When you reach the end of this website, you'll know the following statement is true: It is extremely likely that the songs on this site are considered sacred and revered by countless extraterrestrial civilizations, on countless planets, in countless galaxies, and they have been for billions of years. Are you ready to join this Universal club? All you have to do is give the first song your full attention all the way to the final note.

These are The Cosmic Melodies. 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
 

Welcome home.

If these videos don't show up, you can go directly to my youtube channel

The free sheet music ---> SHEET MUSIC

 

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.

The opening chords sound just like "Heart and Soul".
Right now, this is probably being sung, hummed, and whistled all throughout the Universe.


 

I like to think that somewhere out there exists a Cantina not unlike the one in Mos Eisley from Star Wars, where this tune is being covered by some extremely talented extraterrestrials on similar instruments to ours. Only so many ways to ring a string, resonate a reed, blow through a metal tube, alter waves on a synthesizer, and rhythmically bang on things. 

NOTE: 4/37 (base 10) = 4/31 (base 12)

The songs found in rational numbers must have primes in the denominator. 

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.

thequickbrownfoxjumpedoverthelazydog

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. If you consider the luck it would take to generate random sequences one could arrange into melodies as amazing as these, it's akin to throwing a billion dice up into the air, letting them land, then looking down at them from above and seeing the Mona Lisa. That's how well these melodies dance through the minefield that is the chromatic scale, or all 12 musical tones.

On the free-files page, 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 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's what base 12 means. We use base ten, or decimal. Our standard system uses 10 characters to do math.

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

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.

0,1,2,3,4,5,6,7,8,9,A,B

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".

Here's pi in several different bases.

Then, to connect the math with the music, we line the base 12 digits up with the 12 musical tones.

0=B
1=C
2=Db
3=D
4=Eb
5=E
6=F
7=Gb
8=G
9=Ab
A=A
B=Bb
 
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 is another interesting thing I discovered. If you look at the "tone" of hydrogen using a musical lens, and compare it to Planck time, they're nearly in tune with each other, and they're a major third apart. There seems to be an implied missing frequency.
 

(I realize my mistake in that the value I used for Planck Time is incorrect, but the graphic is close enough to the actual numbers that the harmony, and the cents values shown, are only a fraction of a percent off) 

To make symmetry in the octave, the "missing" frequency is also a major third. It makes an augmented chord, in which all three intervals are major thirds relative to each other. The cents split the way they are means the third frequency is as closely tuned to hydrogen and Planck time as is possible. Any more sharp or flat, and it would have a tuning bias towards one or the other. It’s optimized for maximum harmony and minimum beat frequencies (phase or constructive/destructive interference)

Update Oct 18, 2023: Upon watching a YouTube video, I learned of an anomalous signal detected in 2016 by Eric Trottier and Ermanno Borra. They detected a pulsing of light coming from 234 stars at the same frequency. I realized it is possible, and very easy, to broadcast melodies across vast distances using a single frequency. There is a term in music known as “cents”. It refers to the distance between two semi-tones (half steps) divided into 100 parts. It's basically a percent towards the next semi-tone (half step up or down) in a 12 tone equally-tempered tuning system (standard western tuning). 

The Universe doesn't come with many benchmark frequencies, but I just described the tonality of the most obvious candidates. Since the benchmarks (H and Planck) are slightly out of tune with each other, and the third frequency is the balancing point, it makes sense to use that third frequency as the benchmark, or at least, assume intelligent beings would. It's the elegant solution to the problem of universal tuning bias, and the major third intervals (of H and Planck) are a clue to that.

If the signal we saw was of intelligent origin, it's possible that the pulse rate, when converted into Hz, and examined next to the benchmark tuning, will yield a string of numbers that in base 12, spell out an unmistakably coherent melody. Our first message received from extraterrestrial life might be a little song. 

The 1.65 ps (unfortunately, these calculations require a highly precise initial value) pulse comes out to 606060606060.606 Hz. If you drop that many octaves, you get to 282.219 Hz. This frequency is roughly 86.59% of the way to the next semi-tone from the benchmark frequency (268.546 Hz). So the ET signal melody would be encoded in the 0.8659… % semi-tone deviation from benchmark number, converted to base 12, played in the chromatic scale. The more precise our measurement of that initial pulse, the more melody notes we get out of the comparison "ratio".

Here are three versions of the pi song without numbers or explanation. There is only music, and colors. These three videos are the most Universal presentation possible of The Pi Waltz.

Also, these three versions are 330 digits long. The "symmetrical" one is the most polished.
 

Tuned to Hydrogen
 

Tuned to Planck-time
The “turn-around” at the end of this version grabs you right by the bottom of your guts.
 

Tuned to the symmetrical frequency

I wonder if the musically resolved value of pi (3.184809493E9186644) is a clue to solving the equations that describe the physical Universe, working out the "vacuum catastrophe", Einstein's "cosmological constant", or applied in string theory / M-theory.

"Fudge factors", be gone. Bring everything into focus.

I spent some time with that number, and found its rational expression is interesting. This value for pi is ever-so-slightly smaller than the actual value.

When I discovered the melody in pi and wrote the final note, one of the dozen thoughts I had in that moment was that this song may be the key to unlocking the ultimate technology and becoming masters of matter and space-time. This music is the most beautiful I can imagine. Can you imagine if it is also the key to ending detrimental consumption? It would be overwhelming to learn that the future of humanity was saved by the music of infinity. I can't imagine a more beautiful world than that. A perfect home.

Euler's number played as a melody and resolved can also be expressed rationally.

This value for e is ever-so-slightly larger than the actual number.

This is a slightly unsettling discovery I made recently. Many know about the Mandelbrot set. I view it as a universal piece of art, akin to my music here. I found the songs. Mandelbrot found the painting. Many have noticed that, turned 90 degrees, the Mandelbrot set has a bilateral symmetry. Many have also noticed it bears a resemblance to the sitting Buddha. A team did a more in-depth analysis of the interior of the set and found amazing patterns as the number of iterations went up. They turned Mandelbrot set 90 degrees to show the bilateral symmetry. I mean, there are no rules on orientation, but the symmetry about the vertical axis mimics life, so why not? Here is what the Buddhabrot looks like. 

Since orientation doesn't matter, let's see what the set looks like flipped upside down. Is it us?

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's a binaural meditation tone based on that missing tone in 3 ways.
This will induce Theta waves in your brain (the twilight state).

Do not drive or operate heavy machinery while listening to this.

It's heavy on the bass end. Turn your volume down, then turn it up after the tone starts.

Here is how the colors are derived.

Here are those colors arranged in the circle of fifths. Many find it soothing. Every set of three neighbors is the maximum compliment while the clashing colors are across the circle.