harmonic function


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harmonic function

[här′män·ik ′fəŋk·shən]
(mathematics)
A function of two real variables which is a solution of Laplace's equation in two variables.
A function of three real variables which is a solution of Laplace's equation in three variables.
References in periodicals archive ?
He notes three specific aspects of that influence, " Tonverstellung," applied dominants, and harmonic function, and he discusses at length the role of Johannes Schreyer and the function theory in pedagogical reforms, and the role of Rudolf Louis as the culmination of the function theory.
2 x m in the harmonic function will be matched using artificial immune algorithms (AIS).
All of the compositions in Life is Good will interface seamlessly with any piano method, reinforcing harmonic function and color, concepts of tone production, the coordination of syncopated rhythms, shifting hand positions, voicing and pedaling.
She views the subject of harmonic function by degree with fresh eyes, noting the occasional absence of a strong concentration on the dominant (e.
The value of a harmonic function in the center of a ball equals the average of its values on the boundary sphere; so at every point any sharpness of the harmonic function is lost, flattened out by averaging.
From outside B, one can usually observe P only up to the addition of a harmonic function, which is the potential generated by other sources located outside B.
This fact has been used to deduce theorems for harmonic function on [R.
In our opinion, the shift of physical and emotional conditions is more complicated than a harmonic function; however, we will use harmonic functions as the simplest periodic ones the characteristics of which are well known.
It follows that every analytic function is harmonic, however, a harmonic function may not be analytic.
Taking the blues for example, the "deep" structure consists of the basic I, IV, and V chords; the intermediary "shallow" level reflects the jazz conventions of diminished passing chords, and the ii-V-I progression to the tonic chord during the last four measures of the blues form; and the surface structure has a tightly packed chord progression that may be based closely on the opening melodic theme, or that makes use of the tritone substitution harmonic function.
The cutting forces used for numerical simulation of turning tool vibration are considered in the form of time harmonic function.
Later, the sustaining pedal of the piano often took over this harmonic function.