Death of a Scalesman

Great Thinkers Die Hard.

Socrates was forced to drink hemlock.

Galileo was found guilty of heresy and died under house arrest.

Dana Plato died of an overdose in her car.

And Pythagoras, often referred to as the world’s first pure mathematician, was no exception.

The reports of his death are varied. He is said to have been killed by an angry mob, to have been caught up in a war between the Agrigentum and the Syracusans and killed by the Syracusans, or to have been burned out of his school in Crotona and exiled to Metapontum where he starved himself to death. At least two of the stories include a scene where Pythagoras refused to trample a crop of bean plants in order to escape, and because of this, he was caught.

Oh Boy.

Pythagoras studied odd and even numbers, prime and perfect numbers. He contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra. My hero.

Pythagoras also related music to mathematics. He had long played the seven string lyre, and learned how harmonious the vibrating strings sounded when the lengths of the strings were proportional to whole numbers, such as 2:1, 3:2, 4:3.

He was the first to create a musical scale: that subset of musically relevant frequencies, where the last frequency is exactly double that of the first. Every scale from every culture on earth uses this rule of a doubled frequency that we call an octave. It is based on the human perception that doubling or halving a frequency results in two tones that sound remarkably similar to each other – and that our modern western scale contains eight notes.

Everything in between however is where the fun begins.

So Pythagoras began to play.. and not just on his seven string lyre. He used strings of different lengths, in specific proportions, to create a six note scale.

I don’t believe that Pythagoras had any method of calculating the actual number of vibrations per second.. but I could be wrong. In any case, it really didn’t matter.. because as we will see, it is the proportions of the rate of frequencies to each other that accounts for the basis of a scale. That is to say, if he started with a string vibrating at 440 Hz, he could have doubled the frequency, by halving the length of the string, and wind up with the octave of 880 Hz. Had he started with a string vibrating at 500 Hz, he could have achieved an octave by the same method..producing a tone whose frequency was 1000 Hz. This proportion is 2:1 or conversely, 1:2.

For our example, let’s assume the first string had a frequency of 440 Hz, which corresponds to our present day label of the note known as Concert A.

By cutting another string 4/5 the length of the A, he came up with C, the next note of his Greek scale. To find the frequency of this new C Note, (I could use a few of those) you simply multiply the reciprocal of the string length by the frequency of the first string (5/4*440) to get 550 Hz as the frequency.

Applying the same formula, you can find frequencies for D with a measure of 3/4 of the A string, E – 2/3 of the A string, F – 3/5 of the A string and finally another A measuring 1/2 of the original.

A = 440 Hz (440 Hz*1/1)

C = 550 Hz (440 Hz *5/4)

D = 586.66 Hz (440 Hz*4/3)

E = 660 Hz (440 Hz*3/2)

F = 733.33 Hz (440 Hz*5/3)

A Octave = 800 Hz (440 Hz*2/1)

I guess with a name like Pythagoras, he really had to “Prove” himself.