Pitch Differences
In the 6th century B.C., Pythagoras noticed that different pitches sounded when a blacksmith struck his anvil with diffferent hammer weights. He decided to investigate a little more, and he started observing different ideas that involved strings. Those ideas had to do with the intervals that are heard when different parts of a string are plucked. One of the observations Pythagoras made involved two identical pieces of string. He found that if you pluck one of them as it is and divide the other one in half before plucking it, then the interval that is sounded is an octave. The string that was divided in half before being plucked had a sound exactly one octave higher than the string that was plucked normally.
This theory can also be examined with other string divisions. For example, if the string that was divided in half before is now divided into a different ratio, the difference in pitch will change. For example, if the relationship between the two strings is 2:3, then the pitch difference will be a fifth. (The fifth means that there is an interval made up of 7 half steps between the two sounds.) The pitch will also change if the ratio between the two strings is changed to a 3:4 ratio. (This means that the divided string is split at its 3/4 point and the other string remains the same.) The result of the 3:4 division will be a pitch difference of a fourth, or 5 half steps. After all this investigation done by the Greeks, they formed a mathematical notation to summarize it: 1:2:3:4. |
