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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.
Simple English; Slovenčina ... 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 ...
[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.
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 tonal music, chord progressions have the function of either establishing or otherwise contradicting a tonality, the technical name for what is commonly understood as the "key" of a song or piece. Chord progressions, such as the extremely common chord progression I-V-vi-IV, are usually expressed by Roman numerals in
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.
The English word chord derives from Middle English cord, a back-formation of accord [5] in the original sense of agreement and later, harmonious sound. [6] A sequence of chords is known as a chord progression or harmonic progression. These are frequently used in Western music. [7]
An infinite sequence of real numbers (in blue). This sequence is neither increasing, decreasing, convergent, nor Cauchy.It is, however, bounded. In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.