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Harmonic Ratios in Use. The Harmonic Ratios. 1:1 – Unison 2:1 – Octave 3:2 – Perfect 5 th 4:3 – Perfect 4 th 5:4 – Major 3 rd 6:5 – Minor 3 rd . . . 9:8 – Major Second (Step). What Can You Do With Them? Calculate the length needed for pitches on: String Instruments

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## Harmonic Ratios in Use

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**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)**What Can You Do With Them?**Calculate the length needed for pitches on: • String Instruments • Wind Instruments**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.**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.**Like strings, air passing through tubes vibrate in relation**to the length of the tube. • This includes all wind instruments: brass, woodwinds, didgeridoos, etc.**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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