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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 (B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minor Third On C
Minor may refer to: * Minor (law), a person under the age of certain legal activities. ** A person who has not reached the age of majority * Academic minor, a secondary field of study in undergraduate education Music theory *Minor chord ** Barbershop seventh chord or minor seventh chord *Minor interval *Minor key *Minor scale Mathematics * Minor (graph theory), the relation of one graph to another given certain conditions * Minor (linear algebra), the determinant of a certain submatrix People * Charles Minor (1835–1903), American college administrator * Charles A. Minor (21st-century), Liberian diplomat * Dan Minor (1909–1982), American jazz trombonist * Dave Minor (1922–1998), American basketball player * James T. Minor, US academic administrator and sociologist * Jerry Minor (born 1969), American actor, comedian and writer * Kyle Minor (born 1976), American writer * Mike Minor (actor) (born 1940), American actor * Mike Minor (baseball) (born 1987), American baseball pi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Sethares
William A. Sethares (born April 19, 1955) is an American music theorist and professor of electrical engineering at the University of Wisconsin. In music, he has contributed to the theory of Dynamic Tonality and provided a formalization of consonance. Consonance and dissonance Among the earliest musical traditions, musical consonance was thought to arise in a quasi-mystical manner from ratios of small whole numbers. (For instance, Pythagoras made observations relating to this, and the ancient Chinese Guqin contains a dotted scale representing the harmonic series.) The source of these ratios, in the pattern of vibrations known as the harmonic series, was exposed by Joseph Sauveur the early 18th century and even more clearly by Helmholtz in the 1860s. In 1965, Plomp and Levelt showed that this relationship could be generalized beyond the harmonic series, although they did not elaborate in detail. In the 1990s, Sethares began exploring Plomp and Levelt's generalization, both mathema ... [...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) * Equalizer (other) * Equalization (other) Equalization may refer to: Science and technology * B ... [...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 incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 th ... [...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 t ... [...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 oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Septimal Whole Tone
In music, the septimal whole tone, septimal major second, or supermajor second is the musical interval exactly or approximately equal to an 8/7 ratio of frequencies.Andrew Horner, Lydia Ayres (2002). ''Cooking with Csound: Woodwind and Brass Recipes'', p.131. . "Super-Major Second". It is about 231 cents wide in just intonation.Leta E. Miller, Fredric Lieberman (2006). ''Lou Harrison'', p.72. . 24 equal temperament does not match this interval particularly well, its nearest representation being at 250 cents, approximately 19 cents sharp. The septimal whole tone may be derived from the harmonic series as the interval between the seventh and eighth harmonics and the term ''septimal'' refers to the fact that it utilizes the seventh harmonic. It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh. No close approximation to this interval exists in the standard 12 equal temperament used in most modern western music. The very simple 5 equal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Seventh Chord
The harmonic seventh chord is a major triad plus the harmonic seventh interval (ratio of 7:4, about 968.826 centsBosanquet, Robert Holford Macdowall (1876). ''An elementary treatise on musical intervals and temperament'', pp. 41-42. Diapason Press; Houten, The Netherlands. .). This interval is somewhat narrower (about 48.77 cents flatter, a septimal quarter tone) and is "sweeter in quality" than an "ordinary""On Certain Novel Aspects of Harmony", p.119. Eustace J. Breakspeare. ''Proceedings of the Musical Association'', 13th Sess., (1886–1887), pp. 113–131. Published by: Oxford University Press on behalf of the Royal Musical Association. minor seventh, which has a just intonation ratio of 9:5 (1017.596 cents), or an equal-temperament ratio of 1000 cents (2:1). Uses Since barbershop music tends to be sung in just intonation, the barbershop seventh chord may be accurately termed a harmonic seventh chord. As guitars, pianos, and other equal-temperament instruments cannot pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Seventh
The harmonic seventh interval, also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio (about 969 cents). This is somewhat narrower than and is, "particularly sweet", "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5 (about 1018 cents). The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute a purely consonant major chord with added seventh (root position). When played on the natural horn, as a compromise the note is often adjusted to 16:9 of the root (for C maj7, the substituted note is B, 996.09 cents), but some pieces call for the pure harmonic seventh, including Britten's ''Serenade for Tenor, Horn and Strings''. Composer Ben Johnston uses a small "7" as an accidental to indicate a note is lowered 49 cents ... [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triad (music)
In music, a triad is a set of three notes (or "pitch classes") that can be stacked vertically in thirds.Ronald Pen, ''Introduction to Music'' (New York: McGraw-Hill, 1992): 81. . "A triad is a set of notes consisting of three notes built on successive intervals of a third. A triad can be constructed upon any note by adding alternating notes drawn from the scale.... In each case the note that forms the foundation pitch is called the ''root'', the middle tone of the triad is designated the ''third'' (because it is separated by the interval of a third from the root), and the top tone is referred to as the ''fifth'' (because it is a fifth away from the root)." Triads are the most common chords in Western music. When stacked in thirds, notes produce triads. The triad's members, from lowest-pitched tone to highest, are called: * the root **Note: Inversion does not change the root. (The third or fifth can be the lowest note.) * the third – its interval above the root being a minor thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
