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THREE SISTERS: A Technical Map

THREE SISTERS links three filters for building spectral spaces. They are tied together by macroscopic control over their cutoff frequencies, filter responses, and resonance. The three filters can be configured to be lowpass, crossover, and highpass filters (crossover mode) or three bandpass filters (formant mode). Signals can be patched into individual filters and to all three simultaneously. Each filter's output can be individually tapped, and a mix of all three can be taken. This flexible input and output routing allows the module to process multiple signals in parallel and combine them into a single spectrally-sculpted mix, split a single signal into separate bands for independent processing, or any combination thereof.

Table of Contents

  1. Specifications
  2. Overview
  3. Block Diagrams
  4. LOW Filter Block
  5. HIGH Filter Block
  6. CENTRE Filter Block
  7. CROSSOVER and FORMANT modes
  8. FREQ and SPAN: Cutoff Control
  9. QUALITY: Resonance and Self-Oscillation
  10. QUALITY: Dry/Wet Mixing, and Notch Filters
  11. Spectral Mixing and Gating
  12. Spectrum and Dynamics
  13. Audio-visualization
  14. Formant and Vowel Synthesis
  15. 2-Operator FM Synthesis
  16. Filter Pinging
  17. Calibration
  18. Warranty

Specifications

  • 10HP
  • 30mm depth
  • 100mA @ +12v
  • 93mA @ -12v

Overview

At THREE SISTERS' core are three filter blocks named LOW, CENTRE, and HIGH.

Signals can be patched directly into each filter block via the associated jack: LOW(IN), HIGH(IN), or CENTRE(IN). Additionally, a signal can be patched into all three filter blocks simultaneously via the ALL(IN) jack.

Each filter block is made up of two state-variable filters cascaded in series. These state-variable filters (SVF) are each second order, two-pole filters with one signal input and three outputs: lowpass, bandpass, and highpass. The crossover/formant switch controls how the two SVFs in each pair are combined to determine a final filter response for that pair. Cascading two SVFs allows for a great deal of flexibility as well as steep filter rolloffs.

In crossover mode, the LOW, CENTRE, and HIGH filters are lowpass (24dB/octave), crossover (12dB/octave), and highpass (24dB/octave) filters, respectively. The "crossover" type is a lowpass and a highpass patched in series, providing a response like a bandpass with a variable-width passband (from the cutoff of the highpass up to the cutoff of the lowpass). The CENTRE "crossover" filter passes the frequencies between the cutoffs for the other two filter blocks.

In formant mode, the three filters are each four-pole bandpass filters (12dB/octave).

FREQ and SPAN control the cutoff frequencies for the three filter blocks in a linked fashion.

The clockwise half of the QUALITY knob controls resonance and can push the filters into self-oscillation.

The counterclockwise half of the QUALITY knob controls the level of 'anti-resonance'. Here, the level of the opposing filter response for each block is mixed back in with the original filter: e.g. turning QUALITY counter-clockwise mixes the frequencies above LOW's cutoff back in. This creates a "dry/wet" filter control which blends between the filtered and unfiltered sound, but also makes notch-rejection filter responses possible.

The outputs of the filter blocks can be taken individually via the associated jacks: LOW(OUT), HIGH(OUT), or CENTRE(OUT). Additionally, an equal mix of all three signals can be taken via the ALL(OUT) jack.

Block Diagrams

Cutoff Frequency Calculator

Filter Blocks and I/O Routing

LOW Filter Block

LOW filter block in detail

The LOW filter block feeds the first SVF's lowpass output into the second SVF. The cutoff frequencies of both SVFs in the LOW filter block are always equal. This cutoff frequency is determined by subtracting the SPAN voltage from the FREQ voltage (see FREQ and SPAN).

In crossover mode, the second SVF's lowpass response is the main output of the LOW(OUT) block. As such, before reaching the final LOW(OUT) mixing block, the input signal passes through two lowpass filters in series, each at the same cutoff frequency. In other words, the input to the LOW block passes through a fourth-order lowpass filter with a 24dB/octave slope.

In formant mode, the second SVF's highpass filter is the main output of the LOW(OUT) block. The input signal passes through a lowpass filter then a highpass filter in series, each at the same cutoff frequency. This is equivalent to saying the input signal passes through a bandpass filter with a 12dB/octave slope.

