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In music theory, the circle of fifths is a model of pitch space. It consists all 12 notes of the (equally tempered) chromatic scale. Starting on any note and repeatedly ascending by the musical interval of a perfect fifth, one will eventually land on the same note, after reaching all of the other notes: Music theory is a field of study that describes the elements of music and includes the development and application of methods for analyzing and composing music, and the interrelationship between the notation of music and performance practice. ...
In music pitch space is pitch relations, ie nearness or farness, represented through geometric models, most often multidimensional, how near or far pitches are from each other. ...
Equal temperament is a scheme of musical tuning in which the octave is divided into a series of equal steps (equal frequency ratios). ...
The chromatic scale is any musical scale that contains more than one consecutive half-step (in other words two adjacent pairs of scale degrees or members which are separated by a semitone). ...
In music theory, an interval is the difference (a ratio or logarithmic measure) in pitch between two notes and often refers to those two notes themselves (otherwise known as a dyad). ...
The musical interval of a perfect fifth is the relationship between the first note (the root or tonic) and the fifth note in a major scale. ...
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 Descending by fifths, and ascending or descending by fourths also works, since motion in one direction by a fourth is equivalent to motion in the opposite direction by a fifth. For this reason the circle of fifths is also known as the circle of fourths. Image File history File links This is a diagram of the circle of fifths; see that page for more information. ...
Use
The circle is commonly used to represent the relations between diatonic scales. The numbers on the inside of the circle show how many sharps or flats (accidentals) would be in the key signature for a major scale built on that note. Thus a major scale built on A will have three sharps in its key signature. For minor scales, rotate the numbers clockwise by 3, so that e.g. A minor has 0 accidentals and E minor has 1 sharp. (See relative minor/major for details.) In music theory, a diatonic scale is a scale whose notes are built on the natural staff positions of lines and spaces, with no accidentals, with or without a key signature. ...
In musical notation, a key signature is a series of sharp symbols or flat symbols placed on the staff, designating notes that are to be played one semitone higher or lower unless otherwise noted with an accidental. ...
In music theory, the major scale (or major mode) is one of the diatonic scales. ...
A minor scale in musical theory is a diatonic scale whose third scale degree is an interval of a minor third above the tonic. ...
In music, the relative minor of a particular major key (or the relative major of a minor key) is the key which has the same key signature but a different tonic, as opposed to parallel minor or major, respectively. ...
Moving around the circle of fifths is a common way to modulate. In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another, also known as a key change. ...
For information on the circle of fifths in popular music harmony see Winkler, P. (1978). Profane Culture. London.
Related concepts
diatonic circle of fifths The diatonic circle of fifths is the circle of fifths encompassing only members of the diatonic scale. As such it contains a diminished fifth, in C major between B and F. See structure implies multiplicity. In diatonic set theory structure implies multiplicity is quality of a collection or scale for which the interval series formed by the shortest distance around a diatonic circle of fifths between member of a series indicates the number of unique interval patterns (adjacently, rather than around the circle of fifths...
Relation with chromatic scale The circle of fifths, or fourths, may be mapped from the chromatic scale by multiplication, and vice versus. To map between the circle of fifths and the chromatic scale (in integer notation) multiply by 7 (M7), and for the circle of fourths multiply by 5 (M5). The chromatic scale is any musical scale that contains more than one consecutive half-step (in other words two adjacent pairs of scale degrees or members which are separated by a semitone). ...
In its simplest form, multiplication is the sum of a list of identical numbers. ...
Music notation is a system of writing for music. ...
Twelve-tone technique (also dodecaphony) is a system of musical composition devised by Arnold Schoenberg. ...
Here is a demonstration of this procedure. Start off with an ordered 12-tuple (tone row) of integers Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ...
In music, a tone row or note row is a permutation, an arrangement or ordering, of the twelve notes of the chromatic scale. ...
- (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
representing the notes of the chromatic scale: 0 = C, 2 = D, 4 = E, 5 = F, 7 = G, 9 = A, 11 = B, 1 = C#, 3 = D#, 6 = F#, 8 = G#, 10 = A#. Now multiply the entire 12-tuple by 7: - (0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77)
and then apply a modulo 12 reduction to each of the numbers (subtract 12 from each number as many times as necessary until the number becomes smaller than 12): In advanced theoretical physics, a modulus is a scalar field with no potential energy. ...
- (0, 7, 2, 9, 4, 11, 6, 1, 8, 3, 10, 5)
which is equivalent to - (C, G, D, A, E, B, F#, C#, G#, D#, A#, F),
which is the circle of fifths.
History This was supposedly invented in the sixth century B.C. by Pythagoras. It is said that Pythagoras also had the idea of tuning an instrument by fifths and thus discovered the Pythagorean comma. This topic is considered a necessary subject on Wikipedia, and there is a high-priority on its being cleaned up to conform to a higher standard of quality. ...
When you ascend by a cycle of justly tuned perfect fifths (ratio 3:2), leapfrogging 12 times, you eventually reach a note around seven octaves above the note you started on, which, when lowered to the same octave as your starting point, is 23. ...
Harmonic functionality One theory regarding harmonic functionality is that "functional succession is explained by the circle of fifths (in which, therefore, scale degree II is closer to the dominant than scale degree IV)." According to Goldman's Harmony in Western Music, "the IV chord is actually, in the simplest mechanisms of diatonic relationships, at the greatest distance from I. In terms of the circle of fifths, it leads away from I, rather than toward it." (1965, p.68) Thus the progression I-ii-V-I would comply more with tonal logic. However, Goldman (ibid., chapter 3), as well as Jean-Jacques Nattiez, points out that "the chord on the fourth degree appears long before the chord on II, and the subsequent final I, in the progression I-IV-viio-iii-vi-ii-V-I." (Nattiez 1990, p. 226) Goldman also points out that, "historically the use of the IV chord in harmonic design, and especially in cadences, exhibits some curious features. By and large, one can say that the use of IV in final cadences becomes more common in the nineteenth century than it was in the eighteenth, but that it may also be understood as a substitute for the ii chord when it proceeds V. It may also be quite logically construed as an incomplete ii7 chord (lacking root)." (1968, p.68) However, Nattiez calls this, "a narrow escape: only the theory of a ii chord without a root allows Goldman to maintain that the circle of fifths is completely valid from Bach to Wagner." (1990, p.226) See also: function and functional. ...
See also In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...
In Western musical theory a cadence (Latin cadentia, a falling) is a particular series of intervals (a caesura) or chords that ends a phrase, section, or piece of music. ...
Sonata form refers to both the standard layout of an entire musical composition and more specifically to the standardized form of the first movement. ...
Source - Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0691027145.
- D'Indy (1903).
- Goldman (1965). Harmony in Western Music.
Jean-Jacques Nattiez is a musical semiologist or semiotician and professor of Musicology at the University of Montreal. ...
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