Search results
Results from the WOW.Com Content Network
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.
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.
In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then
[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.
The harmonic progression follows a sequential pattern known as the Romanesca, which according to Robert Gjerdingen was a common schema during the 17th and 18th centuries. [ 26 ] In Germany, Italy and France of the 17th century, some pieces built on an ostinato bass were called chaconnes or passacaglias ; such works sometimes incorporate some ...
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.
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.