I am pleased to offer you a set of user oscillators for the Logue platform which I have developed and thoroughly tested over the past few years. These oscillator models run on the Minilogue XD and Prologue, while NTS with its different hardware architecture is currently not supported.

Oscillators are sold in bundles and also come with presets for the Minilogue XD for demonstration purposes. For a given user-specific oscillator slot-configuration, the preset files can be adjusted in order to point to the correct slots in the synth. These adjustments are done with a small tool app which is also provided.

The following list can be used to navigate to the reference section for each oscillator type. It is also recommended to read the tech notes, which provide additional information regarding some specifications and usability of the products.

SIGMA oscillator collection

SIGMA is the greek letter which is used in math to designate a summation. This oscillator collection is inspired by certain vintage analog synths in which the basic waveforms sawtooth, pulse (or square) and often triangle are used as additive ingredients to form a combined oscillator signal prior to the filter. These waveforms can be regarded as outputs of waveshapers which are phase-locked. To expand the sound palette of SIGMA, the static phase offsets between the basic waveforms can be continuously changed, shifting these waveforms in time. This feature allows for altering the mixed waveform in interesting ways. It also enables the modeling of different phase configurations found in vintage synths.

Finally, a sub oscillator can also be added to the waveform, but unlike in typical analog designs, the sub oscillator constitutes the actual phase reference from which everything else is derived.

SIGMA comes in three different variants named SIGMA, SIGMA2 and SIGMA3.

In the following documentation, the term “waveform” is used to actually designate a periodic signal. This terminology is not 100% correct but more convenient.

The first version, named SIGMA, mixes five waveforms in a linear fashion to generate the output signal. It contains an attack/decay-envelope (AD-env) for a one-shot modulation of the pulse width (PW). The pulse width can also be modulated using the shape LFO to obtain classic PWM.

The output signal is made up of two layers and the sub oscillator. Each layer consists of a mixture of sawtooth and pulse. Hence, five different waveforms are used in total, denoted as saw1, pulse1, saw2, pulse2 and sub. A simplified signal flow without the handling of phases is shown below.

When SHIFT+SHAPE is set to zero, all waves are phase-locked. In this case, layer1 is identical to layer2, both layers appear as one, and the output signal constitutes just one oscillator as described in the introduction. The phase of the oscillator is reset with every new note-one command (key strike).

When SHIFT+SHAPE is increased up to 50%, layer1 and layer2 are progressively detuned in a symmetrical fashion with respect to twice the sub frequency. Strictly speaking, this constellation is made up of three oscillators in parallel, layer1, layer2 and the sub. The phases are reset with every key, and the sound shows the typical phasing of a sampler or ROMpler playing back two detuned copies of the same sample. The maximum detuning is reached for SHIFT+SHAPE at 50%.

For SHIFT+SHAPE above 50% we enter free-run mode for which the three oscillator phases are not reset anymore, typical for analog synths. From this point, the detuning is decreased and finally reaches 0 for SHIFT+SHAPE set to 100%. At this position, the layers and the sub are phase-locked again, but the layers will experience random phase offsets which vary from voice to voice.

SIGMA: controls

In the following, each input is described. The menu parameters “mix”, “sub”, “modify” and SHIFT+SHAPE are overloaded in the sense that they serve two functions at once, providing a linear value as well as a switch. With these build-in switches, you can choose between four different sub oscillator waveforms (triangle, clipped triangle, square and asymmetric pulse), between left-edge and centered PWM as well as between phase-reset mode and free-run mode.

Note: Before starting to program a patch from scratch,it is recommended to quickly reset the bipolar parameters to 0 as described in the tech notes.

SHAPE

Sets the unmodulated, static pulse width of the pulse waveform between 10% (hard left) and 90% (hard right). Both layers use the same pulse width.

SHIFT+SHAPE

Detunes layer1 and layer2 with respect to the sub as described above. Switches between reset-mode (0-50%) and free-run-mode (50-100%).

SHAPE LFO

The LFO modulates the pulse width.

PAR1: MIX

Range 0%…100% (left-edge PWM):

1. Blends between sawtooth (0%) and pulse (100%) for each layer.

2. Selects left-edge PWM: the positive pulse width changes with respect to its left edge, which is static.

Range -1%-100% (centered PWM):

1. Blends between sawtooth (0%) and pulse (-100%) for each layer.

2. Selects centered PWM: both pulse edges move symmetrically around the static middle-point of the pulse.

PAR2: SUB

Range 0%…100% (sub pulse mode):

Blends between the mix of sawtooth/pulse (0%) and the sub oscillator in pulse mode (100%).

Range -1%-100% (sub triangle mode):

Blends between the mix of sawtooth/pulse (0%) and the sub oscillator in triangle mode (-100%).

Note: to obtain equal amplitudes for sawtooth, pulse and sub, choose mix=+-50% and sub=+-33%.

PAR3: MODIFY

Range 0%…100% (sub standard wave):

1. Changes the phase offsets between sawtooth, pulse and sub.

2. Selects a square wave for the sub in pulse mode, a standard triangle wave for the sub in triangle mode.

Range -1%-100% (sub alternative):

1. Changes the phase offsets between sawtooth, pulse and sub in the same way as for positive values.

2. Selects an asymmetric pulse wave for the sub in pulse mode, a clipped triangle wave for the sub in triangle mode.

Note: the effect of the phase shift is most noticable without detuning.

PAR4: ATTACK

Sets the attack time of the A/D-envelope.

PAR5: DECAY

Sets the decay time of the A/D-envelope.

PAR6: AMOUNT

Sets the envelope amount, which can have positive or negative values.

Note: for attack=0, decay=0 the envelope is deactivated.

SIGMA2 is a straight-forward implementation of the original idea as described in the introduction. Three phase-locked “components”, sawtooth, pulse, triangle, and also a square sub are used to construct the oscillator waveform. The weighted sum of these components and the sub is fed into a saturator to form the final output signal in the limited range of +-1. For each component you can select the octave, choose one out of two waveforms and set an individual phase offset. The SHAPE LFO can be used to modulate the pulse width. A simplified signal flow without the handling of phases is shown below.

Note: No dedicated envelope is included, but for the XD, the SHAPE LFO can mimic an envelope with attack=0. This can be done by setting the LFO to one-shot-mode, LFO key-sync to ON, LFO voice-sync to OFF and the LFO waveform to SAW.

SIGMA2: controls

All six menu parameters are bipolar and determine a value and a switch state. The sign is equal to the switch state, while the absolute number determines the value, that is -x% is the same value as +x%, namely x.

The positive range is abbreviated as (pos), the negative as (neg).

Note: Before starting to program a patch from scratch,it is recommended to quickly reset the bipolar parameters to 0 as described in the tech notes.

