These are The Cosmic Melodies (new name!) They are arranged using mathematical constants in base 12, played in the 12 musical tones.
A series of random notes from the chromatic scale typically sounds strange, and it's difficult to arrange into a melody that follows conventional harmonic aesthetics. The tonal center is "floating" and changes often, as opposed to something that has a defined key signature.
What is astonishing is that with minimal intervention, these mathematical chromatic digit sequences sound like they came straight from the mind of a composer.
free sheet music / chord chart ---> SHEET MUSIC
The free sheet music ---> CLICK HERE
Pi and e are irrational constants, which mean they have no repeating patterns in the digits. I recently started digging in to rational constants and found a few good melodies.
NOTE: 4/37 (base 10) = 4/31 (base 12)
NOTE: 17/19 (base 10) = 15/17 (base 12)
The constants, when translated into a series of notes, contain implied melodic phrases. An example would be to ask you to put spaces in this series of letters.
The raw notes of pi and e in base 12 contain this kind of reason in the musical sense. It's akin to a "paint by number" with half of the lines filled in and a few colors already in place. There are infinitely many songs one could derive from the constants, but these arrangements optimize an inherent structure within the digits using "the rules" of harmonic progression that have dominated popular music for centuries. It's easy to see that the tonal center is shifting throughout the piece, but the digits of pi are more "stable" than random data in this arena. In the sheet music folder, there is a PDF (Deep Dive) that explains the more interesting aspects of the structure.
After you read and watch the rest of the vids, scroll back up here if you'd like free MP3s or sheet music.
CLICK --> HERE <-- and download the files you want.
There's a tip jar at the bottom of this page if you want to contribute :)
Here is a version of the first section of pi, played in a minor key.
This is an alternative arrangement to Euler's number. It's METAL!
Under construction New version in the works!
Here are three versions of the pi song without numbers or explanation.
The final note is tuned to the tone of the Hydrogen. The EM frequency of Hydrogen is 1420.405751 MegaHertz, cut that in half (reduce by octaves) 22 times, and you end up at 338.651 Hz, in the audible range.
These three videos are the most Universal presentation possible of The Pi Waltz.
These videos have flashing colors.
If you start to feel uncomfortable, avert or close your eyes.
Here's a version tuned to Planck time.
If the Universe were a video game, Planck time is the framerate. This song is tuned to Planck time.
(1.8550948324478E+43 frames per second) / 2^136 = Ab +44 cents
Finally, here is a version tuned to a missing frequency that resides between Hydrogen and Planck time (C +46 cents). I don't know what to call it. The full derivation is in the picture at the bottom of this site, and also in the description on YouTube.
Here's a binaural meditation tone based on that "green hidden tone" in 3 ways.
This will induce Theta waves in your brain (the twilight state). Heed the warnings.
Here's a little on base 12. We use base ten, or decimal. Our standard system uses 10 characters to do math.
These are just symbols to represent amounts. Think of Roman numeral "X". In our system, we need two digits to express that amount, 10. Roman numeral "X" represents that amount using a single character. Digits are merely symbols to represent amounts. Choosing which base you use is like selecting your language. The whole world just happens to speak base 10.
Base 12 means that we are using 12 characters.
A = ten
B = eleven
I also use:
X = ten
E = eleven
There are other symbols people use. It's only important to understand the concept of "bases".
Then, to connect the math with the music, we line those digits up with the 12 musical tones.
From there, we can play base 12 digit sequences. It didn't take much to reveal the underlying melodic phrases. As you can see, many of the phrases contain long strings of straight quarter notes, which is the simplest possible way to play any sequence.
This Universal tonality calculation.
Hydrogen came out to be
E (+46.76 cents)
Planck Time came out to be
G# (+43.65 cents)
To make symmetry in the octave I split the difference
C (+45.2 cents) 268.547 Hz
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