Noise Engineering Cursus Iteritas User manual

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Type LFSR VCO
Size 10HP Eurorack
Depth 1.5 Inches
Power 2x8 Eurorack
+12 mA 150 / 80 (if 5v on)
-12 mA 5 / 5
+5 mA 0 / 90 (optional)
Noise Engineering
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.

Interface
Tilt
controls the oversampling filter of the wavetable. As this is turned to the
right, it will add musical overtones.
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.
Sync
Center
triggers oscillator reset. Responds to a rising edge of about 3v.
Mode
selects which orthogonal function set is used to produce the wavetable
Pitch
1v/8va pitch control. For more control, see Range below.
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.
Width
Structure
Edge
controls how many different harmonics are used to create the wavetable.
selects the center harmonic used to build the wavetable.
wavefolder. Enough said.
Fold
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.
two-octave offset pitch ranges
Range
audio output - 10vpp
Out
Voltages
CI’s CV ins respond to 0-5v, except the pitch in, which responds to 0-8v.
Noise Engineering
Cursus Iteritas
Dynamically generated wavetable oscillator using orthogonal functions.
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Noise Engineering
Cursus Iteritas
Dynamically generated wavetable oscillator using orthogonal functions.
Patch Tutorial 0 - Introduction
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.
Patch Tutorial 1
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.
Patch Tutorial 1 - Gates and LFO
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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.
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.
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.
Tone Generation
Dynamically generated wavetable oscillator using orthogonal functions.
Cursus Iteritas
Noise Engineering
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Calibration of Tuning
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 CW or
fully CCW) and adds unique aliasing character for other tones.
Variable Sample Rate
Cursus Iteritas can run its processor on the 5V eurorack power rail to reduce noise and load on the 12V
bus. Gently push the switch tab in the direction of the desired rail to use.
Voltage Supply
Pitch calibration is controlled by an linear resistor-divider network. To calibrate the tuning,
attach a volt meter (preferably 4+ digit) to the test points TPCV and TPGND on the rear panel
and adjust the trim pot.
Cursus comes pre-calibrated but over time it may change and need a touch up.
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 volts then
adjust the tuning trim until the test points read 1.2500V. Cursus Iteritas can also be tuned using a
reference supply capable of generating a 1 volt 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.
Dynamically generated wavetable oscillator using orthogonal functions.
Noise Engineering
Cursus Iteritas
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Genesis and Design Notes
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.
This module started many years ago when Scott Jager and Yasi Perera turned me onto Walsh
functions.
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.
Dynamically generated wavetable oscillator using orthogonal functions.
Cursus Iteritas
Noise Engineering
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Special Thanks
Shawn Jimmerson
Kris Kaiser
Scott Jager
Bana Haffar
Yasi Perera
Eric Cheslak
Mickey Bakas
William Mathewson
Tyler Thompson
Alex Anderson
Cursus Iteritas
Noise Engineering
Dynamically generated wavetable oscillator using orthogonal functions.
References
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.
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