#Harmonic interval series#
For example, the fundamental of the first series is 1000 Hz, and the fundamental of the second series is 500 Hz. The lowest frequency component of such a series is called the fundamental. Notice that the difference in frequency between adjacent members of both series is constant, that is to say, the harmonics are equally- spaced. Though musicians sometimes use these terms interchangeably, the term harmonic series specifically refers to a series of numbers related by whole-number ratios. The related term harmonic series is a more precisely defined concept with applications in both music and mathematics. When musicians use the term overtone series, they are generally referring to a set of frequency components that appear above a musical tone. To introduce the harmonic series let’s look at a quote from Reginald Bain who provides a very succinct definition and description: This also helped support the baroque idea that music was a reflection of the divine order (unless you were a minstrel, perhaps).” Like the "golden section" of architecture, musical harmony "imposes order in the hearts and minds of men by virtue of their simple, natural relationships" (Harnoncourt). If the visible proportions of a building can be expressed in numeric ratios, then their relationships can be "heard" as chords. Kepler's "harmony of the spheres" is based on this, as well as harmonically resounding architecture. Furthermore, since the "perfection of sounds" could now be revealed by numbers, all simple numeric ratios could be visualized as sounds. In addition, this elevated music to one of the highest intellectual pursuits. This provided the bridge between the world of physical experience and numerical relationships, giving birth to mathematical physics. “Pythagoras' study of ratios on the monochord led philosophers to believe that these ratios also governed the movement of planets and other cosmic matters (Ptolemy). Jeff Cottrell cites on the importance of the instrument in early cosmology, numerology, and music theory. Other cultures, however, such as in many parts of Africa, Brazil, and Hawaii (just to name a few) have used it as a musical instrument. The instrument is most important in Western music for its scientific research, rather then its musical qualities.
It was used earlier by others, but most of our current knowledge of the instrument is of its use by Pythagoras as early around the 6th century BC for scientific research on the nature of sound. A monochord consists of a single string stretched over a sound box, with the strings held taut by pegs or weights on either end.
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