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Discovering Harmonic Ratios: Musical Theory and Instrumentation

Learn the significance of harmonic ratios in music, explore their application in string and wind instruments, discover the monochord's role in ancient cultures, and delve into the concept of the Music of the Spheres. Experiment with Pythagoras' theory and understand harmonies derived from fundamental tones and overtones. Witness the motion of air in wind instruments and identify intervals through length calculations.

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Discovering Harmonic Ratios: Musical Theory and Instrumentation

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  1. Harmonic Ratios in Use

  2. The Harmonic Ratios • 1:1 – Unison • 2:1 – Octave • 3:2 – Perfect 5th • 4:3 – Perfect 4th • 5:4 – Major 3rd • 6:5 – Minor 3rd . . . • 9:8 – Major Second (Step)

  3. What Can You Do With Them? Calculate the length needed for pitches on: • String Instruments • Wind Instruments

  4. The Monochord • Monochords are ancient instruments that appear in various forms in many cultures. • Pythagoras is said to have refined his theory of harmonic ratios by experimenting on it. • Students were expected to experiment with it when they studied music as part of the Quadrivium in medieval universities.

  5. The Music of the Spheres

  6. From One, Many • When plucked, a string doesn’t only vibrate as a whole, but also a half, third, fourth, etc... • These “overtones” harmonizes with the “fundamental” pitch and the other overtones. • All of the pleasing-sounding harmonies can be drawn from harmonic divisions of the fundamental.

  7. Setting the Air in Motion

  8. Like strings, air passing through tubes vibrate in relation to the length of the tube. • This includes all wind instruments: brass, woodwinds, didgeridoos, etc.

  9. Name that Interval! • Lengths: 180 and 90 • Lengths: 180 and 135 (aka. 12 and 9) • Lengths: 180 and 120 • Lengths: 180 and 144 • Lengths: 180 and 150 • Lengths: 180 and 160

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