SHAPE

Sets the unmodulated, static pulse width of the pulse waveform between 10% (hard left) and 90% (hard right).

SHIFT+SHAPE

Sets the amplitude of the square sub oscillator between 0 and full-scale.

SHAPE LFO

The LFO modulates the pulse width.

PAR1: SAW

Sets the amplitude of the sawtooth between 0 and full-scale (0…+-100%).

Selects the pitch of the sawtooth: (pos)=main, (neg)=one octave down (sub).

PAR2: PULSE

Sets the amplitude of the pulse between 0 and full-scale (0…+-100%).

Selects the pitch of the pulse: (pos)=main, (neg)=one octave down (sub).

PAR3: TRIANGLE

Sets the amplitude of the triangle between 0 and full-scale (0…+-100%).

Selects the pitch of the triangle: (pos)=main, (neg)=one octave down (sub).

PAR4: PhaseSAW

Controls the phase offset of the sawtooth waveform.

Switches between a sawtooth (pos) and a ramp (neg) by flipping the polarity.

PAR5: PhasePLS

Controls the phase offset of the pulse waveform.

Switches between left-edge PWM (pos) and centered PWM (neg).

For left-edge PWM, the positive pulse width changes with respect to its left edge, which is static. For centered PWM, both pulse edges move symmetrically around the static middle-point of the pulse.

PAR6: PhaseTRI

Controls the phase offset of the triangle waveform.

Switches between a standard triangle (pos) and a clipped triangle (neg).

SIGMA3 omits the triangle wave to have more controls for other functions. The output signal consists of the phase-locked components sawtooth and pulse and a square sub, using a similar topology as for SIGMA, but only for one layer. This version introduces shape mod for the sawtooth waveform in two different variations, borrowed from the TONE oscillator. In addition, each component frequency can be more generally set to some overtone of the sub, not just one octave above. The combined waveform is perceived either as a timbre or more as an interval or chord, depending on the chosen harmonics (overtones) and amplitudes applied via the mix and sub mix setting. To avoid such chords, components set to high overtones should be kept rather small in amplitude.

Because there is only one shape LFO as a mod source, the LFO range for pulse modulation (PWM) and sawtooth shape modulation can be individually adjusted, including the choice to switch it off. In addition, the shape mod limit can also be specified between two different ranges. For example for the pulse, you can choose between a pulse width range of 10%-90% or 20%-80%. The idea behind this approach is that when you use PWM for example, the time varying pulse width might bounce against the lower or upper limit, and you might hear the pulse wave with the selected minimum or maximum pulse width for a longer period of time, and, therefore, the limits define the characteristics of such a bouncing sound.

A single mode parameter is used for the sawtooth and another for the pulse to encode a variety of settings, as shown in the following tables. With the exception of the values 10, 20, 30, …, the left digit marks the overtone index (including 0 for the fundamental) and the right digit the “wavetype” for each waveform. The settings for each wavetype are shown in the first and third table. Here, x represents an arbitrary left digit of the mode parameter. The middle table shows the overtone definitions and applies to both waveforms.

Mode parameter encoding

SIGMA3: controls

SHAPE

Sets the unmodulated, static shape of the sawtooth waveform. For the setting hard left, a standard sawtooth is produced.

SHIFT+SHAPE

Blends between the mix of sawtooth/pulse (0%) and the square sub oscillator (100%).

SHAPE LFO

The LFO modulates the shape of the sawtooth and/or the pulse width. This must be enabled by the settings in the sawtooth and/or pulse mode parameters.

PAR1: Mix

Blends between sawtooth (0%) and pulse (100%).

PAR2: PW

Sets the pulse width between minimum (0%) and maximum (100%).

PAR3: ModeSAW

Sets the mode for the sawtooth waveform, which is encoded as shown in the first and second table above.

PAR4: ModePLS

Sets the mode for the pulse waveform, which is encoded as shown in the second and third table above.

PAR5: PhaseSAW

Controls the phase offset of the sawtooth waveform.

PAR6: PhasePLS

Controls the phase offset of the pulse waveform.

Note: tweaking the phase has it’s strongest effect if two waveforms have the same frequency. If one frequency is much higher, the effect might be hardly noticable.

Multi-wave oscillators

A “multi-wave oscillator” shall refer to a stacked layer of detuned sawtooth waves or similar waveforms. This kind of oscillator was introduced in the 90ies and and had a great impact on various music styles due to its dense and powerful sound.

The main oscillator model, called SEVEN, generates one center wave (or main wave) of selectable timbre and six detuned sawtooth waves around it, also denoted as sidewaves. As in the original, the mixture between the center wave and the sidewaves can be adjusted. The oscillator also supports two different detuning patterns, a classic and an alternative one. A detuning pattern defines how much each sidewave is detuned for a rising common detuning factor. Overall, the classic pattern has a wider detuning range. For the main wave you can choose between four different timbres. In addition, four different octave settings exist for the whole constellation.

Also, four different output modes determine how the summed waveform layer is processed before reaching the output. These modes represent different ways to increase the loudness of the signal. Mode 1 uses a clipper, mode 2 a saturator, and mode 3 and 4 make use of a triangle wave – or “carrier” – in different octaves, which is phase-modulated by the seven-tone waveform mix. In general, the achievable maximum loudness increases from mode 1 to mode 2, and from 2 to 3 or 4.

The six detuned sidewaves can be highpassed to reduce loudness fluctuations of the fundamental frequency due to phase cancellations. The center wave is excluded from this thinning process and delivers the base tone of the sound as the highpass is applied more strongly to the sidewaves.

SEVEN: controls

SHAPE

Sets the amount of detuning for the sawtooth sidewaves. The range depends on the chosen detuning pattern.

Note: if you increase the detuning and decrease it back to zero at some point you can get quite appealing sounds for all four output modes. In this case, each voice is static but will sound different.

SHIFT+SHAPE

The function depends on the chosen output mode. For output mode 1 and 2, the knob adjusts the “drive” of the signal into the clipper or saturator. For output mode 3 and 4, it sets the phase modulation amount of the triangle wave. If set to 0 (hard left), only the triangle tone remains, without any modulation.

SHAPE LFO

The LFO modulates the mix between the main wave and detuned sidewaves.

PAR1: Mix [1-11]

Blends between the main wave and the sidewaves. For mix=1, only the main wave remains. For mix=11, all seven waves are equal in amplitude, including the center wave.

PAR2: Timbre [1-8]

Selects the timbre of the main wave and the detuning pattern for the sawtooth sidewaves according to the following timbre-table. For the main timbre, settings 1-4 are identical to 5-8.

PAR3: Octave [1-4]

Sets the pitch for the main wave and the sidewaves, as shown in the octave-table above. “sub octave” means that a tone is shifted down by one octave. For octave mode 4, the sub waves, consisting of the center wave and two sidewaves, are inverted and played back as “ramps”.

