Harmonic Progression (mathematics), Harmonic Progression
Harmonic progression may refer to: * Chord progression in music * Harmonic progression (mathematics) * Sequence (music) In music, a sequence is the restatement (music), restatement of a motif (music), motif or longer melody, melodic (or harmony (music), harmonic) passage at a higher or lower pitch (music), pitch in the same voice.Benward and Saker (2003). ''Music ...

Chord Progression
In a musical composition, a chord progression or harmonic progression (informally chord changes, used as a plural, or simply changes) is a succession of chords. Chord progressions are the foundation of harmony in Western musical tradition from the common practice era of Classical music to the 21st century. Chord progressions are the foundation of popular music styles (e.g., pop music, rock music), traditional music, as well as genres such as blues and jazz. In these genres, chord progressions are the defining feature on which melody and rhythm are built. 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 Classical music theory. In many styles of popular and traditional music, chord progressions are expressed ...
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Harmonic Progression (mathematics)
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. As a third equivalent characterization, it is an infinite sequence of the form : \frac,\ \frac,\ \frac,\ \frac, \cdots, where ''a'' is not zero and −''a''/''d'' is not a natural number, or a finite sequence of the form : \frac,\ \frac,\ \frac,\ \frac, \cdots,\ \frac, where ''a'' is not zero, ''k'' is a natural number and −''a''/''d'' is not a natural number or is greater than ''k''. Examples In the following is a natural number, in sequence: \ n = 1,\ 2,\ 3,\ 4,\ \ldots\ * 1, \tfrac,\ \tfrac,\ \tfrac,\ \tfrac,\ \tfrac,\ \ldots \ , \ \tfrac,\ \ldots \ is called the ''harmonic sequence'' * 12, 6, 4, 3, \ \tfrac,\ 2,\ \ldots\ ,\ \tfrac,\ \ldots\ * 30, −30, −10, −6 ...
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