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Encyclopedia > Circle of fifths

In music theory, the circle of fifths (or cycle of fifths) is an imaginary geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. The circle of fifths was first described by Johann David Heinichen, in his 1728 treatise Der Generalbass in der Composition. Music Theory is a field of study that investigates the nature or mechanics of music. ... An equal temperament is a musical temperament -- that is, a system of tuning intended to approximate some form of just intonation -- in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... The chromatic scale is the scale that contains all twelve pitches of the Western tempered scale. ... Johann David Heinichen (1683 - July 16, 1729) was a Baroque composer and theorist active in Dresden at the court of Augustus the Strong. ...

Contents

Structure and Use

If one starts on any equal-tempered pitch and repeatedly ascends by the musical interval of a perfect fifth, one will eventually land on a pitch with the same pitch class as the initial one, passing through all the other equal-tempered chromatic pitch classes in between. 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 perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...

Since the space is circular, it is also possible to descend by fifths. In pitch class space, 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 Fifths. ...


The circle is commonly used to represent the relations between diatonic scales. Here, the letters on the circle are taken to represent the major scale with that note as tonic. The numbers on the inside of the circle show how many sharps or flats the key signature for this scale would have. Thus a major scale built on A will have three sharps in its key signature. The major scale built on F would have one flat. For minor scales, rotate the letters counter-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 (from the Greek diatonikos, to stretch out; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. ... This key signature – A major or F# minor – consists of three sharps placed after the clef 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 consistently played one semitone higher or lower than the... 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. ...


Tonal music often modulates by moving between adjacent scales on the circle of fifths. This is because diatonic scales contain seven pitch classes that are contiguous on the circle of fifths. It follows that diatonic scales a perfect fifth apart share six of their seven notes. Furthermore, the notes not held in common differ by only a semitone. Thus modulation by perfect fifth can be accomplished in an exceptionally smooth fashion. For example, to move from the C major scale F - C - G - D - A - E - B to the G major scale C - G - D - A - E - B - F♯, one need only move the C major scale's "F" to "F♯." In music, modulation is most commonly the act or process of changing from one key (tonic, or tonal center) to another. ...


In Western tonal music, one also finds chord progressions between chords whose roots are related by perfect fifth. For instance, root progressions such as D-G-C are common. For this reason, the circle of fifths can often be used to represent "harmonic distance" between chords.


The circle of fifths is closely related to the chromatic circle, which also arranges the twelve equal-tempered pitch classes in a circular ordering. A key difference between the two circles is that the chromatic circle can be understood as a continuous space where every point on the circle corresponds to a conceivable pitch class, and every conceivable pitch class corresponds to a point on the circle. By contrast, the circle of fifths is fundamentally a discrete structure, and there is no obvious way to assign pitch classes to each of its points. In this sense, the two circles are mathematically quite different. The chromatic circle is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... The chromatic circle is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...


However, the twelve equal-tempered pitch classes can be represented by the cyclic group of order twelve, or equivalently, the residue classes modulo twelve, Z/12Z. The group Z12 has four generators, which can be identified with the ascending and descending semitones and the ascending and descending perfect fifths. The semitonal generator gives rise to the chromatic circle while the perfect fifth gives rise to the circle of fifths shown here. In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ... In group theory, a cyclic group is a group that can be generated by a single element, in the sense that the group has an element a (called a generator of the group) such that, when written multiplicatively, every element of the group is a power of a (or na... Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic because of its use in the 24-hour clock system) is a system of arithmetic for integers, where numbers wrap around after they reach a certain value — the modulus. ... The chromatic circle is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ...


In layman's terms

A simple way to see the relationship between these notes is by looking at a piano keyboard, and starting at any key and counting 7 keys to the right (both black and white) to get to the next note on the circle above - which is a perfect fifth. 7 half steps or the distance from the 1st to the 8th key on a piano is a perfect fifth. The layout of a typical musical keyboard A musical keyboard is the set of adjacent depressible levers on a musical instrument which cause the instrument to produce sounds. ...


The frequencies of two notes that are a perfect fifth apart differ by a ratio of approximately 3:2 = 1.5. A ratio of exactly 1.5 sounds best, and this explains why a perfect fifth sounds consonant, though for mathematical reasons it is not possible to get the circle of fifths to 'join up' (i.e. return to the original pitch after going round the circle) unless a close approximation to a perfect fifth is used, namely 2 to the power 7/12 = 1.498. This is the basis of the tuning nowadays used for Western instruments, called 'equal temperament', which enables music to be played in any key by having all intervals tuned the same way (i.e. using the same ratios) in all keys.


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 versa. 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 the scale that contains all twelve pitches of the Western tempered scale. ... In mathematics, multiplication is an elementary arithmetic operation. ... Music notation is a system of writing for music. ... Twelve-tone technique (also dodecaphony) is a method 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): The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means a small measure. ...