PAR4: OutpMode [1-4]

Selects the output mode of the oscillator. The choices are

1: clipper
2: saturator
3: carrier1
4: carrier2

For clipper and saturator, SHIFT+SHAPE sets the drive for the oscillator signal.

For carrier1 and carrier2, SHIFT+SHAPE defines the amount of phase modulation applied on the carrier, with the multi-wave acting as the modulator. Carrier1 is a triangle wave generated in the main octave while carrier2 is a triangle generated in the sub octave.

PAR5: Highpass [1-11]

Sets the cutoff of the highpass filter applied to the sidewaves. For higher values, more lows are cut out. For a value of 1, the highpass filter is completely bypassed. For other values 2-11, the filter is activated and the output also attenuated by 6 dB to account for the additional headroom required.

PAR6: Slop [1-24]

Sets the amount of random pitch variation between voices. As you reach the maximum, the tuning appears to be rather wonky.

FIVE is the “little brother” of SEVEN, as it creates only five waves. Instead of generating sawtooth waves directly, it utilizes five sine waves with phase modulation feedback — a technique known from FM synthesis. When the feedback is increased, the “warm”-sounding sine waves gradually transform into sawtooth waves, increasing the brightness of the sound. This allows oscillator brightness to be adjusted before reaching the analog filter, either manually, via the shape LFO, or using a dedicated envelope. In some cases, bypassing the analog filter for this digital oscillator may be preferable, freeing the filter for use with the analog oscillators. The generated sound is very smooth, but cannot be “crunched” for some loudness increase. The sound level can still be increased in the usual way by turning up the gain of the entire patch by a maximum of 6 dB, using the menu.

The diagram below shows the signal flow. The combined SHAPE value controls the gain and cutoff of lowpass filters in the feedback paths. It should be noted that the combined SHAPE value is not bounded to zero and can experience positive or negative values. The sound becomes brighter as the SHAPE value deviates more from zero, in either direction. This might be confusing at first. Unlike the scheme used in SEVEN, the generated waves have a fixed amplitude distribution without a mix-option.

FIVE: controls

SHAPE

Controls the brightness of the sound. The maximum is reached at the right position.

SHIFT+SHAPE

Sets the cutoff of the highpass applied to the (detuned) sidewaves. As the knob is turned right, the sidewaves are gradually thinned out.

SHAPE LFO

The LFO also modulates the brightness, just like the SHAPE knob and the envelope.

PAR1: detune [0-100%]

Sets the degree of detuning for the sidewaves. Each wave has its own individual detuning factor.

PAR2: octave [1-2]

Sets the pitch of the center wave in terms of octave position. For octave=1, this wave has the standard pitch. For octave=2, the pitch is shifted one octave down. Sidewaves always have the standard pitch assigned.

PAR3: envmode [1-4]

Defines the mode of the envelope according to the following table.

Note: The behavior for settings 1 and 2 is the most commonly encountered, but the other is also interesting and useful.

PAR4: attack [0-100%]

Sets the attack time of the A/D-envelope.

PAR5: decay [0-100%]

Sets the decay time of the A/D-envelope.

PAR6: amount [0-100%]

Sets the envelope amount. The polarity is chosen via the envelope mode.

Preset oscillators

The products in this series are based on the same concept: integrating a larger set of different, relatively fixed oscillator models into a single user oscillator. These modes are easily selectable and work much like presets. Each model, on its own, does not involve too much tweaking. For some products, the different oscillator models are embedded into a common outer framework which can provide additional modulation sources and/or post-processing stages.

The minimalistic TONE oscillator can serve on its own or as a supplemental oscillator for the existing analog VCOs, offering basic waveforms in high audio-quality. But it also includes many alternative waveforms to be explored. Each waveform can be manually modified using two controls, SHAPE and modify.

For this oscillator, each model is called a tone in the menu. A tone can be made to sound warmer or fuller by applying either an internal low-shelf filter or a sub-oscillator. The idea behind the first option (EQ) is that the analog filter, with its resonance, can be opened more before sounding harsh and generally reacts a bit differently to a tamed oscillator.

TONE also includes a flexible modulator (MOD) which can either work as an envelope (ENV) or LFO. The LFO shall be called xLFO to distinguish it from the standard SHAPE LFO. This xLFO can be used to perform audio-rate modulation, can operate statically or with a fade-in or fade-out, and can also optionally be locked to the oscillator’s frequency or a fraction of it. The LFO waveform is either a triangle or a sine, depending on the chosen model (tone).

When the xLFO is locked and has a frequency equal either to the main pitch or is transposed by one or two octaves down, the resulting waveform will remain in tune, although optionally transposed. This approach greatly extends the synthesis possibilities as the modulation can be used to change the timbre. Using fade-in or fade-out for the xLFO leads to evolving sounds and expands the possibilities further.

TONE: operation and controls

This section provides a reference for the operation and the controls of TONE. Note that when you change the envelope mode in the menu, this change applies not immediately but for the next active voice. The only bipolar parameter used is Bass. You may want to reset it immediately to 0 when beginning to programm a new patch, starting with an uncolored sound. This reset procedure is described in the tech notes.

SHAPE

Acts as the first modifier for the currently selected tone (waveform).

SHIFT+SHAPE

The modulation mode is selected with ModMode. When the modulator works in envelope mode, SHIFT+SHAPE sets the release time of the envelope, shown in the first diagram below.

When the modulator works in LFO mode, SHIFT+SHAPE sets the xLFO frequency (2. and 3. diagram). Using the ModMode-parameter, two different frequency ranges for SHIFT+SHAPE can be selected. The first range includes a slow zone ranging from 0 to 30 Hz and a locked zone where the xLFO is locked to the pitch or fraction of the pitch of the oscillator. For example for “1/4”, the xLFO swings two octaves below the oscillator frequency. Range 2 covers frequencies from 0-200 Hz.

Use of SHIFT+SHAPE-knob

SHAPE LFO

For most (but not all) models, the SHAPE LFO controls the same parameter as the SHAPE knob and the modulation source (ENV or xLFO). Details are provided in the model description.

PAR1: Tone [1…22]

Selects the oscillator model. A description of the models is given here.

PAR2: Bass [-100%…+100%]

Parameter to increase the warmth or weight of the sound, or just to add a “solid” fundamental.

Range -100% to 0%: The lower the value, the more the spectrum is boosted in the lows while keeping the overall level nearly constant. The maximum effect is achieved at -100%.

Range 0% to 100%: The main oscillator signal is accompanied by a sub-oscillator. This parameter controls the mix between the main and sub tone. The type of sub-oscillator depends on the model. At 100%, only the sub tone remains.

PAR3: Modify [0…100%]

Acts as the second modifier for the currently selected tone (waveform).

