- The ancient Greeks found three relationships between notes especially pleasing.

Now we call them an octave, a fifth, and a fourth.

- An octave is easy to remember because it's the first two notes of "Somewhere Over the Rainbow," ♪ Somewhere ♪ (string bass plays two notes) A fifth sounds like this.

♪ La la ♪ Or the first two notes of ♪ Twinkle Twinkle Little Star ♪ (plucks strings twice) And a fourth sounds like ♪ La la ♪ (plucks strings twice) You can think of it as the first two notes of "Here Comes the Bride."

(plucks strings twice) - In the sixth century BCE, the Greek philosopher Pythagoras is said to have discovered that those beautiful musical relationships were also beautiful mathematical relationships by measuring the lengths of the vibrating strings.

In an octave, the string lengths create a ratio of two to one.

(string bass plays two notes) In a fifth, the ratio is three to two, (string bass plays two notes) and in a fourth, it is four to three.

(string bass plays two notes) - Seeing a common pattern throughout sound, that could be a big eye-opener of saying, "Well, if this exists in sound, and if it's true, universally through all sounds, this ratio could exist universally everywhere, right?"

And doesn't it?

- Pythagoreans worship the idea of numbers.

The fact that simple ratios produced harmonious sounds was proof of a hidden order in the natural world, and that order was made of numbers, a profound insight that mathematicians and scientists continue to explore to this day.