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:
“All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
—Roger Bacon (c. 1214–c. 1294)
“In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality.”
—Karl Popper (1902–1994)
“Buddhists and Christians contrive to agree about death
Making death their ideal basis for different ideals.
The Communists however disapprove of death
Except when practical.”
—William Empson (1906–1984)