PAR4: ModMode [1…24]

This parameter determines the type and behavior of the modulator (MOD). Modes 1-8 select the envelope (ENV), modes 9-16 the xLFO with range 1 and modes 17-24 the xLFO with range 2. The envelope release range and xLFO ranges are defined here.

For the envelope, you can choose between positive and negative polarity, exponential or linear shape, and either an envelope where an active attack phase switches to the release phase when the key is released, or a full-cycle envelope that maintains the attack phase until the end, regardless of note-off. This results in 2x2x2=8 combinations shown below.

For the xLFO, you can choose between fade-in and fade-out and four different start offsets, again resulting in 2×4=8 combinations for each range.

The xLFO, when in free-run mode, always resets its phase upon striking a new key (note-on). In this case, the phase offset simply defines the starting position. In locked mode, the chosen phase offset of the xLFO is permanently maintainted in relation to the phase of the main wave.

PAR5: Amount [0…100%]

Adjusts the intensity of the modulator (MOD as ENV or xLFO).

PAR6: Attack [0…100%]

In envelope mode, this parameter adjusts the attack time, with slower attacks at higher values.

In LFO mode with fade-in, it defines the fade time, with longer transitions at higher values.

In LFO mode with fade-out, it defines the fade time, but with shorter transitions at higher values. In this mode, when attack is set to 0% the fade-out has no effect.

TONE: OSC models

This section describes the implemented oscillator models, or tones, which represent different types of waveforms. These waveforms are altered in various ways using the first modifier, SHAPE, and the second modifier, MODIFY (PAR3).

Default configuration

It is convenient to introduce a default configuration, allowing the models to be described in a much more compact way. The following points, which are used most often, apply to a model unless otherwise specified:

By default, …

• the modulator and the SHAPE LFO affect the same waveform property which is determined by the static SHAPE knob.
• a square wave is used as a sub, one octave below the main waveform.
• MODIFY affects the phase shift between the main wave and the sub wave.
• the triangle waveform is used for the xLFO.

Tone 1: sawtooth with flipped section (+ square sub)

This model uses a sawtooth wave which is flipped within a certain section of the waveform cycle. SHAPE defines the width of this section, starting at zero. The model is somewhat similar to the analog VCOs operating in sawtooth mode but works in the same octave and leads to different results.

Tone 2: sawtooth with flipped section + square wave

Same as for tone 1, but uses a square wave for bass in the same octave, not one octave below.

Tone 3: sawtooth hard-synced

This model uses a pitched-up sawtooth oscillator that is synced to the standard pitch by resetting its phase with each waveform period. This allows for the reproduction of typical hard sync sounds. SHAPE sets the amount of up-shifting of the oscillator pitch.

Tone 4: sawtooth squeezed

A sawtooth wave is squeezed into a smaller fraction of the waveform cycle as SHAPE increases, while the remaining portion is nulled. The effect is somewhat similar to a high-pass filter but produces a distinct sound.

Tone 5: phase-modulated sawtooth, triangle/square sub

In this simple model, a sawtooth wave is phase-modulated by SHAPE. MODIFY is used to define the sub waveform by fading between a triangle and a square wave, starting with the triangle. The xLFO, if activated, uses a sine wave instead of a triangle wave.

An audible, useful effect is achieved in different ways. One way is to mix the main wave with the sub. The SHAPE knob, SHAPE LFO or the modulator can be used to slowly change the phase shift and achieve a “fatter sound” through the fluctuating spectrum.

Another way is to apply the xLFO at audio-rate frequencies. If the xLFO is locked, the waveform basically remains in tune while new timbres can be generated, similar to phase-distortion synthesis. SHAPE or the SHAPE-LFO can be used to statically change or slowly vary the timbre since the phase shift between the xLFO and the main wave is modified.

Note: if the sawtooth is used naked without the sub and without modulation, SHAPE has no lasting effect.

Tone 6: two phase-modulated sawtooths (+ square sub)

In this model, two sawtooth waves are phase-shifted simultaneously using SHAPE. MODIFY determines the individual phase shift intensities for sawtooth 1 and sawtooth 2. The xLFO, if activated, uses a sine wave instead of a triangle wave.

For MODIFY=0%, the sawtooths are equally phase-shifted in opposite directions with rising SHAPE. As MODIFY is increased, the phase shift intensity is reduced for sawtooth 1 and increased for sawtooth 2. For MODIFY=100%, all phase shifting is performed for sawtooth 2 while sawtooth 1 remains static.

In addition, the phase offset for the sub is also changed with rising MODIFY. The impact of MODIFY becomes clear when the waveform is blended with the sub and/or the xLFO performs audio rate modulation.

Tone 7: one static and two phase-modulated sawtooths

Three sawtooth waves are mixed together. Wave 1 is static while wave 2 and 3 are phase-modulated using SHAPE. Wave 2 has a fixed modulation intensity while wave 3 uses a variable modulation intensity adjusted with MODIFY. A square sub can be added in the usual way.

For MODIFY=0%, wave 3 has a maximum positive modulation intensity. As MODIFY is increased, this intensity is decreased, approaching zero for MODIFY=50%. Finally, at MODIFY=100%, wave 3 sees a maximum negative modulation intensity.

Tone 8: triangle wave with feedback and clipped triangle sub

In this simple model, feedback is applied to a triangle to transform it into a sawtooth or a ramp (inverted sawtooth) using SHAPE. When SHAPE is set to hard left, negative feedback is applied, resulting in a ramp. When SHAPE is set to hard right, positive feedback is applied, producing a sawtooth. In the middle position, a pure triangle appears. The in-between values for SHAPE produce intermediate waveforms.

The model uses a triangle wave as a sub. The MODIFY control can be used to boost and clip the triangle, altering its sound towards a square wave and increasing its volume.

Tone 9: two phase-shifted triangle waves with feedback and opposite polarity (A)

This model uses two triangle waves which are generated in the same way as in the previous model. As before, SHAPE defines the feedback factor which here is chosen equal for both waves. The triangles have opposite polarity and a variable phase offset between them which is determined by MODIFY.

It is well known that a pulse wave can be created using two phase-locked sawtooth waves of opposite polarity. The pulse width is determined by the phase offset between these sawtooths. When SHAPE is at its minimum or maximum position, feedback is maximized, and the triangles become sawtooths, producing a sharp pulse wave. With lower feedback—when SHAPE is closer to the middle position—this wave is smoothed out. The pulse width corresponds to the phase offset and is therefore defined by MODIFY. When MODIFY is set to 50%, a square wave is produced.

The SHAPE LFO modulates the feedback while the envelope or xLFO modulates the phase shift between the waves and, consequently, the pulse width. In particular, the xLFO can be used to perform PWM. The model uses no sub. When the bass-parameter is increased to positive values, the signal is tamed by reducing the cutoff frequency of a filter in the feedback paths.