Cutoff Sweep, LOW in crossover mode

HIGH Filter Block

HIGH filter block in detail

The HIGH filter block is the inverse of the LOW block. The first filter block is always a highpass, and the second block switches between lowpass & highpass depending on the mode. The cutoff frequencies of both SVFs in the HIGH filter block are always equal. This cutoff frequency is determined by adding the SPAN voltage to the FREQ voltage (see FREQ and SPAN).

In crossover mode, the second SVF's highpass output is taken as the HIGH(OUT) output. As such, before reaching the final HIGH(OUT) mixing block, the input signal passes through two highpass filters in series, each at the same cutoff frequency. This acts as a fourth-order highpass filter with a 24dB/octave slope.

In formant mode, the second SVF's lowpass filter is tapped as the HIGH(OUT) output. The input signal is highpass filtered then lowpass filtered in series, at the same cutoff frequency. This creates a bandpass filter with a 12dB/octave slope.

Cutoff Sweep, HIGH in crossover mode

CENTRE Filter Block

CENTRE filter block in detail

The CENTRE filter block has a static routing. The input is first highpass filtered by the first SVF, then lowpass filtered by the second. Unlike the LOW and HIGH filter blocks, the cutoff frequencies of the two SVFs are not always the same.

In crossover mode, the first SVF's cutoff frequency (highpass mode) is equal to the LOW block's cutoff frequency, and the second SVF's cutoff frequency (lowpass mode) is equal to the HIGH block's cutoff frequency (see FREQ and Span). The result is a "crossover" filter with two 12dB/octave rolloffs: frequencies between the two cutoffs (in the crossover region) are passed unaffected, while frequencies outside the boundaries are filtered out.

In formant mode, both SVFs' cutoff frequencies are identical. This cutoff frequency is determined solely by the FREQ voltage (see FREQ and Span). The input signal passes through a highpass filter followed by a lowpass filter in series, each at the same cutoff frequency. This is another bandpass filter with a 12dB/octave slope.

Cutoff Sweep, CENTRE in crossover mode

crossover and formant modes

Try using this demo to explore the relationship between crossover and formant by toggling the slider labelled "mode". Play with the FREQ and SPAN controls as well. It may help to use the sliders labelled "separate" and "shaded" to see the individual frequency responses.

In crossover mode, the frequency range is divided into three regions using two cutoff frequencies. The LOW block passes the lowest region, the CENTRE block passes the region between the two cutoffs, and the HIGH block passes the highest region. The three filters allow different frequency regions to be routed and processed separately, or can be used to give three different signals their own space in a single mix. To achieve this, the LOW block is a lowpass filter, the HIGH block is a highpass filter, and the CENTRE block is made of a lowpass & a highpass filter in series. CENTRE passes the band of frequencies between the HIGH cutoff and the LOW cutoff while rejecting the frequencies outside of the two cutoffs.

In formant mode, THREE SISTERS passes three narrow bands of the spectrum, one for each filter, operating as bandpass filters. This mode can be used to emphasize specific regions of the spectrum for a single sound source, or process three sounds into their own frequency band.

Steeper rolloffs can be achieved by patching the filter blocks in series. For example, make a 24dB/octave crossover filter by patching a signal to HIGH(IN), patching HIGH(OUT) to LOW(IN), and taking the output from LOW(OUT) while in crossover mode, with SPAN in the CCW direction.

crossover and formant mode bode plots

FREQ and SPAN: Cutoff Control

Cutoff frequencies for the three filter blocks are determined by a combination of the FREQ and SPAN controls. This creates a a macroscopic control applied to all three filter blocks simultaneously.

Adjusting FREQ will push the cutoff frequencies of all three filter blocks in the same direction.

Adjusting SPAN will push and pull the LOW and HIGH cutoffs in opposite directions around a centre-point determined by FREQ.

CENTRE responds to SPAN differently depending on the mode selection. CENTRE's pass band is widened and narrowed by SPAN in crossover mode. The passband's centre-point is determined FREQ. CENTRE's bandpass filter is unaffected by SPAN in FORMANT mode; the bandpass' cutoff is determined solely by FREQ.

The FREQ and SPAN CV jacks are added to the corresponding knobs.

