Στοιχεῖα is a dual Euclidean Sequencer that 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.
With its switch in the centre position, the sequence is turned off. To turn it on (Trigger Mode), push the switch up. In trigger mode, the sequence will switch its output high when receiving a clock signal rising edge (low to high transition), provided the next beat in the sequence is ‘on’. When the clock signal falling edge is received (high to low transition), the output will be switched back to low (0v). This means that the output trigger signals have the same pulse width as the input clock. So if the clocks are generated with very short pulses, the output triggers will be equally short. As a consequence, a pulse width modulation on the input clock signal will be passed on through the sequencer.
Pushing the switch down from its centre (off) position puts the sequence into Alternating Mode. In alternating mode, the output goes high on the first ‘on’ beat, and remains high until the next ‘on’ beat. In other words, the output toggles on every ‘on’ beat in the sequence. The up and down transitions occur on the rising edge of the input clock.
The centre jack can be used to connect a reset trigger. When a reset is received, both sequences restart at their first position. This takes into consideration the rotation setting: If sequence A and B have different rotations, they will remain offset in respect to each other. Reset can also be manually triggered by pushing the centre switch momentarily upwards.
The centre switch can be pushed down, which enables Chained mode. When chained, the two sequences are repeated one after the other, instead of concurrently. This is very useful to build up more complex patterns. In chained mode, the output of the combined sequence is available at both output jacks. On startup, the first sequence will play through to its determined length. It will then stop, and the second sequence will play through to the end, at which point the first one starts up again. For example, setting the first sequence to length 12, and the second to length 4, will result in a combined 16-step sequence. A reset signal in Chained mode brings the combined sequence to the start of the first pattern. Rotation works as in regular mode. Chained mode can also be used to create sequences longer than 16 steps.
Στοιχεῖα 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.
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- Eurorack Format
- Depth: 30mm
- Requires +5v
- PTC fuse and diode protected
- +12v: < 10mA / -12v: 0mA / +5v: < 25mA
- Voltage Range: Output low: 0v / Output high: 5.1v