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833 Cents Scale
The 833 cents scale is a musical tuning and scale proposed by Heinz Bohlen based on combination tones, an interval of 833.09 cents, and, coincidentally, the Fibonacci sequence.Bohlen, Heinz (last updated 2012).An 833 Cents Scale: An experiment on harmony, ''Huygens-Fokker.org''. The golden ratio is \varphi = \frac = 1.6180339887\ldots., which as a musical interval is 833.09 cents (). In the 833 cents scale this interval is taken as an alternative to the octave as the interval of repetition,833 Cent Golden Scale (Bohlen) , ''Xenharmonic Wiki''. however the golden ratio is not regarded as an interval (notes 833.09 cents apart are not "the same" in the 833 ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Golden Ratio Line
Golden means made of, or relating to gold. Golden may also refer to: Places United Kingdom *Golden, in the parish of Probus, Cornwall *Golden Cap, Dorset *Golden Square, Soho, London *Golden Valley, a valley on the River Frome in Gloucestershire *Golden Valley, Herefordshire United States *Golden, Colorado, a town West of Denver, county seat of Jefferson County *Golden, Idaho, an unincorporated community *Golden, Illinois, a village *Golden Township, Michigan *Golden, Mississippi, a village *Golden City, Missouri, a city *Golden, Missouri, an unincorporated community *Golden, Nebraska, ghost town in Burt County * Golden Township, Holt County, Nebraska *Golden, New Mexico, a sparsely populated ghost town *Golden, Oregon, an abandoned mining town *Golden, Texas, an unincorporated community *Golden, Utah, a ghost town * Golden, Marshall County, West Virginia, an unincorporated community Elsewhere *Golden, County Tipperary, Ireland, a village on the River Suir * Golden Vale, Munste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
833 Cents Scale Lattice To 4 And -3
__NOTOC__ Year 833 ( DCCCXXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Byzantine-Arab War: Emperor Theophilos signs an armistice for peace with the Abbasid Caliphate. He offers Caliph Al-Ma'mun 100,000 gold dinars, in return for 7,000 Byzantine prisoners.J. Norwich, ''Byzantine: The Apogee'', p. 47. Europe * June – Lothair I, eldest son of Emperor Louis the Pious, joins the rebellion of his brothers Pepin I and Louis the German, with the assistance of Archbishop Ebbo. Louis is forced to abdicate, on the plains of Rothfield (near Colmar). * Mojmir I, Moravian duke, expels Prince Pribina from his homeland (western part of modern Slovakia). He unifies Great Moravia and becomes the first known ruler of the Moravian Slavs, who founds the House of Mojmir (approximate date). * Galindo Aznárez I, Frankish count, usurps the Catalan counties ('' pagi'') of Palla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler Triangle
A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is \sqrt\varphi where \varphi=(1+\sqrt)/2 is the golden ratio, and the progression can be written: or approximately . Squares on the edges of this triangle have areas in another geometric progression, 1:\varphi:\varphi^2. Alternative definitions of the same triangle characterize it in terms of the three Pythagorean means of two numbers, or via the inradius of isosceles triangles. This triangle is named after Johannes Kepler, but can be found in earlier sources. Although some sources claim that ancient Egyptian pyramids had proportions based on a Kepler triangle, most scholars believe that the golden ratio was not known to Egyptian mathematics and architecture. History The Kepler triangle is named after the German mathematician and astronomer Johannes Kepler (1571–1630), who wrote about this shape in a 1597 letter. Two concepts that can be used to analyze this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
36 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] |
Generated Collection
In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection or scale is formed. All scales with the deep scale property can be generated by any interval coprime with (in twelve-tone equal temperament) twelve. (Johnson, 2003, p. 83) The C major diatonic collection can be generated by adding a cycle of perfect fifths (C7) starting at F: F-C-G-D-A-E-B = C-D-E-F-G-A-B. Using integer notation and modulo 12: 5 + 7 = 0, 0 + 7 = 7, 7 + 7 = 2, 2 + 7 = 9, 9 + 7 = 4, 4 + 7 = 11. The C major scale could also be generated using cycle of perfect fourths (C5), as 12 minus any coprime of twelve is also coprime with twelve: 12 − 7 = 5. B-E-A-D-G-C-F. A gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Of Fifths
