Real Kecak System
Year: 2002 Authors: Akio Hizume
Core claim
Continued-fraction structure in real numbers can be used to compose infinite, non-periodic music without random processes.
Topics
interactive computer music, continued fractions, polyrhythm, irrational numbers
Domains
real numbers, continued fractions, Euclidean algorithm, irrational numbers, music composition, computer music, algorithmic art
Methods
number input, continued-fraction expansion, convergence mapping, parameterized playback
Media
computer software, music playback, images
Paper text
The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.
BRIDGES Mathematical Connections in Art, Music, and Science
Real Kecak System
Akio Hizume Star Cage Institute of Geometry Email: starcage@mbb.nifty.com http://homepage1.nifty.com/starcage/
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 converged corresponds to a planet in the RKS. Next, input starting point of time. You can set up it from to . Zero is special point. All of planets line up exact same direction and do not count. If you like, you can choose any instrument (according to the General Mail Standard), duration of event, 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 “resol” 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 FBDRACCI 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, FBDRACCI KECAK SYSTEM is the rarest conjunction of planets. After comparing various numbers system, you should be aware that the Golden Mean is or most real number. In contrast with this, any integer has no planet.
REAL KECAK SYSTEM (a)1999-2000 Akio HIZUME 1.618034 You have 17 planets Choose any planets by increasing volume
This example will not be repeated for 522,629,966,200,000,000 years.
The “Real Kecak System” is interactive computer music in which polyrhythms correspond to any combination of real numbers. In this work, it was my main aim to innovate musical form through recursive structures of any irrational numbers. No random numbers or stochastic processes were used in this work, which was based on the quite deterministic laws of mathematics. The real numbers are infinite; musical forms are infinite!
Any real number has their own hierarchy of the convergences derived from a continued fraction. Each convergence has their own periodic sequence. The Real Kecak System plays polyrhythm music consists of these sequences of convergences. When you input an irrational number, e.g., SQR2, SQR3, EXP1, or Golden Mean, the music is fantastic, and we do not get tired of it. The musical texture goes on changing little by little beyond the astronomical period. We enjoy it as ethnic music. We can exhaustively make the best use of the self-similitude of irrational numbers for music. Our ears can recognize the characters of real numbers. Since most of the real numbers are irrational numbers, most of the music made should be non-periodic and eternal.
Acknowledgement: I would like to thank Shoji Yotsutani and Robert Hickling for their support.
Supported by The Japan Foundation