(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. Note that this is enharmonically identical to: In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ...

(C, G, D, A, E, B, G♭, D♭, A♭, E♭, B♭, F)

Infinite Series

The “bottom keys” of the circle of fifths are often written in flats and sharps, as they are easily interchanged using enharmonics. For example, the key of B, with five sharps, is enharmonically equivalent to the key of C♭, with 7 flats. But the circle of sharps doesn’t stop at 7 sharps (C♯) nor 7 flats (C♭). Following the same pattern, one can construct a circle of fifths with all sharp keys, or all flat keys.


After C♯ comes the key of G♯ (following the pattern of being a fifth higher, and, coincidently, enharmonically equivalent to the key of A♭). The “8th sharp” is placed on the F♯, to make it F♯♯. The key of D♯, with 9 sharps, has another sharp placed on the C♯, making it C♯♯. The same for key signatures with flats is true; The key of E (four sharps) is equivalent to the key of F♭ (again, one fifth below the key of C♭, following the pattern of flat key signatures. The double-flat is placed on the B♭)


The circle used in instrument building

Piano keys translated to the tuning of Landmans Moodswinger
Piano keys translated to the tuning of Landmans Moodswinger

Experimental luthier Yuri Landman created a twelve string overtone zither and tuned this in a circle of fourths: Image File history File linksMetadata Size of this preview: 800 × 196 pixelsFull resolution (2894 × 709 pixel, file size: 180 KB, MIME type: image/jpeg) my own drawing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Circle of fifths... Image File history File linksMetadata Size of this preview: 800 × 196 pixelsFull resolution (2894 × 709 pixel, file size: 180 KB, MIME type: image/jpeg) my own drawing File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Circle of fifths... In 2006 luthier Yuri Landman built the Moodswinger, a 12 string overtone zither for Aaron Hemphill of the noiseband Liars The Moodswinger is a custom made string instrument made by Yuri Landman. ... An engravers impression of Antonio Stradivari examining an instrument. ... Yuri Landman (born 1-2-1973) is a dutch multi disciplined artist most well known for his work as an experimental luthier, but also active as a comic artist, illustrator, musician, singer, graphic designer and furniture designer. ... In 2006 luthier Yuri Landman built the Moodswinger, a 12 string overtone zither for Aaron Hemphill of the noiseband Liars The Moodswinger is a custom made string instrument made by Yuri Landman. ...


E-A-D-G-C-F-A#-D#-G#-C#-F#-B, arranged in 3 clusters of 4 strings to make the field of strings more readable.


Because of this tuning all five neighbouring strings form a harmonic pentatonic scale and all seven neighbouring strings form a major scale, available in every key. This allows a very easy fingerpicking technique without picking false notes, if the right key is chosen. In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. ... In music, a pentatonic scale is a scale with five notes per octave. ... In music theory, the major scale (or major mode) is one of the diatonic scales. ... In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ... It has been suggested that this article or section be merged with Fingerstyle guitar. ...


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 or chords that ends a phrase, section, or piece of music. ... Sonata form is a musical form that has been used widely since the early Classical period. ... The chromatic circle is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale. ... Well temperament (also circular or circulating temperament) is a type of tempered tuning described in twentieth-century music theory. ...

Diatonic Scales and Keys
Flats Sharps
Major minor Major minor
0 C (Major), a (minor)
1 F d G e
2 B♭ g D b
3 E♭ c A f♯
4 A♭ f E c♯
5 D♭ b♭ B g♯
6 G♭ e♭ F♯ d♯
7 C♭ a♭ C♯ a♯
lower case letters are minor

