Music: Symphony of Numbers

http://www.youtube.com/watch?v=Qf0t4qIVWF4

http://youtu.be/1zw0uWCNsyw?t=7m2s

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What is one like? What is two like? How is three

different than them both?

What do they really look like?

1

The Quality of Numbers

Ancient Greeks influenced by the ideas of Pythagoras (including Plato, Aristotle, and Nicomachus) believed that the quality of numbers was just as important as their quantity.

Quantity = number, total. Quality = what they are like, how they act.

Instead of thinking as a number as a quantity of something, think of it as a structure of reality.

Meet “One”

“One” didn’t mean “one of many” but rather “everything as one.”

One is unity, the thing that is the same inside everything, unchanging.

One is manifested visually in the point and the circle/sphere.

Meet “Two”

Two described the division in things.

The division could be conflict and separation…

Or it could be different things trying to come together in harmony.

Two can be represented by the line, or the “ying-yang” symbol.

Meet “Three”

Three is a “sturdy” number; three strands of hair can be braided, triangles keep structures from folding.

Three feels more complete, comes full circle.

Simple Number Qualities Create

Function and Beauty

Pre-Pythagoras: Mysterious, Magical

Music

Pythagoras (570- 495 BC)

Pythagoras was one of the first philosophers in the Greek tradition. He greatly influenced the thought of later philosophers like Plato and Aristotle.

He is most famous for his proof of the “Pythagorean Theorem”: a2 + b2 = c2

Even more importantly, he discovered the numbers behind natural phenomenon like music.

The Blacksmiths’ Hammers

According to Nicomachus (abt 100 AD) and others, Pythagoras was walking by a blacksmith shop when he heard different intervals being sounded by the hammering; some were beautiful, some were not.

He went in to try to figure out what made the difference. First tried having them hammer harder. No change. He tried using different shaped hammers. No change. What changed the pitches was the weight of the hammers.

The Blacksmiths’ Hammers

Further investigation into the weight of the hammers revealed some interesting things: If the hammers were

equal weight, the pitches were equal.

If one hammer was exactly 1/2 as heavy as another, the pitch it made was an octave higher.

If the weight was 2/3 as heavy, the pitch was a 5th higher.

If the weight was 3/4 as heavy, the pitch was a 4th higher.

The “Magic” Numbers of Harmony

Pythagoras discovered that not only could beautiful musical intervals be explained by numbers, they were created by the simplest ratios:

These intervals were called “perfect.” In the 1500s Zarlino added two more

harmonic ratios:

Unison – 1:1 Octave – 2:1

5th – 3:2 4th – 4:3

Major 3rd – 5:4 Minor 3rd: 6:5

Remember: 1:2:3:4:5:6 Unison, Octave, 5th 4th, Major 3rd, Minor 3rd

This “harmonic intervals” make up chords How can knowing this ratios help you?