OVERTONES

Overtones

. . . The spectrum of the world of sound is the harmonic or overtone series. A tone produced by a voice or instrument carries with it a greater or lesser number of barely audible overtones. Their order is not arbitrary: it is determined by a strict law, and is a immutable as the color series of the rainbow. The series extends theoretically to infinite heights, but in practice a sounding tone is supported by only a limited number of overtones. [Paul Hindemith, Craft of Musical Composition, I. Theory, Associated Music Publishers, Inc., New York, 1942, p16]

 

PART I: TONE COMBINATIONS

I. The Influence of Overtones in Music

. . . each tone produced generates a series of overtones which are related to that tone, and to each other, by definite mathematical ratios. These overtones stretch upwards indefinitely. Our ear can follow them a certain distance; instruments can follow them further yet; but the theoretical range of them is beyond our power to follow. [Henry Cowell, New Musical Resources, Cambridge University Press, 1996, p4]

. . . Professor Dayton Miller, well-known acoustician and author of The Science of Musical Sound, speaks of having heard the forty-fourth overtone with his unaided ear. . . . overtones should be made the basis of musical theory to a far greater extent than they have been, and that in particular the new types of chords found in contemporary music might be studied in relation to higher overtone combinations. [Henry Cowell, New Musical Resources, Cambridge University Press, 1996, p5]

OVERTONES AND HARMONICS

Harmonic Intervals in Cents

Tran Quang Hai KHOOMEI - Overtone Singing

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December 4, 2003