# 225 Digits of π: An Irrational Auralization

## 1. What is This?

225 Digits of π is a mathematic auralizer, a system by which the digits of π are converted to music. The piece was conceived and created by Amin Osman and Greg Karber.

You can purchase it on iTunes.

## 2. The Structure of 225 Digits of π.

The digits 0-9 were mapped to two octaves of a pentatonic scale.

We chose the pentatonic scale for three reasons. Firstly, each octave contains five notes, so the digits may be mapped evenly onto two octaves. Secondly, since the pentatonic scale lacks semitones and tritones, its pitches can be played in almost any arrangement without creating dissonance.

Thirdly, as this wonderful performance by Bobby McFerrin illustrates, the pentatonic scale seems hardwired into our brains. A fundamental scale for a fundamental number.

We chose the key of A and assigned the digits as follows:

0 = A2
1 = B2
2 = C#3
3 = E3
4 = F#3
5 = A3
6 = B3
7 = C#4
8 = E4
9 = F#4

However, while using the pentatonic scale removes dissonance, it also eliminates tension. As such, we added a bassline which followed a simple chord progression:

F#m F#m
D D
F#m F#m
D D
A A
F#m F#m
E A

This contextualized π's melody and gave it a dynamism which did not exist on its own.

We additionally mapped the a spectrum of colors to each of the digits, as follows:

0 =
1 =
2 =
3 =
4 =
5 =
6 =
7 =
8 =
9 =

A pastel spectrum was chosen for the same reason as the pentatonic scale: we felt it would produce less dissonance and be more pleasing to the senses.

## 3. Why π Fascinates Us.

π is, of course, most well known for expressing the relationship between the diameter and the circumference of a circle.

C = πd

However, this is not the only occurence of π. It recurs in several fields of mathematics, from statistics to number theory, often in situations where the connection to circles is difficult to fathom.

The most striking of these, perhaps, is this version of the Leibniz series:

This series sums so slowly it takes 300 terms before it is accurate for the first two digits of π. To calculate 10 correct decimal points of π would require five billion terms.

Early mathematicians believed π to be rational, meaning they thought it could be represented by one whole number divided by another. Sometimes these mathematicians claimed that π equaled 22/7. It doesn't, but 22/7 is accurate for the first two digits, and that's close enough for almost all ancient uses.

You only need about 40 decimal places of π to calculate the circumference of the known universe to within a margin of error of about half the diameter of a proton.

The digits of π are thought to be random. However, no proof of such randomness exists. (If you could prove it, you could get a lot of attention and probably a number of new Twitter followers.)

If π is random, then its infinite length means that every finite pattern that could possibly exist exists within it. This has some mindblowing consequences. For example, let's say that we assigned each letter of the alphabet to a two-digit number:

A = 01
B = 02
C = 03
...
X = 24
Y = 25
Z = 26

Assuming randomness, every single possible string of letters would be represented somewhere within π. This would include the Declaration of Independence, the lyrics to Gungnam Style, and the complete works of Shakespeare.

## 4. An Unfinishable Symphony...

While π never ends, "225 Digits of Pi" does. (Obviously, it ends after 225 digits.) However, this does not necessarily have to be so.

Through procedural generation, the digits of π could be determined on-the-fly by a computer, which could assign the digits to tones automatically (eliminating the very tedious project of individually entering notes). Then, the bassline, beat, and other assorted instruments could be cued to enter and leave based on a few simple rules.

If the rules were clever enough, they could retain musical dynamism indefinitely, so that the piece could -- thereotically -- go on forever...