Tone 10: two phase-shifted triangle waves with feedback and opposite polarity (B)

This model works the same way as before, with one key difference: SHAPE / SHAPE LFO and MODIFY / MOD have switched roles. SHAPE / SHAPE LFO now control/modulate the phase offset (pulse width), while MODIFY / MOD (ENV or xLFO) control/modulate the feedback factor. Therefore, in this model, PWM is achieved via the SHAPE LFO.

The following models deal with all kinds of pulse waves and pulse width modulation (PWM). When a pulse wave is declared DC-free for all settings (i.e., its waveform average is always 0), it has a certain advantage. For non-locked, LFO-based audio-rate modulation, there will be no sub-bass rumble in the sound. For example, a standard pulse wave contains DC. When applying PWM at high LFO frequencies, such as 50 Hz or above, you may notice an unwanted low-frequent rumble. The advantage of such a wave is merely that it utilizes the entire headroom and is simple to generate. Even if a high-pass filter is inserted after the signal generation, at sufficiently high audio-rate modulation frequencies, the rumble can still pass through the filter.

Tone 11-13: standard pulse wave

These three modes cover a standard pulse wave with the default configuration (square sub, phase shift, triangle LFO). For tone 11, the pulse range is limited to 20-80% using left-edge PWM, for tone 12 we have a wider pulse range of 10-90%, also using left-edge PWM, while tone 13 uses a pulse range of 10-90% and centered PWM. The tonal differences become clear for audio-rate modulation. In practice, the user can switch between these modes to explore which one fits best. In some cases, the differences might be rather subtle. For left-edge PWM, the left edge of the positive pulse is not moving, only the right edge. For centered PWM, both edges are moving in opposite directions, keeping the center static.

The following oscillators serve as alternatives to, or extensions of, a rectangular pulse wave.

Tone 14: ternary pulse wave, type 1

When SHAPE is exactly equal to 50%, an ideal square wave is produced. For SHAPE values below 50%, the square wave is gradually shrinked to the left, leaving a blank area on the right side of the single cycle waveform. For SHAPE values above 50%, the shrinking happens to the right, leaving a blank area on the left. Since there are three signal values, +1, 0, -1, this pulse wave appears to be ternary. DC-free.

Tone 15: ternary pulse wave, type 2, symmetric modulation

This pulse wave results from two square waves with a phase offset. When SHAPE is exactly 50%, the square waves overlap perfectly, producing an ideal square wave. For SHAPE values smaller or larger, the square waves are shifted in opposite directions, creating two areas where they cancel each other out, resulting in a ternary waveform. DC-free.

Tone 16: ternary pulse wave, type 2, non-symmetric mod.

This tone produces the same type of waveform but applies the phase shift in only one direction. When SHAPE is set to hard left, the phase shift is maximized, whereas at hard right, a square wave is produced with a small residual phase error. In some sense, this corresponds to the VCO’s standard pulse wave with a single-sided pulse width range, but inverted. DC-free.

Tone 17: concatenated pulse waves, equal pulse widths

This tone uses a waveform which is a concatenation of two pulse waves of different length. If T denotes the period of the waveform for a given pitch, T₁ and T₂ are the periods of the first and second pulse wave so that T=T₁+T₂. The ratio T₁:T₂ is controlled by MODIFY. When MODIFY is set to 0%, the first pulse wave is the longest, while at 100%, both waves are almost identical. If the two pulse waves were exactly equal, this would result in a simple octave shift upwards. SHAPE controls the pulse width of both waves. A clipped triangle wave is used as a sub.

Tone 18: concatenated pulse waves, opposite pulse widths

This tone works similarly but has a few key differences. The ratio between the length T₁ of the first pulse wave and T₂ of the second is fixed at T₁:T₂ = 70:30. For this version, SHAPE affects the two pulse widths in opposite directions. The sub is also a pulse wave whose width is controlled by MODIFY. When MODIFY is set to 0%, an ideal square wave is produced. For larger values, the width is reduced.

Tone 19-20: symmetric pulse

This waveform is generated by taking a standard pulse wave, flipping it both horizontally and vertically, and appending the result to the original single-cycle waveform. The resulting concatenated waveform is DC-free. As usual, SHAPE controls the pulse width. For a pulse width of 50%, a square wave is obtained one octave above. A clipped triangle wave is used as a sub, with MODIFY defining the clipping gain. Tone 19 uses a narrower pulse width range and tone 20 a wider range.

Tone 21: DC-free standard pulse, one-sided PWM

This type of pulse wave is generated using two shifted sawtooths according to a well-known scheme. The penalty are 6 dB loudness decrease, but in return, you get a very smooth PWM without lowend rumble. SHAPE controls the pulse width between the smallest value and 50% (one-sided pulse width range). The sub is initially a square wave. As MODIFY is turned up, the sub is progressively affected by SHAPE, the SHAPE LFO and MOD. The sub wave itself is in general not DC-free, only for MODIFY=0%.

Tone 22: DC-free standard pulse, two-sided PWM

This pulse is generated via two sawtooths as before, but uses two-sided PWM. MODIFY fades between left-edge (0%) and centered PWM (100%). The sub is a simple square.

SUB can be regarded as the little brother of TONE. The main purpose is to add a sub oscillator to the analog VCOs. The modulator is a exponential envelope and, as such, much simpler than the one in the TONE oscillator. There are 17 waveforms to choose from, which are called models. Each model is accompanied by an alternative, related model. One special feature is the ability to randomly select a waveform when a new note is played (a new key is striked). For this purpose, the user can set a number of adjacent models which can be randomly selected, starting with the chosen model.

Another key principle of this oscillator is to provide a power-consistent SHAPE transformation of a waveform, which should sound constantly loud, no matter how SHAPE is set. This feature can be called gain compensation. Such balancing is, to some extent, also maintained across the main models. The aforementioned alternative waveform has been introduced to allow for a choice between a gain-compensated and not gain-compensated (=alternative) model. Since gain compensation is achieved with attenuation, the alternative waveform is, on average, louder. For many models though, the alternative model is more meant to be a variation of the theme.

SUB: controls

SHAPE

Acts as the main shape control for the selected waveform.

SHIFT+SHAPE

Acts as an additional shape control or filter for the selected waveform.

SHAPE LFO

Used to modulate SHAPE or another parameter of the current model.

PAR1: MODEL [1…17]

Selects one out of 17 models, or better model pairs. The choice between the main and alternative model is handled with the MODE parameter. The model description is given in a separate section below.

PAR2: OCTAVE [1…3]

Selects the octave of the oscillator, which can be transposed either two octaves below the given pitch (OCTAVE=1), one octave below (OCTAVE=2) or at the same pitch (OCTAVE=3). However, for some models, different definitions apply.

