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This section has audio and video pieces based on five famous mathematical constants. The constants were "sonified" by assigning notes from various musical instruments to the digits 0 through 9.
What are the five famous constants? Two of the five are 1 and 0. These need little explanation. Most of us are familiar with the third: pi (π) or the circumference of a circle divided by its diameter. This works out to 3.141592…for all circles. The three dots mean that the decimal part goes on forever. The fourth is "e" which is equal to 2.718281…and is the base of the natural logarithms. It also goes forever. The last is i, the square root of minus 1, or what is called an imaginary number.
Leonhard Euler ( pronounced "oiler") related all five of these constants in what many consider to be the most beautiful equation in all of mathematics. This mysterious relationship is sometimes called the Magic 5 Equation:
e to the power πi+1=0
All five of the constants are sonified in two separate audio pieces: Magic 5: Euler All At Once, and my personal favorite, Euler's Samba. Pi just by itself is sonified in two different ways. Straight, as a Piano Solo, and in a more complicated way with Piano, Bass and Flute. It's represented visually as an animated pattern matrix in Pi's Digit Matrix. Finally, the Reverend Pi 357 video is my salute to all the number mystics out there. Like the weather sonifications, these result are surprisingly musical even though the original intent was not to write music but to listen for patterns.
By selecting the various links below you can hear some of the "math songs". They are also available on a CD entitled, Pi on the Piano, Eee with a Queeka. I love the sound of the cuica (pronounced "queeka"). Click here to hear it and learn some about it if you don't already know: queeka
I encourage you to use QuickTime 7.0 or higher to hear and see all of the streamed audio and video pieces on this site. If you don't have QuickTime 7, you can download it for free, for either Mac OS or Windows, by clicking here. If you just don't want to get QuickTime for free, some of the audio and video pieces can still be viewed using Windows Media Player, albeit at a lower video quality. Look for a link to Media Player by the description of a particular piece after clicking on it below.
Math Songs: The Sonifications and Videos
1 - Pi to 500 Decimal Places: Piano Solo. Audio with keyboard graphic. A good one to start with to familiarize yourself with how these sonifications were done. The same digit to pitch mapping was used in most of the following songs. The zero is usually not played as a note but shows up as a rest of the same duration as the notes in the particular piece. (3:11)
2 - Pi to 1,000 Decimal Places: Piano Solo. Audio with pi matrix. About four notes per second. (4:19) Update: Also an improvisation by Chis Mear based on this piece.
3 - Pi to 1,000 Decimal Places: Piano, Bass, Flute. Audio with graphics. A more complex mapping than the first two. (4:15)
4 - Pi's Digit Matrix for the First 100 Digits. Video animation, no audio. Visually explores the digit pattern in the first 1,000 digits of pi. (0:47)
5 - e to 500 Decimal Places: Piano Solo. Audio with e matrix. (1:47)
6 - The Reverend Pi 357. Audio, including voice, and a fairly involved video animation with lots of symbols. (2:23) Note: The Very Reverend Dr. Pi is an ordained minister in the Universal Life Church and a real doctor. He is available to perform legal weddings, baptisms, funerals, spiritual counseling, and other ministerial duties and he will assist you in designing a Pi or other mathematically themed ritual. Email me at this web page to arrange an appointment or booking with the Reverend Dr. Pi.
7 - Magic 5: Eulers Constants All at Once. Audio, a fixed image of the Magic 5 formula, 500 decimal places. Pi=bass; e=piano; 1&0=metal mallets; i=trumpet. (1:47)
8 - Magic 5: Eulers Constants All at Once. Same as above except a small video image of Euler himself. Pi=bass; e=piano; 1&0=metal mallets; i=trumpet. (1:47)
9 - Euler's Samba. A more interpretive view of the Magic 5 constants but no digits have been changed. Audio and a little video animation, 500 decimal places. Pi=bass; e=piano; i=trumpet and sax; 1&0=metal mallets; 1=whistle and, of course, 0=the cuica. (1:47)