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:
“The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
—Marquis De Custine (1790–1857)
“We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.”
—Thomas Carlyle (1795–1881)
“The cultivation of literary pursuits forms the basis of all sciences, and in their perfection consist the reputation and prosperity of kingdoms.”
—Marquês De Pombal (1699–1782)