Cello: Natural Harmonics — Ex. 4, Dividing the String in Fifths
Cello: Natural Harmonics — Example 4, Dividing the String in Fifths
All the pitches in this section are played on the G string.
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“Open string: The entire length of the string from nut to bridge is allowed to vibrate freely.”
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“Lightly touching the string 1/5 of its length from the bridge forces the string to vibrate in 5 sections, each 1/5 of the total string length. The sound produced is 5 times the frequency of the open string, the 5th partial, sounding 2 octaves and a major third higher than the open string.”
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“Lightly touching the string 2/5 of its length from the bridge also forces the string to vibrate in 5 sections, each 1/5 of the total string length. The sound produced is 5 times the frequency of the open string, the 5th partial, sounding 2 octaves and a major third higher than the open string.”
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“Pressing down in this same place allows only 2/5 of the string to vibrate. Since this length is 2 times that of the 5th partial, it sounds an octave lower than the 5th partial, an octave and a major third higher than the open string.”
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“Lightly touching the string 3/5 of its length from the bridge also forces the string to vibrate in 5 sections, each 1/5 of the total string length. The sound produced is 5 times the frequency of the open string, the 5th partial, sounding 2 octaves and a major third higher than the open string.”
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“Pressing down in this same place allows only 3/5 of the string to vibrate. Since this length is 3 times that of the 5th partial, it sounds an octave and a perfect fifth lower than the 5th partial, a major sixth higher than the open string.”
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“Lightly touching the string 4/5 of its length from the bridge also forces the string to vibrate in 5 sections, each 1/5 of the total string length. The sound produced is 5 times the frequency of the open string, the 5th partial, sounding 2 octaves and a major third higher than the open string.”
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“Pressing down in this same place allows only 4/5 of the string to vibrate. Since this length is 4 times that of the 5th partial, it sounds 2 octaves lower than the 5th partial, a major third higher than the open string.”