Try using this demo to explore the relationship between crossover, formant, FREQ and SPAN. It may help to use the sliders labelled "separate" and "shaded" to see the individual frequency responses.

The FREQ CV input is a volt-per-octave input (indicated on the panel by "v/8"). A 1V increase at this input will result in a doubling of all cutoff frequencies. The LOW filter block is calibrated to accurately track volt-per-octave inputs over ~5 octaves.

The FM (frequency modulation) CV jack sends the signal through the grey attenuverter knob before adding the signal to FREQ. Like all CV inputs on THREE SISTERS, FM accepts both control-rate and audio-rate modulation.

Cutoff Calculator

LOW Cutoff

The cutoff frequency of the LOW block is controlled by:

As FREQ increases, the cutoff frequency of the LOW block increases. As SPAN increases, the cutoff of the LOW block decreases.

HIGH Cutoff

The cutoff frequency of the HIGH block is controlled by:

As FREQ increases, the cutoff frequency of the HIGH block increases. As SPAN increases, the cutoff of the HIGH block also increases.

CENTRE Cutoff

In crossover mode, frequencies between the LOW cutoff and the HIGH cutoff are passed by the CENTRE block, while frequencies outside of this range are rejected. When the "upper" cutoff passes below the "lower" cutoff (ie. when SPAN is CCW of 10:00), the signal is increasingly attenuated. This allows SPAN to 'close' the CENTRE passband like a VCA.

In formant mode, the cutoff of the CENTRE block bandpass filter is simply:

SPAN Sweep, self-oscillation in formant mode

SPAN Sweep, noise gate in crossover mode

These spectrograms illustrate sweeping SPAN from CCW to CW in formant mode (top) and crossover mode (bottom). The top image shows the cutoff frequencies of the three filter blocks via self-oscillating sinewaves (QUALITY at maximum) in formant mode. The bottom image shows the width of the CENTRE passband increasing in crossover mode as the CENTRE block processes white noise.

QUALITY: Resonance and Self-Oscillation

QUALITY Clockwise

The QUALITY knob sets the resonance of the filter blocks. Resonance, or Q (Quality Factor), is the extent to which filters amplify signals at the cutoff frequency beyond unity. This has the effect of emphasizing the harmonic content at and around the cutoff frequency.

  • With QUALITY at noon, resonance is at its minimum.

  • Turning QUALITY clockwise increases resonance.

  • When QUALITY reaches approximately 3 o'clock, the filter blocks will go into self-oscillation and produce sine waves at the cutoff frequencies, without any input.

The value of QUALITY CV is added to the knob. When the knob is at noon, sweeping the QUALITY CV input from -5V to +5V is equivalent to sweeping the knob from fully CCW to fully CW.

QUALITY: Dry/Wet Mixing and Notch Filters

QUALITY CCW

The QUALITY knob can also be used to create notch-rejection filter responses and blend between the filtered and unfiltered input. To achieve this, the outputs of each filter block are each sent to a mixing block. The first SVF in each filter block also sends its unused complementary output to the corresponding mixing block through a VCA controlled by the CCW portion of QUALITY:

  • The LOW filter block output is mixed with the highpass output of the first SVF.
  • The HIGH filter block output is mixed with the lowpass output of the first SVF.
  • The CENTRE filter block output is mixed with the lowpass output of the first SVF, and the highpass output of the second SVF.

Turning QUALITY CCW from noon begins opening the !Q VCAs, increasing the amount of complementary signal mixed in with each filter block's output.

Due to the nature of the SVF, the main output & complementary output are always 180 degrees out of phase, or simply 'inverted' relative to each other. In the pass bands this has no impact on the sonic quality. Around the cutoff frequency however, the two signals will cancel each other out, resulting in a 'notch' filter response.

The CCW half of the QUALITY knob acts as a "dry/wet" filter control. This control blends between the filtered and unfiltered sound by re-introducing frequencies rejected by the primary filter block. As QUALITY approaches the CCW limit, the behaviour is similar to a low-shelf filter, but with some cancellation of frequencies around the cutoff.

  • With QUALITY at noon (or further clockwise), none of the rejected frequencies are mixed back in.
  • Turning QUALITY counterclockwise increases the amplitude of the inverted, rejected frequencies, to be mixed back in.

