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In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.
It can be viewed in a counterclockwise direction as a circle of fourths. Harmonic progressions in Western music commonly use adjacent keys in this system, making it a useful reference for musical composition and harmony. [1] The top of the circle shows the key of C Major, with no sharps or flats. Proceeding clockwise, the pitches ascend by fifths.
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means.. It is the most appropriate average for ratios and rates such as speeds, [1] [2] and is normally only used for positive arguments.
I−vi−ii−V is one of the most common chord progressions in jazz. [5] The progression is often used [6] as a turnaround, occurring as the last two bars of a chorus or section. [7] The I−vi−ii−V chord progression occurs as a two-bar pattern in the A section of the rhythm changes, [8] the progression based on George Gershwin's "I Got ...
[1] [2] Every term of the harmonic series after the first is the harmonic mean of the neighboring terms, so the terms form a harmonic progression; the phrases harmonic mean and harmonic progression likewise derive from music. [2] Beyond music, harmonic sequences have also had a certain popularity with architects.
In music theory, Roman numeral analysis is a type of harmonic analysis in which chords are represented by Roman numerals, which encode the chord's degree and harmonic function within a given musical key. Specific notation conventions vary: some theorists use uppercase numerals (e.g.
In a progression going up a fourth, if the first chord is a minor seventh chord, it can also be substituted for a seventh chord; a relative second degree can also be added before it to create a ii–V–I turnaround. (A sole minor seventh or seventh chord can be perceived as a second degree or its dominant quality substitution, in which case a ...
Euler's Tonnetz. The Tonnetz originally appeared in Leonhard Euler's 1739 Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae.Euler's Tonnetz, pictured at left, shows the triadic relationships of the perfect fifth and the major third: at the top of the image is the note F, and to the left underneath is C (a perfect fifth above F), and to the right is A (a ...