Published on Jun 30, 2013
There is a much better version here.
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I arranged these chords and melodic timing to the chromatic "notes" of pi. Instead of the standard decimal (base 10) number, I used pi in base 12 counting, where there are 12 digits in the counting system, and lined those digits up with the chromatic scale, which is all 12 musical tones in an octave so there's one digit per tone.
What was revealed is absolutely amazing. You might think the digits of pi would create a random sounding directionless melody, but the notes have as much musical structure as the notes a composer would choose. I recognized this and made it into this song by timing the notes and adding the chord progression based on the implied structure and context of the notes with each other.
The first 16 digits are an astonishing melodic section, or phrase. Note the interval structures that create the illusion of repetition. It's efficiency in covering a wide range of emotion potential, the echoing interval structures, its balance creating such a gentle resolve, and the fact that it is not man-made are all elements that lead me to believe that it is the most beautiful melody that can exist, if there is such a thing.
This melody is inherent in the laws of mathematics, "written on the wall". In some sense, information (pi) is eternal, and certainly accessible to any intelligence that may discover it from any corner of the Universe, at any time.
If you need to understand what BASE 12 means, watch this video. http://youtu.be/xHSHEUvvT0I
I recently figured out the first repeating sections of Euler's # and tau base 12. Here is the link.
I also started exploring The Golden Ratio Base 12 but I can't "see" the musical solution to it yet.
I have recordings of this song in every key in 3/4 time, several timing iterations of the melody in 4/4 time with this chord structure, and as a dance mix, orchestral piece, dubstep-ish, blues, swing, rock, jazz, even reggae... every genre of music I could think of with this chord structure with every melodic iteration I could think of. In 3/4 time, the timing of the notes fall perfectly in the measures, but in 4/4, there are several ways to phrase the timing of the notes.
The melody sets the song to be in the key of "4". I moved the tape down to put C=4 so that the first 16 digit section could be played in C major. I didn't assign pi to the white keys to get a song in C major, I adjusted the position of the chromatic version to reveal that it's in a major scale all on its own. There are long sections of the melody that progress with a stable diatonic set with slight variations that direct the chord progression in interesting ways, and sections that modulate from one key to another. This is based on the context of the notes with each other. Trained musicians recognize how it does have some phrasing like something a composer would write. I seriously question the randomness of these digits in the musical sense. There are so many common musical structures that all fit together very neatly and flow in time within very common chord structures. I found musical order in the digits of pi base 12 set to the 12 tones.
One of my main goals is the most straightforward presentation of the digits as a melody. There are 97 quarter notes in the song out of 160 digits. The 3/4 time signature is a key element to achieve this goal.
3.184809493B918664 = can be repeated as many times as you want.
The next digit is a "5", but playing "4" instead brings it to perfect resolution.
3 | 1 | 848 | 0 | 949 | 3B9 | 186 | 6 | 4 4 |
The song could end (or repeat all the way back to the beginning) when any melodic section resolves to the key of "4".
So pi in base 12 is irrational and the digits go on forever, but in the musical sense it's perfectly rational and ends with a "4".
Now you know the final digit of pi.
I wonder how many civilizations throughout the Universe have heard this song, or one very similar to it. It's probably ancient history to them, discovered in the blink of an eye at the dawn of the information age.
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