QUALITY Sweep

This spectrogram illustrates sweeping QUALITY from fully CCW to fully CW as CENTRE processes white noise. Fully CCW, the entire spectrum of white noise is passed. As QUALITY approaches noon, the complementary frequencies are attenuated. At noon, only the CENTRE passband is passed. As QUALITY approaches 3:00, the cutoff frequency is emphasized, and eventually the filter goes into self-oscillation.

Passive Output Mixing

The ALL(OUT) mix can distort when three very loud input signals are used or when all three filters are in self-oscillation. To avoid this, you can passively mix these signals by directly connecting the three output jacks using stackable cables, or a passive mult. Many manufacturers discourage this output-to-output connection, but we've extensively tested it with Mannequins modules with no issues, and officially support the practice. This technique is also useful If you only wish to combine two of the three outputs (e.g. connecting LOW(OUT) and HIGH(OUT) with a stackable) while using the third output independently. This will reduce the level of the signal as more outputs are connected together.

NB: The distortion is caused by a limitation of Eurorack's power supply system. Eurorack only supports 24V peak-to-peak signals, but 3 sine-waves at 10V peak-to-peak will surpass this limit when the peaks align, causing clipping to occur.

Spectral Mixing and Gating

In crossover mode, THREE SISTERS can be used as a unique mixing tool: rather than controlling gain for each of the inputs, THREE SISTERS carves out spectral space for each signal. FREQ and SPAN become macro-controls for determining the space allotted to each input.

Mixing

Patching three distinct sound sources to LOW(IN), CENTRE(IN) and HIGH(IN) results in each input having its own spectral space in the mixed output at ALL(OUT). The low end will come from the signal patched to LOW(IN). The mids come from CENTRE(IN), and the high end comes from the signal patched to HIGH(IN). Start with QUALITY at noon. Patch your three signals to the corresponding inputs and tap your output from ALL(OUT).

Increasing FREQ will give more space to the LOW input signal and take space away from the HIGH signal: more and more of the LOW signal is passed and more and more of the HIGH signal gets filtered out. CENTRE will shift the range of its passband up while leaving the width of its passband unaffected. With CENTRE(IN) unpatched and SPAN around 10 o'clock to noon, FREQ controls spectral crossfading between the LOW and HIGH signals only.

Increasing SPAN will take space away from both LOW and HIGH as their cutoff frequencies decrease and increase respectively, filtering out more and more of both of their input signals. Simultaneously, CENTRE will increase the width of its passband, allowing more and more of the CENTRE(IN) signal to pass through to the output. The CENTRE signal starts to dominate while the LOW and HIGH filters recede. Try this with the same signal patched to both LOW(IN) and HIGH(IN) and a different signal patched to CENTRE(IN).

Decreasing QUALITY from noon toward its minimum will re-introduce all signals at equal levels into your mix. Conversely, keeping QUALITY at its minimum will pass all signals by default (with some subtle notch-filtering, controllable by SPAN and FREQ), and then increasing it toward noon will result in the spectrally-sculpted mix.

Patching a signal to ALL(IN) will result in a signal that is always present in the mix, but with subtle spectral differences to the original due to the various notching created by the signal passing through the distinct filter blocks in parallel.

Gating

With LOW(IN) and HIGH(IN) unpatched, patching a signal to CENTRE(IN) allows for a unique form of gating different from LPGs or VCAs controlled by SPAN in crossover mode. With SPAN at minimum, the passband of the crossover filter is minimized, but as SPAN increases, the passband widens, allowing for more of the CENTRE(IN) signal to pass through to CENTRE(OUT). Try controlling SPAN using bipolar modulation with the knob set to noon, or with unipolar positive modulation when the knob is fully CCW. CENTRE can be used similarly to a VCA or LPG with its own spectral coloring.

The following spectrogram illustrates CENTRE processing white noise in crossover mode. The width of CENTRE's crossover passband is controlled by SPAN. The SPAN knob is set fully CCW to completely close the CENTRE band. Unipolar CV is used to ramp SPAN upward, opening up the width of the crossover block and allowing the noise to pass through.