PAR3: MODE [1…98]

The MODE value is treated as two separate digits, which control different things.

The left digit sets the number of adjacent models which can also be randomly picked for the next key, starting from MODEL+1. If the chosen index exceeds 17, the system uses wrap-around logic to start over at index 1, etc. If the left digit is 0 (not shown in the screen), random selection is disabled.

The right digit controls three different settings, as defined in the table below. The most important function is switching between the main and alternative models. As shown in the table, only 8 out of the 10 possible choices (0-9) are distinguished.

PAR4: ATTACK [0…100%]

Sets the attack time of the A/D-envelope.

PAR5: DECAY [0…100%]

Sets the decay time of the A/D-envelope.

PAR6: AMOUNT [-100%…100%]

Sets the envelope amount, which can have positive or negative values.

Note: for attack=0, decay=0 the envelope is deactivated.

SUB: OSC models

This section describes the implemented main and alternative oscillator models, which represent different types of waveforms. These shall be abbreviated as MAIN and ALT. The waveforms are altered in various ways, mainly using SHAPE, but may also depend on SHIFT+SHAPE or OCTAVE. The envelope is abbreviated as ENV.

Octave settings

Some models do not use the standard definition of the OCTAVE parameter with three identical timbres in different octaves. This is done to achieve more variety in the generated sound. If the model deviates from the standard case, often a table is provided to give the user an idea of the arrangement. For many models there are two oscillators involved which are always locked in phase. It is good to remember that for each OCTAVE setting, always the oscillator with the lower octave position – which can have the values -2 (two octaves down), -1 (one octave down) or 0 (main pitch) – defines the pitch of the final sound.

Default configuration

It is convenient to introduce a default configuration, allowing the models to be described in a much more compact way. The following points, which are used most often, apply to a model unless otherwise specified:

By default, …

• SHAPE is the only parameter to shape the original waveform.
• SHIFT+SHAPE is used to apply a mild lowpass on the original waveform.
• SHAPE LFO and the envelope (ENV) both modulate SHAPE.
• the main model (MAIN) is gain-compensated for SHAPE.
• the alternative model (ALT) is just the gain-uncompensated version of the main model.
• the OCTAVE-parameter yields three waveforms of the same timbre, just in different octaves.

Model 1: clipped triangle-wave

The triangle-wave is widely used as an added sub-oscillator, along with the square wave. However, in combination with other main oscillators such as sawtooth or pulse, the triangle wave often sounds too mellow to be clearly recognized or must be relatively loud, requiring a large amount of headroom. Boosting and clipping the triangle wave adds harmonics without using additional headroom. Such a signal can be better heard on small speaker systems and, not to forget, sounds different. The more you crank up SHAPE, the more the triangle turns into a square, but without the prominent high frequencies. For SHAPE=0%, no clipping is applied.

Tip: A positive envelope can add a nice initial punch to an otherwise pure triangle wave.

Model 2: phase-shifted triangle waves

In this model, a similar waveform is obtained using MAIN (= main waveform), just with a different technique. Two identical triangle waves are phase-shifted against each other. The phase shift is controlled by SHAPE. With active modulation, this method sounds different compared to model 1. SHIFT+SHAPE applies a mild lowpass filter (standard behavior).

For ALT (= alternative waveform), the two triangle waves are generated the same way, but can also be phase-modulated by a square wave. The modulation intensity is determined by SHIFT+SHAPE and ENV (=envelope). OCTAVE works differently for carrier (the triangle waves) and modulator, similar to model 5.

Model 3: linear FM, absolute, ratio 1:2

In this model, a carrier is modulated by a sine wave using linear FM (through-zero). For MAIN, the carrier is a triangle wave, for ALT a sine wave. The frequency ratio is 1:2 (carrier:modulator) and SHAPE sets the modulation amount. SHIFT+SHAPE adjusts the (initial) phase shift between the carrier and modulator and has a very subtle effect, unless SHIFT+SHAPE is tweaked during the decay of the sound or using the motion sequencer (XD). The FM modulation is strongest for low frequencies and declines for higher frequencies, because the maximum frequency deviation is absolute, i.e. independent of the carrier frequency.

Model 4: linear FM , absolute, ratio 1:3

This model is similar, but uses a ratio of 1:3. SHIFT+SHAPE adjusts the standard lowpass filter instead of a phase shift.

Model 5: linear FM, relative, variable ratio

This model performs another form of through-zero linear FM where the created timbre is independent of pitch, because the maximum frequency deviation is proportional to the carrier frequency. A sine carrier is modulated by a sine. The octave position (pitch) of the modulated carrier and the ratio depend on OCTAVE as shown below. The resulting pitch is equal to the modulator pitch as it is either lower or equal to the carrier.

Model 6-7: PM using triangle modulator

In model 6, a carrier is phase-modulated by a triangle wave, controlled by SHAPE. For MAIN, the carrier is a triangle, for ALT a sine. SHIFT+SHAPE applies a phase shift between carrier and modulator. The octave settings are given below. The resulting pitch is equal to the carrier pitch as it is either lower or equal to the modulator.

In model 7, for MAIN we have the same arrangement as before, but the SHAPE LFO modulates the phase shift between the carrier and modulator. For ALT, a triangle carrier is also used, but the SHAPE LFO signal is bent in a way that a fullscale LFO triangle wave becomes a perfect sine wave, preventing an audible two-frequency toggling of the affected modulator, which happens for MAIN.

Model 8: dynamic waveform mixing (triangle, square)

MAIN is a mix of a triangle wave and a square wave. SHAPE controls the fading while SHIFT+SHAPE applies a phase shift between these waveforms. When SHIFT+SHAPE is 100%, the waves are out of phase and produce a characteristic sound without the lowend when SHAPE is around 50%.

ALT uses a different arrangement with three square waves in different octaves, W1-W3. W1 plays two octaves lower, W2 one octave lower and W3 at the main pitch. SHAPE and SHIFT+SHAPE are used to mix the squares in any proportion. OCTAVE defines which of the waves are mixed first, using SHAPE. These are the ones for which the fading can be modulated. The role of SHAPE and SHIFT+SHAPE for MAIN and ALT is shown below. As usual, the SHAPE LFO and the ENV modulate SHAPE.

NOTE: For ALT, you won’t hear any effect of SHAPE as long as SHIFT+SHAPE remains at 0%, since the “cross-fader” is fully set to the third waveform, and not to the mix between the other waveforms. For example, for OCTAVE=1 this would be W1.

Model 9: ring-mod between folded triangle wave and sub wave

The generated timbre arises from a ring-modulation of a folded triangle wave and a lower-pitched sub wave . SHAPE adjusts the folding. As expected, the pitch of the ring modulator output is equal to the sub wave pitch.

