The Bohlen–Pierce scale (BP scale) is a musical tuning and scale, first described in the 1970s, that offers an alternative to the octave-repeating scales typical in Western and other musics, specifically the equal-tempered diatonic scale. The interval 3:1 (often called by a new name, ''tritave'') serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave) with a perfect twelfth (an octave higher than a perfect fifth). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent. The BP scale divides the tritave into 13 steps, either equal tempered (the most popular form), or in a justly tuned version. Compared with octave-repeating scales, the BP scale's intervals are more consonant with certain types of acoustic spectra. The scale was independently described by Heinz Bohlen, Kees van Prooijen and John R. Pierce. Pierce, who, with Max Mathews and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delta Scale
The δ (delta) scale is a non-octave repeating musical scale. It may be regarded as the beta scale's reciprocal, since it is "as far 'down' the ( 0 3 6 9) circle from α as β is 'up'".Taruskin, Richard (1996). ''Stravinsky and the Russian Traditions: A Biography of the Works through Mavra'', p. 1394. . As such it would split the minor second (presumably 16:15) into eight equal parts of approximately 14 cents each . This would total approximately 85.7 steps per octave. The scale step may also precisely be derived from using 50:28 (25:14, 1003.8 cents, A, ) to approximate the interval , which equals 6:5 (E, 315.64 cents, ). Thus the step is approximately 13.946 cents, and there are 86.049 steps per octave. :\begin \frac = 0.011\,621\,2701 \\ 0.011\,621\,2701 \times 1200 = 13.945\,524\,1627 \end () The Bohlen–Pierce delta scale is based on the tritave and the 7:5:3 "wide" triad () and the 9:7:5 "narrow" triad () (rather than the conventional 4:5:6 triad). Notes in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Scale
The β (beta) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album ''Beauty in the Beast'' (1986). It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into eleven equal parts 3:2) ≈ 63.8 cents It may be approximated by splitting the perfect fourth (4:3) into two equal parts 4:3)Milano, Dominic (November 1986)"A Many-Colored Jungle of Exotic Tunings" ''Keyboard''. or eight equal parts 4:3) = 64 centsCarlos, Wendy (2000/1986). "Liner notes", ''Beauty in the Beast''. ESD 81552. totaling approximately 18.8 steps per octave. The scale step may also precisely be derived from using 11:6 (B, 1049.36 cents, ) to approximate the interval , which equals 6:5 . \frac=0.05319411048 and 0.05319411048\times1200=63.832932576 () Although neither has an octave, one advantage to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha Scale
The α (alpha) scale is a non-octave-repeating musical scale invented by Wendy Carlos and first used on her album ''Beauty in the Beast'' (1986). It is derived from approximating just intervals using multiples of a single interval, but without requiring (as equal temperaments normally do) an octave (2:1). It may be approximated by dividing the perfect fifth (3:2) into nine equal steps (3:2),Carlos, Wendy (1989–96)"Three Asymmetric Divisions of the Octave" ''WendyCarlos.com''. "9 steps to the perfect (no kidding) fifth." The alpha scale "splits the minor third exactly in half (also into quarters)." or by dividing the minor third (6:5) into four steps (6:5).Milano, Dominic (November 1986)"A Many-Colored Jungle of Exotic Tunings" ''Keyboard''. "The idea was to split a minor third into two equal parts. Then that was divided again."Carlos, Wendy (2000/1986). "Liner notes", ''Beauty in the Beast''. ESD 81552. The size of this scale step may also be precisely derived from using 9:5 ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diatonic Scale
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other (i.e. separated by at least two whole steps). The seven pitches of any diatonic scale can also be obtained by using a chain of six perfect fifths. For instance, the seven natural pitch classes that form the C-major scale can be obtained from a stack of perfect fifths starting from F: :F–C–G–D–A–E–B Any sequence of seven successive natural notes, such as C–D–E–F–G–A–B, and any transposition thereof, is a diatonic scale. Modern musical keyboards are designed so that the white notes form a diatonic scale, though transpositions of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neutral Third
A neutral third is a musical interval wider than a minor third but narrower than a major third , named by Jan Pieter Land in 1880. Land makes reference to the neutral third attributed to Zalzal (8th c.), described by Al-Farabi (10th c.) as corresponding to a ratio of 27:22 (354.5 cents) and by Avicenna (Ibn Sina, 11th c.) as 39:32 (342.5 cents). The Zalzalian third may have been a mobile interval. Three distinct intervals may be termed neutral thirds: * The ''undecimal neutral third'' has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents . This ratio is the mathematical mediant of the major third 5/4 and the minor third 6/5, and as such, has the property that if harmonic notes of frequency ''f'' and (11/9) ''f'' are played together, the beat frequency of the 5th harmonic of the lower pitch against the 4th of the upper, i.e. , 5 f - 4 (11/9) f, = (1/9) f, is the same as the beat frequency of the 6th harmonic of the lower pitch against the 5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromatic Circle
The chromatic circle is a clock diagram for displaying relationships among the 12 equal-tempered pitch classes making up the familiar chromatic scale on a circle. Explanation If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a semitone, one will eventually land on a pitch with the same pitch class as the initial one, having passed through all the other equal-tempered chromatic pitch classes in between. Since the space is circular, it is also possible to descend by semitone. The chromatic circle is useful because it represents melodic distance, which is often correlated with physical distance on musical instruments. For instance, to move from any C on a piano keyboard to the nearest E, one must move up four semitones, corresponding to four clockwise steps on the chromatic circle. One can also move ''down'' by eight semitones, corresponding to eight counterclockwise steps on the pitch class circle. Larger motions on the piano (or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fifth
In music theory, a perfect fifth is the musical interval corresponding to a pair of 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 five consecutive notes in a diatonic scale. The perfect fifth (often abbreviated P5) spans seven semitones, while the 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 as the interval between the second and third harmonics. In a diatonic scale, the dominant note is a perfect fifth above the tonic note. The perfect fifth is more consonant, or stable, than any other interval except the unison and the octave. It occurs above the root of all major and minor chords (triads) and their extensions. Until the late 19th century, it was often referred to by one of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
