p/q – rational number decimals as rhythmic pattern.

In this project I am searching for repeating decimal numbers to be used as rhythmic patterns. To do so an algorithm finds a repeating pattern in the result of 1 divided by prime numbers. These patterns are then used as input to a rhythm machine.

Rational numbers are numbers that can be written as a ratio of two integers: e.g.: 1/3. Some rational numbers are decimal numbers either ending after a number of digits: e.g.: 5/4 = 1.25, or repeat e.g.: 1/3 = 0.3333…, 1/37 = 0.027027…, 1/7 = 0.142857142857…

I use prime numbers because it seems that 1 divided by a prime number produces a repeating pattern more often.

This project was first presented at PIFCamp 2024.

Generating rhythms / Knocking the KUbUS:

To generate a rhythm from a pattern of digits the pattern equals the length of one bar where each digit defines the delay to the next trigger-event. A specific BPM then defines the length of these delays and long patterns are split into several bars.

Each trigger contains the value of the digit (0 to 9) and drives one of the 10 solenoids to knock the KUbUS at different spots in the rhythm of the repeating pattern.

The strength of the solenoids slowly fades out as the sequence progresses into insignificance.

Thanks to Stefan Voglsinger who made the performance on the KUbUS possible and recorded the session with several microphones on the metal structure.

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1 / 4649 = 0.00021510002151…
Pattern: 0 0 0 2 1 5 1

1 / 73 = 0.0136986301369863…
Pattern: 0 1 3 6 9 8 6 3

1 / 9091 = 0.0001099989
Pattern: 0 0 0 1 0 9 9 9 8 9

1 / 53 = 0.01886792452830188679245283…
Pattern: 0 1 8 8 6 7 9 2 4 5 2 8 3

1 / 3541 = 0.0002824060999717593900028240609997175939…
Pattern: 0 0 0 2 8 2 4 0 6 0 9 9 9 7 1 7 5 9 3 9

1 / 103 = 0.00970873786407766990291262135922330097087378640776699029126213592233…
Pattern: 0 0 9 7 0 8 7 3 7 8 6 4 0 7 7 6 6 9 9 0 2 9 1 2 6 2 1 3 5 9 2 2 3 3

1 / 4013 = 0.00024919013207076999750809867929230002491901320707699975080986792923
Pattern: 0 0 0 2 4 9 1 9 0 1 3 2 0 7 0 7 6 9 9 9 7 5 0 8 0 9 8 6 7 9 2 9 2 3

1 / 71 = 0.0140845070422535211267605633802816901408450704225352112676056338028169…
Pattern: 0 1 4 0 8 4 5 0 7 0 4 2 2 5 3 5 2 1 1 2 6 7 6 0 5 6 3 3 8 0 2 8 1 6 9

1 / 83 = 0.01204819277108433734939759036144578313253…
Pattern: 0 1 2 0 4 8 1 9 2 7 7 1 0 8 4 3 3 7 3 4 9 3 9 7 5 9 0 3 6 1 4 4 5 7 8 3 1 3 2 5 3

1 / 1231 = 0.00081234768480909829406986190089358245329…
Pattern: 0 0 0 8 1 2 3 4 7 6 8 4 8 0 9 0 9 8 2 9 4 0 6 9 8 6 1 9 0 0 8 9 3 5 8 2 4 5 3 2 9

1 / 127 = 0.007874015748031496062992125984251968503937…
Pattern: 0 0 7 8 7 4 0 1 5 7 4 8 0 3 1 4 9 6 0 6 2 9 9 2 1 2 5 9 8 4 2 5 1 9 6 8 5 0 3 9 3 7

1 / 2689 = 0.000371885459278542208999628114540721457791…
Pattern: 0 0 0 3 7 1 8 8 5 4 5 9 2 7 8 5 4 2 2 0 8 9 9 9 6 2 8 1 1 4 5 4 0 7 2 1 4 5 7 7 9 1

1 / 173 = 0.0057803468208092485549132947976878612716763…
Pattern: 0 0 5 7 8 0 3 4 6 8 2 0 8 0 9 2 4 8 5 5 4 9 1 3 2 9 4 7 9 7 6 8 7 8 6 1 2 7 1 6 7 6 3

1 / 89 = 0.01123595505617977528089887640449438202247191…
Pattern: 0 1 1 2 3 5 9 5 5 0 5 6 1 7 9 7 7 5 2 8 0 8 9 8 8 7 6 4 0 4 4 9 4 3 8 2 0 2 2 4 7 1 9 1

1 / 47 = 0.0212765957446808510638297872340425531914893617…
Pattern: 0 2 1 2 7 6 5 9 5 7 4 4 6 8 0 8 5 1 0 6 3 8 2 9 7 8 7 2 3 4 0 4 2 5 5 3 1 9 1 4 8 9 3 6 1 7

1 / 139 = 0.0071942446043165467625899280575539568345323741…
Pattern: 0 0 7 1 9 4 2 4 4 6 0 4 3 1 6 5 4 6 7 6 2 5 8 9 9 2 8 0 5 7 5 5 3 9 5 6 8 3 4 5 3 2 3 7 4 1

1 / 2531 = 0.0003951007506914263137099960489924930857368629…
Pattern: 0 0 0 3 9 5 1 0 0 7 5 0 6 9 1 4 2 6 3 1 3 7 0 9 9 9 6 0 4 8 9 9 2 4 9 3 0 8 5 7 3 6 8 6 2 9

1 / 251 = 0.00398406374501992031872509960159362549800796812749…
Pattern: 0 0 3 9 8 4 0 6 3 7 4 5 0 1 9 9 2 0 3 1 8 7 2 5 0 9 9 6 0 1 5 9 3 6 2 5 4 9 8 0 0 7 9 6 8 1 2 7 4 9

1 / 5051 = 0.00019798059790140566224509998020194020985943377549…
Pattern: 0 0 0 1 9 7 9 8 0 5 9 7 9 0 1 4 0 5 6 6 2 2 4 5 0 9 9 9 8 0 2 0 1 9 4 0 2 0 9 8 5 9 4 3 3 7 7 5 4 9

1 / 613 = 0.001631321370309951060358890701468189233278955954323…
Pattern: 0 0 1 6 3 1 3 2 1 3 7 0 3 0 9 9 5 1 0 6 0 3 5 8 8 9 0 7 0 1 4 6 8 1 8 9 2 3 3 2 7 8 9 5 5 9 5 4 3 2 3

1 / 521 = 0.0019193857965451055662188099808061420345489443378119…
Pattern: 0 0 1 9 1 9 3 8 5 7 9 6 5 4 5 1 0 5 5 6 6 2 1 8 8 0 9 9 8 0 8 0 6 1 4 2 0 3 4 5 4 8 9 4 4 3 3 7 8 1 1 9