For MAIN, the sub wave is a square. As usual, SHAPE LFO and ENV modulate SHAPE while SHIFT+SHAPE controls a mild lowpass.

For ALT, the sub wave is a boosted and clipped triangle whose gain factor is controlled by SHIFT+SHAPE. The SHAPE LFO creates an oscillating phase shift between the triangle wave and the sub wave. The OCTAVE settings are given below. Equal octave difference for case 1 and 3 results in the same type of timbre while case 2 sounds different.

Model 10-11: sub wave, AM-modulated by a pulse wave

Model 10 uses a sub wave which is AM-modulated by a main wave. The octave arrangement is the same as for model 9. For MAIN, the sub wave is a triangle, for ALT a sine wave. SHAPE controls the positive width of the pulse wave while SHIFT+SHAPE defines the amount of amplitude modulation (AM). For SHIFT+SHAPE=0%, the AM modulation is highest, resulting in a ring-modulation. For increasing values of SHIFT+SHAPE, the AM modulation is progressively reduced leading to a mellower sound.

Model 11 works similar, but uses a different phase offset between the sub wave and the pulse wave.

Model 12: two square-waves, phase-shifted relative to each other

This waveform is similar to one model included in TONE, but provides gain compensation for MAIN.

Model 13: classic pulse wave, centered PWM

MAIN consists of a DC-free pulse wave created with two phase-shifted sawtooths, gain-compensated. The pulse width changes around a static center of the pulse. ALT is a standard pulse wave, not DC-free, without gain compensation, but also using centered PWM.

Model 14: square wave, FM-modulated by a triangle

This simple model replaces direct pulse-width modulation with frequency modulation to achieve a similar effect, using a triangle modulator and a square wave carrier. The octave settings are the same as for model 5.

Model 15: ternary pulse wave, FM-modulated by a triangle

This model is a variation of the previous one, using a ternary pulse wave instead of a standard square as the carrier.

Model 16-17: Sub square wave, AM-modulated by variable pulse wave

For model 16, a sub square wave is AM-modulated by a pulse wave with variable width, which is controlled by SHAPE. The modulation is set by SHIFT+SHAPE. For SHIFT+SHAPE=0%, full modulation is applied, resulting in a ring-modulation. For higher values the AM-modulation is reduced, sounding more mellow.

Model 17 is essentially the same, but uses a different phase shift between main and sub wave.

CRUDE uses lo-fi effects on a selected oscillator model to obtain interesting sound textures. You can choose between 20 different basic oscillator models which all have just one waveform parameter SHAPE. The available effects are rate reduction using sample-hold, bit crushing, slew-rate limitation, saturation and clipping. Two different topologies are offered, which determine the order of the signal manipulators. The sample-hold effect, when heavily applied, will ultimately destroy the tuning in the upper octaves, which can be useful to create certain sound effects or percussive sounds. The SHAPE LFO can be used as usual to modulate the basic waveforms. In combination with the bit crusher, rich and complex tones can be generated. In contrast to the other oscillators, CRUDE disregards aliasing performance of the effects to abandon any restrictions on waveform manipulation.

For topology 2, the saturator comes before the quantizer (bit crusher). In this way, the effect of the quantizer can be fine-tuned. On the other hand, the signal cannot be independently saturated as in topology 1. Another difference is a change in the quantization curve.

CRUDE: operation and controls

SHAPE

Adjusts the model-depend shape of the waveform.

SHIFT+SHAPE

Sets the degree of tuning variation across voices.

SHAPE LFO

Modulates the model-dependent shape of the waveform.

PAR1: WAVE [-100%…100%]

The WAVE parameter requires a clear explanation. First, the percentage mode (%) is used solely to enable access to negative values. The bipolar usage of this parameter effectively doubles the number of available values, meaning that the percentage symbol itself should be disregarded in interpretation.

• In principle, the WAVE parameter selects the topology, the basic oscillator model and the degree of quantization applied on the waveform of the model.
• Each oscillator model is associated with five adjacent indices, representing different quantization settings. The lowest index corresponds to no quantization, while the highest index represents maximum quantization, corresponding to the lowest bit depth.
• Negative WAVE values refer to the same model and quantizer setting as their positive counterparts (absolute values), but use topology 2, whereas positive values use topology 1.

The first model for topology 1 occupies indices 0…4, where index 0 stands for no quantization and index 4 represents maximum quantization. The corresponding mirrored model for topology 2 uses only the indices -1…-4, leaving out the unquantized mode which would also occupy index 0. The second model uses indices 5 to 9, with its mirrored counterpart using -5 to -9, and so on.

The list of the models is given below. It is sufficient to consider only the positive part (topology 1), since the negative part is just mirrored. For the FM modes (which are actually PM), ratio is defined as carrier:modulator.

PAR2: DECIMATE [0…100%]

Adjusts the degree of decimation using sample-and-hold logic. This effect introduces aliasing, resulting in atonal sound content mixed with the waveform. At higher settings, the original pitch may disappear entirely. At 0%, no decimation occurs.

PAR3: SLEW LIM [0…100%]

Sets the degree of slew rate limitation. In this context, the slew rate defines the maximum signal change from sample to sample. For higher parameter values, this rate is gradually reduced. The effect is non-linear but sounds much like a lowpass. It models early-age analog OPAMPS where the maximum slope of the output voltage is limited due to circuit limitations. For a value of 0%, no slew rate limitation occurs.

PAR4: SATURATE [0…100%]

Adjusts the amount of saturation. At 0%, the signal lies in the linear region.

PAR5: CLIP [0…100%]

Sets the amount of clipping gain. At 0%, no clipping occurs.

PAR6: HIGHPASS [0…100%]

Adjusts the amount of highpass filtering. Such filtering can be desirable to suppress low-frequent artefacts. Also, if there is a DC component present in the signal, this component can be removed and this will influence the limiter. For a value of 0%, no highpass filtering occurs.

The double-fold oscillator DBFOLD explores different oscillator constellations where basic waveforms such as sine or triangle can be folded once or twice, realized in eleven different models. The folded result can be mixed back with the unprocessed waveform or another base tone. For some of the models, one folding operation is replaced with FM. An essential part of the waveform shaping is a built-in saturator or clipper to make the sound stand out better. For modulation, the oscillator incorporates a linear envelope (ENV), which can be optionally looped. Combined with the SHAPE LFO, interesting sound structures can be realized. Four modulation modes exist with different assignments for ENV and SHAPE LFO. The selection of the oscillator model and envelope mode is handled with one single parameter mode.

DBFOLD: controls

SHAPE

SHAPE controls either the first folding of an initial waveform or the FM-modulation intensity applied on such a waveform.

SHIFT+SHAPE

SHIFT-SHAPE adjusts the amount of clipping or saturation, depending on the model. In one case, though, SHIFT-SHAPE controls a third folding.

