Real Kecak System
interactive computer music
©1999-2000 Akio HIZUME

The Real Kecak System (RKS) is an application for composing music. First, input any real number you like and then click the ENTER button. The RKS will display its expansion into continued fraction and convergence based on the Euclidean algorithm. Each n-th convergent corresponds to a planet in the RKS. Next, input starting point of time. You can set up it from (-2^31) to (2^31). Zero is special point. All of planets line up exact same direction and do not sound. If you like, you can choose any instrument (according to the General Midi Standard), duration of sound, speed (milliseconds) and key. Finally, click the "play" button. Unique planets system will start to orbit and play music. When you want to stop playing, click the "stop". The "cont." button restarts the music from last time stopped continually. If you want to change some parameters, please stop the playing then click the "reset" button. Change anything you like. Click the "play" button again, you can see updated planets system. You can change anything as many times as you like.
I published the FIBONACCI KECAK (1995) using the Golden Mean based on the same algorithm. The Golden Mean (1.618034 or 0.618034) has the most numbers of planets because it is the hardest to approximate the Golden Mean using fraction. In other words, FIBONACCI KECAK SYSTEM is the rarest conjunction of planets. After comparing various numbers system, you should be aware that the Golden Mean is critical real number. In contrast with this, any integer has no planet.

Fibonacci Kecak (90" 540KB)
Square Kecak (60" 372KB)
Delta Kecak (60" 380KB)
EXP1 Kecak(60" 372KB)
submitted piece for ICMC2002 (9'11" 3.3MB)

Downloadable Paper
realkecaksystem.pdf (64KB)