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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.
[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.
A harmonic is any member of the harmonic series, an ideal set of frequencies that are positive integer multiples of a common fundamental frequency. The fundamental is a harmonic because it is one times itself. A harmonic partial is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic. [3]
In the Schuman example (Three Score Set for Piano), the inversions of the chords suggest a bichordal effect. [ 3 ] In the example on the top right, we see a series of quartal chords in parallel motion, in which the intervallic relationship between each consecutive chord member, in this case a minor second , is consistent.
In computer science, specifically information retrieval and machine learning, the harmonic mean of the precision (true positives per predicted positive) and the recall (true positives per real positive) is often used as an aggregated performance score for the evaluation of algorithms and systems: the F-score (or F-measure).
The real and imaginary part of any holomorphic function yield harmonic functions on (these are said to be a pair of harmonic conjugate functions). Conversely, any harmonic function u on an open subset Ω of R 2 {\displaystyle \mathbb {R} ^{2}} is locally the real part of a holomorphic function.
By thinking of this blues progression in Roman numerals, a backup band or rhythm section could be instructed by a bandleader to play the chord progression in any key. For example, if the bandleader asked the band to play this chord progression in the key of B ♭ major, the chords would be B ♭-B ♭-B ♭-B ♭, E ♭-E ♭-B ♭-B ♭, F-E ...
Harmonic analysis is a branch of mathematics concerned with investigating the connections between a function and its representation in frequency.The frequency representation is found by using the Fourier transform for functions on unbounded domains such as the full real line or by Fourier series for functions on bounded domains, especially periodic functions on finite intervals.