Converting pi to duodecimal now produces a mysterious and beautiful melody

It can be said that art and mathematics are inseparable from each other because works of art are born not only from human sensibilities but also from precise calculations, but if 'mathematics' is replaced with music, art will be born. is. A movie that plays a beautiful melody by converting the pi, which is a mathematically important number, into a duodecimal number has been released.

The Ancient Melodies

Western music consists of '12 equal temperament ', which is an octave divided into 12 equal temperaments. In other words, since the scale has 12 cycles, it can be said that it has an affinity with 'duodecimal number' mathematically.

By the way, the pi is an irrational number that continues forever without circulating as '3.141592 ...' ...

This notation is, of course, written in decimal.

But the base notation can be converted. For example, if you write the pi in binary, it will be '11.0010010001 ...' ...

If the decimal number 10 is written as 'A' and 11 is written as 'B', the circumference can be written as '3.184809493B911 ...' in decimal.

Then, what kind of melody will be played if a number is assigned to each of the 12 temperaments on the piano keyboard and the sound is produced according to the pi of the 12-ary number that has become more music-friendly?

You can see how 'Pi by Duodecimal' is played in the following movie.

The Melody of Pi --226 digits --chromatic π base 12 waltz --by Jim Zamerski --YouTube

A mysterious and beautiful melody that can never be played with random numbers was born.

By arranging the rhythm, tempo, and accompaniment, it is possible to handle various tunes. Requiem with duodecimal pi looks like this.

The Requiem of Pi --chromatic π base 12 --YouTube

It is not only the pi that can play wonderful music in duodecimal. If you convert the exponential (Napier number ) used at the base of the natural logarithm into a duodecimal number, you can see how it becomes metal in the following movie.

Euler's Metal --141 digits --chromatic e base 12 --YouTube

It will be like this when the number of napiers is tailored to tango.

Euler's Tango --141 digits --chromatic e base 12 --YouTube

The new music, which is a fusion of the natural providence of playing sounds in mathematics and human sensibilities, is the work of Jim Zamerski , and can also be purchased as an MP3 format sound source from the official website. It is said that 50% of the proceeds from download sales will be donated to charity.

in Science,   Video,   Art, Posted by darkhorse_log