There are newer versions and they're avaliable here http://goo.gl/S7qEm8
-- 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 (A = the 10th digit ; B = the 11th digit), 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 226th 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 entirely 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.
In a sense, mathematics is ubiquitous and eternal. I wonder how many civilizations throughout our vast Universe have heard this song, or one very similar to it, written 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. The digits go on forever.
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, blues, swing, rock, jazz, even reggae, every genre of music I could think of 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". Also, there is one digit per tone. The only scale alternative is to "move the tape" on the keyboard so that the numbers are over different keys. All that would do is transpose the same interval sequence into a different key. There are no scale alternatives in the base 12 method.
I really want to develop and perform this around the world, while I continue to compose further into the digits... sending last minute revisions to the next venue. Good thing it's mostly quarter notes, right? Ha!
I also want to establish a philanthropic organization to channel a portion of the revenue (ad rev, royalties, sales) to support music programs, grow the organization's resources, and its reach. That side of this work is only right considering the voice that speaks the loudest in this song is existence itself.
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 phrase brings resolution.
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 go back to the beginning) when any section resolves to the key of "4". In the version in this video, within my arrangement of 226 digits, there are five places to end/repeat the song.
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).
Guitar players can play along with the digits as tablature if you stay on the B-string.
A =10th fret
B =11th fret
0 = open/12
There are many places in the raw notes that contain the mind of a composer. There are many conventional interval structures in 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. I made a few small changes since this version, one of which created amazing arpeggios in the 2nd to last phrase (229B)
I made a Tango of Euler's #. Also, I have explored phi/golden ratio but no music yet.