CENTRE gate

Instead of using CV to modulate SPAN, patch ALL(OUT) to an envelope follower and attenuvert/offset the envelope before patching it to SPAN to create a spectral compressor. COLD MAC's FOLLOW circuit can be used for this purpose. You can also try a variant of this by multing a copy of the input signal to the envelope follower instead of the output!

Spectrum & Dynamics

When paired with envelope followers and VCAs, crossover mode can be used as the core of a multi-band compressor by splitting a signal into different frequency bands. Each frequency band can be patched through a compressor; without a compressor, each band can be multed to an envelope follower and a VCA; each envelope follower output can be used to open or close the VCAs. Mixing the VCA outputs will recover the multi-band compressed signal.

Paired with just a single COLD MAC, THREE SISTERS can act as a side-chain EQ while COLD MAC acts as a compressor.

  • Patch your signal to compress to ALL(IN). Set QUALITY to noon.
  • FREQ and SPAN control the location and width of your bands: lows, mids, and highs.
  • Choose a band for your compressor to respond to, and patch the corresponding output to COLD MAC's SLOPE input.
  • Patch your signal to compress to COLD MAC's LEFT input; if you want to use the same input signal as THREE SISTERS, you can take it from ALL(OUT). Patch a dummy cable to RIGHT.
  • Patch COLD MAC's FOLLOW output to SURVEY (or patch it to OR1 and use a DC offset to OR2 for threshold control). Make sure FADE is unpatched.
  • Use the LEFT(OUT) jack for compression and the RIGHT(OUT) jack for expansion. SURVEY controls makeup gain.
  • Switch THREE SISTERS to formant mode to narrow the side-chain EQ in on a specific frequency.

Audio-visualization

With an analog video synthesizer, THREE SISTERS can be used for audio-visualization of your patches. The technique is similar to what is outlined in the previous section on multiband compression. Unlike the multiband compressor, the output of THREE SISTERS is not being used in the audio chain, so using formant mode bandpass filters is a viable choice for narrowing the bands in on certain frequencies which you want your video synthesizer to respond to. Increasing QUALITY past noon will help in narrowing the bands in on particular frequencies. For instance if you want your kick and hihat to each trigger different events or control different parameters in your video synthesizer, you would patch your kick to LOW(IN) and your hihat to HIGH(IN), while using FREQ & SPAN in formant mode to dial in their frequencies.

  • Patch your audio signal to visualize to ALL(IN).
  • FREQ and SPAN will control the location and spacing of the bands to respond to.
  • Patch the output of each filter block to its own envelope follower.
  • Patch the envelope outputs to whatever video synthesis parameters you wish to control! You may wish to patch the envelopes through further processing utilities for additional control.

Formant and Vowel Synthesis

A sound-processing object's formants can be thought of as bands of resonant frequencies, or parts of the frequency spectrum that are always emphasized. For instance, the human voice has formants determined by the diameter and length of cavities in the vocal tract, a room has formants as revealed beautifully in Alvin Lucier's "I Am Sitting in a Room", and acoustic instruments like bassoons and saxophones have their own formants as well! In the context of modular synthesis and electronic music, formants can be used to provide a spectral context to a sound source and to define regions of the frequency range where that sound "lives" and pops out. This can help prevent overlap between voices, and harmonic conflicts as they fight for the same bands of the spectrum.

THREE SISTERS can be used to impose a formant structure onto a sound source by patching the sound into ALL(IN), taking the output from ALL(OUT), and setting the module to formant mode. THREE SISTERS acts as three bandpass filters processing the same sound source in parallel; the processed bands are then mixed together, returning the input signal in its new spectral context. FREQ and SPAN control the location and spacing of the formants, allowing you to dial in the spectral regions to be emphasized. Adjusting QUALITY will control the size of the formants, narrowing them as QUALITY turns clockwise away from noon. Turning QUALITY counter-clockwise from noon will bring up the frequency content outside of the formants, to create a blended response.

Using an oscillator as a sound source allows primitive vowel synthesis; try gating the oscillator before the filter, or after the filter. FREQ and SPAN will allow you to dial in different vowels, since each vowel can be modeled as an oscillator with a specific set of formants. Read more about vowel synthesis here!