In music theory, the circle of fifths is a way of organizing the 12 chromatic pitches as a sequence of perfect fifths. (This is strictly true in the standard 12-tone equal temperament system — using a different system requires one interval of diminished sixth to be treated as a fifth). If C is chosen as a starting point, the sequence is: C, G, D, A, E, B (=C), F (=G), C (=D), A, E, B, F. Continuing the pattern from F returns the sequence to its starting point of C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle. Definition The circle of fifths organizes pitches in a sequence of perfect fifths, generally shown as a circle with the pitches (and their corresponding keys) in a clockwise progression. Musicians and composers often use the circle of fifths to describe the musical relationships between pitches. Its design is helpful in composing and harmonizing melodies, building chords, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
833 Cents Scale Generator Circle W P5 And P4 Bnw 7
__NOTOC__ Year 833 ( DCCCXXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Byzantine-Arab War: Emperor Theophilos signs an armistice for peace with the Abbasid Caliphate. He offers Caliph Al-Ma'mun 100,000 gold dinars, in return for 7,000 Byzantine prisoners.J. Norwich, ''Byzantine: The Apogee'', p. 47. Europe * June – Lothair I, eldest son of Emperor Louis the Pious, joins the rebellion of his brothers Pepin I and Louis the German, with the assistance of Archbishop Ebbo. Louis is forced to abdicate, on the plains of Rothfield (near Colmar). * Mojmir I, Moravian duke, expels Prince Pribina from his homeland (western part of modern Slovakia). He unifies Great Moravia and becomes the first known ruler of the Moravian Slavs, who founds the House of Mojmir (approximate date). * Galindo Aznárez I, Frankish count, usurps the Catalan counties ('' pagi'') of Pallars and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptatonic Scale
A heptatonic scale is a musical scale that has seven pitches, or tones, per octave. Examples include the major scale or minor scale; e.g., in C major: C D E F G A B C—and in the relative minor, A minor, natural minor: A B C D E F G A; the melodic minor scale, A B C D E FGA ascending, A G F E D C B A descending; the harmonic minor scale, A B C D E F GA; and a scale variously known as the Byzantine, and Hungarian,''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell (London, 2001) scale, C D E F G A B C. Indian classical theory postulates seventy-two seven-tone scale types, collectively called ''thaat'', whereas others postulate twelve or ten (depending on the theorist) seven-tone scale types. Several heptatonic scales in Western, Roman, Spanish, Hungarian, and Greek music can be analyzed as juxtapositions of tetrachords.Dupré, Marcel (1962). ''Cours Complet d'Improvisation a l'Orgue'', v.2, p. 35, trans. John Fensterm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetric Scale
In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger and further developed by Nicolas Slonimsky as part of his famous ''Thesaurus of Scales and Melodic Patterns''. In twelve-tone equal temperament, the octave can only be equally divided into two, three, four, six, or twelve parts, which consequently may be filled in by adding the same exact interval or sequence of intervals to each resulting note (called "interpolation of notes"). Examples include the octatonic scale (also known as the ''symmetric diminished'' scale; its mirror image is known as the ''inverse symmetric diminished'' scale) and the two-semitone tritone scale: As explained above, both are composed of repeating sub-units within an octave. This property allows these scales to be transposed to other notes, yet retain exactly the same notes as the original scale (Translational symmetry). This may be seen quite readil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irrational Number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being '' incommensurable'', meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself. Among irrational numbers are the ratio of a circle's circumference to its diameter, Euler's number ''e'', the golden ratio ''φ'', and the square root of two. In fact, all square roots of natural numbers, other than of perfect squares, are irrational. Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lattice (music)
In musical tuning, a lattice "is a way of modeling the tuning relationships of a just intonation system. It is an array of points in a periodic multidimensional pattern. Each point on the lattice corresponds to a ratio (i.e., a pitch, or an interval with respect to some other point on the lattice). The lattice can be two-, three-, or ''n''-dimensional, with each dimension corresponding to a different prime-number partial ."Gilmore, Bob (2006). "Introduction", p.xviii, ''"Maximum Clarity" and Other Writings on Music'', edited by Bob Gilmore. Urbana: University of Illinois Press. . When listed in a spreadsheet a lattice may be referred to as a tuning table. The points in a lattice represent pitch classes (or pitches if octaves are represented), and the connectors in a lattice represent the intervals between them. The connecting lines in a lattice display intervals as vectors, so that a line of the same length and angle always has the same intervalic relationship between the point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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