Alternate Tuning

The ancient Greeks, who had only simple stringed instruments and flutes, noticed two things about pitches produced by a vibrating string. They noticed that a string of half the length of another but with the same tension and thickness sounded similar. For example if the original string played a frequency of 880 Hz the string of half the length would play a note of 440 Hz, an octave lower. The same thing happens by holding the string down in the center; each half will sound a note and octave higher than the full length. They also noticed that holding a string down at 2/3 of its length would produce two notes (by plucking each side) that sounded pleasant together. We call the interval between these two notes a perfect fifth (if you sing the children’s song Baa Baa Black Sheep the first Baa and Black are a fifth apart). Two other notes that sound good together are the notes produced by the long part of the 2/3 of the string and the note formed from holding the string down at its center. The interval between these two notes is called a perfect fourth and the ratio between them is 4/3 (the first two notes of Hark the Herald Angels Sing). Continue reading →