# Pythagorean Tuning

## Purpose

To demonstrate how the length of a piece of string can affect sound.

Pythagoras of Samos, born between 580 and 572 BC, was an Ionian Greek mathematician whom was revered for his contributions to math and science. He was the first man to dub himself a philosopher and lover of wisdom. He founded the religious movement called Pythagoreanism and his followers were aptly named Pythagoreans. With a devote following of music, Pythagoras and his Pythagoreans set out to improve the music of there day, which was criticized by Pythagoras as being too hectic and non-harmonious.

It so happened that one day Pythagoras was passing by a Blacksmith's when he heard the sounds of hammers ringing down on anvils. Pythagoras thought the sound to be beautiful and harmonious and determined whatever scientific law caused the sound to be produced must be mathematical. It was through this epiphany that Pythagoras discovered that musical notes could be translated into mathematical equations. Each anvil was a simple ratio of the other. That is, one anvil was half the size of the first anvil and the second was 2/3 the size, and so forth and so on. Soon the system of musical tuning in which frequency relationships are intervals based on a 3:2 ratio was born. This is the Pythagorean Tuning system.

## Required materials

• Hard string or fishing line about 6 feet in length. You may also consider using a pack of steel or nylon guitar strings, which can be found at any instrument store or large retailer (such as Walmart).
• 2 bricks
• Ruler
• Pen or pencil (optional)
• Journal (optional)

## Step-By-Step Procedure

• 1. Take the string and wrap some of it around one of the bricks as tightly as possible.
• 2. Measure out 3 ruler lengths of string (about 3 feet) and wrap the rest of the string around the other brick.
• 3. Move the bricks apart until the string is very tight and can be plucked.
• 4. Pluck the string. What sound does it make?
• 5. Shorten the length of the string between bricks by rolling move of it around one of the bricks. Once again move the bricks apart to keep the string tight.
• 6. Pluck the string. What sound does it make?
• 7. Repeat steps 5 and 6 several times until, noting the sound each time the string is plucked. Keep repeating until the bricks are only a few inches apart.

## Note

You may optionally track the variance of sound in your journal. Create a chart with two columns, the first column reading "String Distance", and the second reading "Description". As you pluck

## Observation

Can you explain why this experiment is similar to the tuning of a guitar or other string instrument? How do you think the size (thickness) of the string effects the sound produced? What would the sound be like if you plucked the string harder? What about if you plucked it softer? Can you produce sounds from your string without actually plucking it?

## Result

Sound is produced by vibrations through the air. The longer strings produces a longer vibration, resulting in a lower pitch note. As the string shortens, the vibration is reduced and the sound produced is at a higher pitch.

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