Stoicheia_ Rebel Technology

215 EUR / Out of stock.

Στοιχεῖα is a dual Euclidean Sequencer. It algorithmically generates rhythmic sequences from an input trigger signal.

The name (Στοιχεῖα, Stoicheia, or Elements) comes from the title of Euclid’s book Elements in which the algorithm was first described.

Each sequence is controlled by a column of three knobs and a switch. The input parameters to the algorithm are sequence length and fills.

The length of the sequence, measured in clocks or beats, is controlled by the second knob from the top. The range goes from 1 (fully counter clockwise) to 16 (fully clockwise), with 8 in the centre position.

The number of fills, or on-beats, is set by the third knob. In fully counter-clockwise position, this is set to 1. Centre position will set every other beat ‘on’, or 50% . Fully clockwise sets every beat ‘on’, in other words: the number of fills are equal to the sequence length.

The top knob adjusts which beat the sequence starts on – and hence resets to. In its centre position, the sequence will start on its first step. The start position can be changed by turning the top knob left or right: this will have the effect of rotating the sequence left or right, respectively.

> tech specs

Height: 3U / 128.50mm
Width: 10HP / 50.50mm
Depth: 20mm
Weight: 135g

16-pin Doepfer/Eurorack
Requires +5v
PTC fuse and diode protected
+12v: < 10mA
-12v: 0mA
+5v: < 25mA

Outputs: < 1.1k
Inputs: > 100k
Voltage Range

Output low: 0v
Output high: 5.1v


This goes way back. In the third century BCE, the Greek mathematician Euclid described a way to determine the largest common denominator of any two integers. As it turns out, his method is the same as what people have used to divide beats into rhythms. Across the globe, from ancient to modern times; the rhythms that pervade human existence can be generated using the same, simple algorithm.

The cultural and historical range covered by these rhythms is nothing short of breathtaking. From Brazilian Samba and Bossa-Nova, to Bulgarian folk dances, thirteenth century Persian drum patterns, and complex poly-rhythms of West and Central Africa.

Of course, Euclid’s work can be applied to more than just rhythmic patterns. A scientist named Bjorklund applied it to nuclear physics, in order to optimise the operation of the SNS particle accelerator. He also published his work with a proof of the efficiency of his method. Then, in 2005, a Professor of Computer Science called Godfried Toussaint linked up the dots and presented in a research paper the connection between the work of Euclid, Bjorklund, and musical rhythms.
We have based our implementation on the work of Toussaint, Bjorklund and Euclid.



is driven by a micro controller which interfaces modular signal levels through discrete transistor networks. It functions by responding to incoming trigger signals using the MCU’s built in hardware interrupts. The step sequences are pre-calculated in the main processor loop and updated when the knobs are turned, which means that the interrupts can be processed very efficiently. This leads to a very low on/off latency.

Efficient design, solid code and good use of hardware interrupts means that Stoicheia can process clock signals well into audible frequencies.

The circuit board has a 6-pin header which brings out the serial and reset pins of the MCU. It mates with an FTDI USB TTL Serial Cable. It is compatible with 3.3v and 5v TTL levels.

The MCU is an AVR ATMega168. It is loaded with the Arduino Bootloader, and can be programmed as an Arduino Diecimila. The firmware is dependent only on avr-gcc, and on Arduino/Wiring for the optional serial debug interface.