A Guided Tour Through The Harmonic Series

A monochord consists of a single string stretched over a sound box, with the strings held taut by pegs or weights on either end. 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. The instrument is most important in Western music for its scientific research, rather then its musical qualities. 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. Jeff Cottrell cites on the importance of the instrument in early cosmology, numerology, and music theory. “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). This provided the bridge between the world of physical experience and numerical relationships, giving birth to mathematical physics. In addition, this elevated music to one of the highest intellectual pursuits. Furthermore, since the “perfection of sounds” could now be revealed by numbers, all simple numeric ratios could be visualized as sounds. Kepler’s “harmony of the spheres” is based on this, as well as harmonically resounding architecture. If the visible proportions of a building can be expressed in numeric ratios, then their relationships can be “heard” as chords. 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). This also helped support the baroque idea that music was a reflection of the divine order (unless you were a minstrel, perhaps).”

The Harmonic Series The harmonic series is a series of “harmonics” or “overtones” which sound together at the same time to create the note that is sounding. We will look at the first sixteen harmonics from the harmonic series and examine how these intervals. The Monochord used for demonstration has two bridges 100cm apart, below is a chart with note of harmonic, ratio of the harmonic, where the nodal point is, and what interval the harmonic sounds in relation to the fundamental.