note. Now put your finger on a fret exactly halfway up the string and pluck it again. The vibrating part of the string is now half as long as it used to be—a ratio of 1 to 2—and it sounds precisely an octave higher than the original note (the musical distance from one do to the next in the do-re-mi-fa-sol-la-ti-do scale). If instead the vibrating string is ⅔ of its original length, the note it makes goes up by a fifth (the interval from do to sol; think of the first two notes of the Star Wars theme). And if the vibrating part is ¾ as long as it was before, the note goes up by a fourth (the
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