Possible Mathematical and Scientific Basis
The concept of root has some basis in the physical properties of waves. When two notes of an interval from the harmonic series are played at the same time, people sometimes perceive the fundamental note of the interval. For example, if notes with frequency ratios of 7:6 (a septimal minor third) were played, people could perceive a note whose frequency was 1/6th of the lower interval. The following sound file demonstrates this phenomenon, using sine waves, pure and simple waves for which this phenomenon is most easily evident.
This concept formed the basis for the method by which the composer Paul Hindemith used to determine and identify roots of chords in his harmonic system which he used both to write music and to analyze the music of other composers. Hindemith's system has been criticized for being based generically in theory derived rules and not on perception of specific instances.
Read more about this topic: Root (chord)
Famous quotes containing the words mathematical, scientific and/or basis:
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“Bad times have a scientific value. These are occasions a good learner would not miss.”
—Ralph Waldo Emerson (1803–1882)
“Protoplasm, simple or nucleated, is the formal basis of all life. It is the clay of the potter: which, bake it and paint it as he will, remains clay, separated by artifice, and not by nature from the commonest brick or sun-dried clod.”
—Thomas Henry Huxley (1825–1895)