Two Operator FM Synthesis

Self-patching THREE SISTERS allows for 2-operator FM synthesis. When in formant mode with QUALITY at max and no inputs, each output produces a sine wave at the associated filter block's cutoff frequency. Since the cutoff frequency of the CENTRE bandpass filter is unaffected by SPAN in formant mode, patching CENTRE(OUT) to SPAN will use the CENTRE sine wave as the modulating operator. Both LOW and HIGH act as carrier operators in parallel. Listen to LOW(OUT) or HIGH(OUT) for the resulting FM tones. Try patching them in stereo!

Adjusting SPAN will control the FM ratio (i.e. frequency ratio of carrier and operator).

To control the FM index, or amount of the FM applied by the modulator to the carriers, patch CENTRE(OUT) through a VCA before patching it to SPAN.

Since SPAN uses exponential frequency modulation, tones will not be entirely "musical" at all times. You can however sequence the sounds with the V/8 jack and they should remain largely constant over the pitch range.

FM Ratio Sweep

FM Index Sweep

Filter Pinging

In formant mode THREE SISTERS can be used to generate percussive sounds using only triggers as inputs. With QUALITY just below the point of self-oscillation (2:00 to 3:00), send a trigger, gate, or fast envelope into an audio input to "ping" the filter. The trigger excites the filter, causing it to ring at the cutoff frequency before fading out. Playing with the pulse-width and shape of these transients will affect the attack and decay time of the tones. Modulate FREQ and SPAN to control tuning of the different 'drums.' You can also try crossover mode, where CENTRE will have a 2-note tone.

Calibration

The steps below will guide you through the calibration process for THREE SISTERS (or any other analog oscillator).

YOU WILL NEED:

  • A tool to measure the frequency of the oscillator (a tuner or oscilloscope)
  • An accurate voltage reference (if possible, use the module that will drive the FREQ input of your oscillator most often)
  • A small flathead screwdriver.

OVERVIEW

The goal is to turn a trimpot accessed through the back of the module such that the frequency of the oscillator when 2V is sent to the v/octave input is exactly four times the frequency when 0V is sent in to the oscillators v/octave input. In other words, to make sure that the oscillator is exactly two octaves above the 0V frequency when 2V is sent in. It does not matter what you choose to tune your oscillator to for the 0V frequency, as long as you make sure to set the 2V frequency to be four times the 0V one.

PROCEDURE

  1. Turn your system on and wait at least 10 minutes for the module to warm up.
  2. Send the output of your oscillator to the input of your tuning device (turn the QUALITY of Three Sisters to max and use the LOW output).
  3. Select a base frequency which will correspond to 0V. The choice is arbitrary. If you choose 100Hz for 0V, then the goal is to get 2V into the oscillator generating a 400Hz oscillation. If you prefer to use a chromatic scale, then choosing C2 for 0V would mean that your goal is to get 2V to generate C4.
  4. Send 0V from your voltage source into the v/octave input of your oscillator (FREQ input for THREE SISTERS). Don't just remove the cable for 0V, actually send 0v from your source to the oscillator!
  5. With 0V going into your oscillator, now use the frequency control knobs to tune it to your base frequency; in this case, tune it to 100Hz.
  6. Now send 2V in to your oscillator.
  7. Check the frequency of the oscillation. If it is precisely 4 times your base frequency (in this case, 400Hz), then you are done. If not, proceed to step 8.
  8. If it is flat (e.g. below 400 Hz), turn the trimpot on the rear of the module a few degrees CCW. If it is sharp, turn the trimpot a few degrees CW (these directions are for THREE SISTERS; the polarity may be reversed for other oscillators). NB: You are not trying to tune it to 400Hz! You are instead changing the scaling of the input voltage range, will need to repeat the process!
  9. Repeat Steps 4-9.

Keep in mind you'll likely need to repeat steps 4-9, ten or more times to have the module well tuned.

Warranty

No matter if you just bought your first module, or found a grimey old relic, we're committed to keeping it running in top form.

Formally, Whimsical Raps warrants each product to be free of defects in materials or construction for a period of one year from the date of original purchase (proof of purchase required). Malfunction caused by abuse of the product, or any other cause that we determine to be the user's fault, will not be covered by this warranty.

Formalities aside, if you've got an issue we absolutely want to help sort it out. Send us an email and let us know how we can help. Our service fees are only our direct costs, and we typically ask you to pay shipping one-way. Here's to keeping synths out of landfill!

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