Cursus Iteritas#

Dynamically generated wavetable oscillator using orthogonal functions


Cursus Iteritas is an oscillator that works from a dynamically generated wavetable. It gives the user spectral-like controls over three different modes based on different conceptualizations of frequency: Fourier, which uses sine waves; Daubechies, using wavelets, and Walsh mode, using the Walsh transform. Cursus Iteritas parametrizes a wide variety of sounds, but because the sounds are all based off of orthogonal functions, it has a musical tone structure and can produce an extremely wide variety of harmonic sounds.

  • Type: LFSR VCO
  • Size: 10HP Eurorack
  • Depth: 1.5 inches
  • Power: 2x8 Eurorack
  • +12 V: 150 mA (80 mA when using 5 V supply)
  • -12 V: 5 mA
  • 5 V: 90 mA (optional)


Power connector

To power your Noise Engineering module, turn off your case. Plug one end of your ribbon cable into your power board so that the red stripe on the ribbon cable is aligned to the side that says -12 V and each pin on the power header is plugged into the connector on the ribbon. Make sure no pins are overhanging the connector! If they are, unplug it and realign.

Line up the red stripe on the ribbon cable so that it matches the white stripe and/or -12 V indication on the board and plug in the connector.

Screw your module into your case before powering on the module. You risk bumping the module's PCB against something metallic and damaging it if it's not properly secured when powered on.

You should be good to go if you followed these instructions. Now go make some noise!

A final note. Some modules have other headers -- they may have a different number of pins or may say "not power". In general, unless a manual tells you otherwise, do not connect those to power.


Illustration of Cursus Iteritas's interface

All knobs on Cursus Iteritas function as offsets for the input jacks. The controls function similar to a bandpass filter; center, width, and tilt allow the filter to be asymmetric.

1 V / octave pitch control. For more control, see Range below.
Selects the center harmonic used to build the wavetable.
Allows selection of harmonics included in the output. In the center position, all harmonics are included. Fully left only even harmonics; fully right, only odd.
Controls the oversampling filter of the wavetable. As this is turned to the right, it will add musical overtones.
Wavefolder. Enough said.
Controls how many different harmonics are used to create the wavetable.
Weights the spread of harmonics. In the middle it is symmetric; at left, lower harmonics are louder while at right, higher harmonics get more volume.
Triggers oscillator reset. Responds to a rising edge of about 3 V.
Selects which orthogonal function set is used to produce the wavetable
Two-octave offset pitch ranges
Audio output - 10 V peak to peak
CI's CV ins respond to 0 V to 5 V, except the pitch in, which responds to 0 V to 8 V.

Patch tutorial#

The easiest way to get to know Cursus is to just plug in the output and play with the knobs to get a feel for the sounds it can make.
Gates and LFO

Cursus works very well with any LFO, gate or envelope source the more the better. Patching the outputs of the Numeric repetitor directly into the parameter inputs on Cursus is a great way to generate complex rhythmic tonality variation.

Every LFO source is fun with Cursus. We highly reccomend patching Sinc Iter, Malekko Voltage Block, Malekko AD/LFO, Mannequins Just Friends, Make Noise Wogglebug, and WMD PDO with Cursus.

Photo of the Gates & LFO patch

Tone generation#

Cursus Iteritas generates a spectral description based on knob positions. Center, Width, Tilt, Structure determine amplitudes for each harmonic. This description is fed into the inverse transform for the current function set to produce the time-domain wavetable. The wavetable is normalized to reduce amplitude variations across spectral changes.

Oversampling of the wavetable depends on pitch: lower octaves have higher oversampling since the sample rate only varies by a factor of two. The Edge control interpolates the oversampling from point sampling to a cubic-spline interpolation (NURBS). As the period of the full length of the wavetable always evenly divides the sample rate, the additional aliasing is largely harmonic in nature. Fold controls the signal wavefolding.

