Published on Jun 30, 2013
There is a new version that goes up to 226 digits on my channel.
A few people have called this "the holy grail of music". All I did was "solve the puzzle" :)
I arranged this melodic timing and chords to the chromatic "notes" of pi. Instead of the standard decimal (base 10) number, I used 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.
What was revealed is amazing. You might think the digits of pi would create a random, directionless, dissonant sequence of notes from the chromatic scale, but the notes contain as much musical structure as those 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. The song goes up to the 72nd digit.
The first 17 digits can easily be turned into a truly amazing melodic phrase. The phrase'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 melodic phrase imaginable, if there is such a thing... saying so much with so little.
This melody is inherent in the laws of mathematics, "written on the wall", and certainly accessible to any intelligence that may discover it from any corner of the Universe, at any time.
Guitar players can play along with the digits as tablature if you stick to the B-string exclusively.
A =10th fret
B =11th fret
0 = open/12
You have to figure out the octaves by ear or read the sheet music.
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 that sounded good. In 4/4, there are several ways to phrase the notes, but almost all of the 4/4 versions feel a bit strange no matter how well they are arranged. The melody drags and pulls compared to 3/4, where there are exactly the right amount of notes to make the melody "POP" all throughout.
The opening section melody notes set the song to be in the key of "4". I moved the tape to set 4=Eb.
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. There are so many places in the raw notes that contain the mind of a composer. There are many conventional interval structures to the notes that all fit together very neatly and flow in time while simultaneously establishing conventional harmonic structures. I found musical order in the digits of pi base 12 set to the 12 tones.
The final note is the only melody note I added. Since the song begins in the key of "4", playing a "4" at the end of the section brings resolution back to where the song began.
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~ |
So 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 ... sort of.
... or maybe the perfect "resolution" (3.184809493B9186644) that might actually have a real-world application somewhere in physics, in the area of dimensional phasing. Perhaps some important cosmological fudge-factor exists in the difference/ratio between the expanded value of pi and the musically resolved value of pi (in base 12).
Some say mathematics is the voice of God, ubiquitous and eternal. I wonder how many civilizations throughout the Universe have heard this song, or one very similar to it, discovered in the blink-of-an-eye at the dawn of the information age. It's probably ancient history to them, and also an endless artistic endeavor to continue arranging the digits of pi into a greater piece of music, for as long as their race can endure the perils of natural disasters.
explanation of base 12 - 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.
If you want to use any of this, contact me.