the table indicates the number of sharps or flats in each scale In music theory, a diatonic scale (from the Greek diatonikos, to stretch out; also known as the heptatonia prima; set form 7-35) is a seven-note musical scale comprising five whole-tone and two half-tone steps, in which the half tones are maximally separated. ... In music, a scale is a collection of tones. ... In music theory, the key identifies the tonic triad, the chord, major or minor, which represents the final point of rest for a piece, or the focal point of a section. ... Image File history File links Circle_of_fifths. ... Figure 1. ... Figure 1. ... 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 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. ... A one octave music scale in C major. ... A minor (abbreviated Am) is a minor scale based on A, consisting of the pitches A, B, C, D, E, F, G and A (natural minor scale - the harmonic minor scale contains a G♯ instead of a G natural). ... F major is a musical major scale based on F, consisting of the pitches F, G, A, B♭, C, D, E, and F. Its key signature consists of one flat. ... D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B-flat, C♯, and D (harmonic minor scale). ... G major is a major scale based on G, consisting of the pitches G, A, B, C, D, E, F# and G. Its key signature consists of one sharp. ... E minor is a musical minor scale based on the note E, consisting of the pitches E, F#, G, A, B, C, D# and E . ... B flat major is a major scale based on B flat, consisting of the pitches B flat, C, D, E flat, F, G, A, and B flat. ... G minor is a minor scale based on G, consisting of the pitches G, A, B-flat, C, D, E-flat, F, and G (natural minor scale). ... D major is a major scale based on D, consisting of the pitches D, E, F♯, G, A, B, C♯ and D. Its key signature consists of two sharps. ... B minor is a minor scale based on B, consisting of the pitches B, C#, D, E, F#, G, A and B. (natural minor scale - the harmonic minor scale contains a A# instead of a A). ... E flat major is a major scale consisting of the pitches E flat, F, G, A flat, B flat, C, D, and E flat. ... C minor (abbreviated Cm) is a minor scale based on C, consisting of the pitches C, D, E-flat, F, G, A-flat, B-flat (often raised to B natural to function as a leading tone) and C. Its key signature consists of three flats. ... A major is a major scale based on A, consisting of the pitches A, B, C♯, D, E, F♯, G♯, and A. Its key signature consists of three sharps. ... F sharp minor is a minor scale based on F sharp, consisting of the pitches F sharp, G sharp, A, B, C sharp, D, E sharp and F sharp (harmonic minor scale). ... A flat major is a major scale based on A flat, consisting of the pitches A flat, B flat, C, D flat, E flat, F, G, and A flat. ... F minor is a minor scale based on F, consisting of the pitches F, G, A-flat, B-flat, C, D-flat, E-flat and F. (natural minor scale. ... E major is a major scale based on E, consisting of the pitches E, F#, G#, A, B, C#, D# and E. Its key signature consists of four sharps. ... C sharp minor is a minor scale based on C sharp, consisting of the pitches C sharp, D sharp, E, F sharp, G sharp, A, B and C sharp (natural minor scale). ... D flat major is a major scale based on D flat, consisting of the pitches D flat, E flat, F, G flat, A flat, B flat, C, and D flat. ... B flat minor is a minor scale based on B flat, consisting of the pitches B flat, C, D flat, E flat, F, G flat, A flat and B flat (natural minor scale). ... B major is a major scale based on B, consisting of the pitches B, C#, D#, E, F#, G#, A#, and B. Its key signature consists of five sharps. ... G sharp minor is a minor scale based on G sharp, consisting of the pitches G sharp, A sharp, B, C sharp, D sharp, E, F double sharp and G sharp (harmonic minor scale). ... G flat major is a major scale based on G flat, consisting of the pitches G flat, A flat, B flat, C flat (enharmonic to B natural,) D flat, E flat, F, and G flat. ... E flat minor is a minor scale based on E flat, consisting of the pitches E flat, F, G flat, A flat, B flat, C flat, D flat, and E flat (natural minor scale – the harmonic minor scale contains a D instead of a D flat). ... F sharp major is a major scale based on F sharp, consisting of the pitches F sharp, G sharp, A sharp, B, C sharp, D sharp, E sharp (enharmonic to F natural) and F sharp. ... D sharp minor is a minor scale based on D sharp, consisting of the pitches D sharp, E sharp, F sharp, G sharp, A sharp, B, C double sharp and D sharp. ... C flat major is a major scale based on C flat, consisting of the pitches C flat, D flat, E flat, F flat, G flat, A flat, B flat and C flat. ... A flat minor is a minor scale based on A flat, consisting of the pitches A flat, B flat, C flat, D flat, E flat, F flat, G flat. ... C sharp major is a major scale based on C sharp, consisting of the pitches C sharp, D sharp, E sharp (enharmonic to F natural), F sharp, G sharp, A sharp, B sharp (enharmonic to C natural) and C sharp. ... A sharp minor is a minor scale based on A sharp. ...

External links

  • Bach's Tuning by Bradley Lehman
  • mnemonics
  • Circle of Fifths - Memory Technique
  • Circle of Fifths - Diagram
  • Circle of Fifths - Complete Detailed Diagram
  • Circle of Fifths - In Bass Clef
  • Free learning tool for the Circle of Fifths

  Results from FactBites:
 
Circle of fifths - Wikipedia, the free encyclopedia (1171 words)
In music theory, the circle of fifths (or cycle of fifths) is a geometrical space that depicts relationships among the 12 equal-tempered pitch classes comprising the familiar chromatic scale.
The circle of fifths, or fourths, may be mapped from the chromatic scale by multiplication, and vice versa.
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).
Circle of fifths (105 words)
In music theory, the circle of fifths is a sequence encompassing all of the notes in the chromatic scale.
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.
Moving around the circle of fifths is a common way to modulate.
  More results at FactBites »

 
 

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