In many places in the signal path, there are soft clipping stages to mimic analog-style clipping to give more warmth and complexity to the sounds generated.

Variable sample rate#

Cursus Iteritas uses a sample rate that is a multiple of the fundamental (lowest) oscillator frequency. This moves alias power that is a multiple of the fundamental to be mapped to a multiple of this tone, therefore making the aliasing align with the harmonics of the tone. This works well for settings with a strong harmonic structure (spread fully clockwise or fully counterclockwise) and adds unique aliasing character for other tones.

Tuning calibration#

Cursus comes pre-calibrated and should not need adjustment. If the trim pot gets bumped and needs a tuneup, follow this procedure to calibrate your module.

Pitch calibration is controlled by an linear resistor-divider network. To calibrate the tuning, attach a volt meter (preferably 4 or more digit) to the test points CAL and GND on the rear panel and adjust the trim pot.

The voltage measured should be 5/16 (.3125) times the input voltage applied to the CV input. A reasonable way to tune the scale is to use an adjustable voltage source to generate 4 V then adjust the tuning trim until the test points read 1.2500 V.

Cursus Iteritas can also be tuned using a reference supply capable of generating a 1 V difference and using a stroboscope such as the Peterson 490 to tune to an octave interval. This is method is preferred to the meter-only method.

Voltage supply#

Cursus Iteritas can run its processor on the 5 volt eurorack power rail to reduce noise and load on the 12 volt bus. Gently push the switch tab in the direction of the desired rail to use.

Picture of voltage supply switch

Genesis & design notes#

This module started many years ago when Scott Jager and Yasi Perera turned me onto Walsh functions.

The big question was how to reduce the large number of variables (32 harmonic volumes for a 32 band Walsh synthesizer) into a reasonable control set. Bandpass filter-like controls seemed to be a good solution and there already exist similar controls in the various existant Harmonic Oscillators. A software prototype was written that proved that a sequency bandpass control scheme was usable. The then project went to sleep for a couple years as other modules took priority.

When I started working on it again I wanted it to have three modes much like our other current modules so I went searching for other orthogonal function sets that could fit in the same control scheme.

The Fourier Series was an obvious second set of orthogonal functions to use which perfectly mapped to the bandpass-like controls.

Modern mathematics have given us an ocean of orthogonal function sets in wavelets so that seemed another good place to look. The Daubechies 4 wavelet fit the bill being easy to compute and having an interesting—and somewhat sawtooth-like—waveform. The controls were a little less natural since this wavelet has more time precision and more frequency redundancy. With some work however it worked out quite naturally.


We will repair or replace (at our discretion) any product that we manufactured as long as we are in business and are able to get the parts to do so. We aim to support modules that have been discontinued for as long as possible. This warranty does not apply to normal wear and tear, including art/panel wear, or any products that have been modified, abused, or misused. Our warranty is limited to manufacturing defects.

Warranty repairs/replacements are free. Repairs due to user modification or other damage are charged at an affordable rate. Customers are responsible for the cost of shipping to Noise Engineering for repair.

All returns must be coordinated through Noise Engineering; returns without a Return Authorization will be refused and returned to sender.

Please contact us if you think one of your modules needs a repair.

Special thanks#

  • Kris Kaiser
  • Scott Jager
  • Yasi Perera
  • Shawn Jimmerson
  • Eric Cheslak
  • Bana Haffar
  • William Mathewson
  • Mickey Bakas
  • Tyler Thompson
  • Alex Anderson


  • Hutchins Jr, Bernard A. "Experimental electronic music devices employing Walsh functions." Journal of the Audio Engineering Society 21.8 (1973): 640-645.
  • Brown, Owen. A Digital Waveform Synthesizer Using Walsh Functions. Diss. 1971.
  • Rozenberg, Maurice. "Microcomputer-controlled sound processing using Walsh Functions." Computer Music Journal (1979): 42-47.