SHAPE LFO

Can be used to either modulate the first or second transformation (folding), depending on the modulation setting.

PAR1: FOLD2 [0…100%]

Adjusts the degree of the second folding of a waveform.

PAR2: BASE [0…100%]

Adjusts the mix between the folded waveform and the original waveform or some other base tone. For some ring-modulation models, though, BASE adjusts the phase offset of the base tone.

PAR3: MODE [1…101]

Selects the oscillator model with the left digit and the envelope mode with the right digit. In the first table below, x stands for any left digit (or for “10” for index 101). For modes 2 and 7, the LFO is inverted. For modes 5 and 10, the LFO amount is modulated by the envelope.

In the second table above we see the mapping of the MODE parameter. The modulation mode table is repeated 10 times, each time for a different oscillator model. This means that index range 1-10, 11-20, 21-30, and so forth correspond to the modulation mode table. For model 11, though, we only have one index 101. For this model, envelope mode 3 applies. The actual model descriptions are found here.

PAR4: ATTACK [0…100%]

Sets the rise time of the linear A/D-envelope.

PAR5: DECAY [0…100%]

Sets the fall time of the linear A/D-envelope.

PAR6: AMOUNT [-100%…100%]

Sets the envelope amount, which can have positive or negative values.

Note: for attack=0, decay=0 the envelope is deactivated.

DBFOLD: model description

Model 1

A sine wave is double-folded using sinusoidal wave-folders (SHAPE, FOLD2). The resulting wave is mixed with a base tone (BASE) and finally clipped (SHIFT+SHAPE).

Model 2

A sine wave is double-folded using sinusoidal wave-folders. The resulting wave is first clipped and then mixed with a base tone.

Model 3

A sine wave is double-folded using triangular wave-folders. The resulting wave is mixed with a base tone and finally clipped.

Model 4

A sine wave is double-folded using triangular wave-folders. The resulting wave is first clipped and then mixed with a base tone.

For this model, the modulation range of both folds is extended to negative values by simple mirroring the positive range. Negative values can only be reached through modulators (ENV, LFO).

Model 5

A triangle wave is double-folded using triangular wave-folders. The resulting wave is mixed with a base tone and then saturated.

The modulation range for the second folding is extended to negative values.

Model 6

A triangle wave is first folded with a triangular and then with a sinusoidal wave-folder. The result is first saturated and then mixed with a triangle base tone.

Model 7

An octave-shifted triangle wave is folded with a triangular wave-folder (SHAPE). In parallel, a sine wave, which is regarded as the base tone, is folded using a sinusoidal wave-folder (FOLD2).

The ring-modulation product of these waves is finally clipped (SHIFT+SHAPE).

The BASE parameter controls the phase offset of the sinusoidal base tone relative to the main triangle wave (BASE).

Model 8

An octave-shifted triangle wave is folded with a triangular wave-folder. In parallel, a sine wave, which is regarded as the base tone, is folded using a sinusoidal wave-folder. The BASE parameter controls the phase offset of this base tone.

The ring-modulation product of these waves feeds another triangular wave-folder (SHIFT+SHAPE).

Model 9

An octave-shifted sine wave is folded by a sinusoidal wave-folder (FOLD2). The produced wave is used to perform FM-modulation of a sinusoidal carrier (SHAPE). The result is mixed with a triangle base tone (BASE) and finally saturated (SHIFT+SHAPE).

Model 10

An octave-shifted sine wave is folded by a sinusoidal wave-folder. The produced wave is used to perform FM-modulation of a triangle carrier. The result is mixed with a triangle base tone and finally saturated.

Model 11

This model is similar to 10, but uses a phase-shifted triangle base tone.

One-trick pony oscillators

The next oscillators have a somewhat smaller range of sound, but can do one “trick” quite well. Nevertheless, these oscillators can surprise for certain settings. The simplicity of their controls is a benefit. An oscillator like FIVE could also have been included in this group.

HARMON is a straightforward oscillator that utilizes a form of rudimentary additive synthesis. The signal is constructed using only the first eight harmonics. The amplitudes and polarities of harmonics 2–7 are determined by the menu parameters 1–6, while the 8th harmonic is defined by SHIFT-SHAPE. One convenient feature is that the signal is automatically normalized to preserve consistent headroom. When you increase the amplitude of a harmonic by adjusting its parameter, all other harmonics, including the fundamental, are (slightly) decreased. The first harmonic, which is called the fundamental, does not require any adjustment and has a fixed amplitude of 1 (100%).

As expected, the resulting signal is rather dull in the lower octaves. Real additive synthesizers require 256 harmonics or more to fill the whole audio spectrum for all notes, also very low ones. To optionally enrich and brighten the sound, the signal is fed into a sinusoidal waveshaper, which generates additional overtones. This waveshaper is an essential part of the oscillator and is controlled by SHAPE and SHAPE LFO.

Since bipolar parameters are used, the default signal has the amplitudes of the harmonics 2-7 set to -100%. It is, thererfore, recommended to reset the amplitudes to 0 before starting to tweak the patch, as described in the tech notes.

When you crank up SHAPE and use a strong harmonic setting, the oscillator wave can become quite harsh in the upper octaves, being brighter than the analog VCOs. You can use the filter to reduce the spectrum in the usual way. Additionally, the filter envelope can be utilized to obtain a sharp attack if desired.

HARMON: controls

SHAPE

Adjusts the input gain of the signal going into the waveshaper and, therefore, adjusts its impact. When set hard left, the waveshaper has no audible effect.

SHIFT+SHAPE

Sets the amplitude and polarity of the 8th harmonic according to the following mapping. Up to 50% the positive amplitude rises to its maximum. For higher values, it decreases back to zero and eventually reaches its most negative value. In this way, the default value is 0.

SHAPE LFO

Modulates the waveshaper impact (input gain).

PAR1-PAR6 [-100%…100%]

Adjusts amplitude and polarity of harmonics 2-7. For negative values, the amplitude is inverted. The polarity has an effect as soon as the waveshaper comes into play.

A well-known technique for obtaining a sawtooth from a sine or triangle wave is to apply phase modulation (PM) feedback. For CHAOS, this scheme has been extended in order to (hopefully) obtain other, more complex waveforms. The extension is done in two ways.

First, the oscillator uses feedback applied to a basic three-component waveform in order to attain a signal with a full overtone spectrum, shown in the Figure below. The original waveform can consist of either three partials (sine waves) or three triangle waves at partial frequencies. These components are locked in phase, but the upper two (M and N) can start to drift if activated. Second, the PM feedback can be accompanied by FM feedback.

For the PM/FM-scheme to work and deliver low-artefact waveforms which stay in tune, an adjustable lowpass and a fixed highpass filter is inserted in the feedback path. The user must manually set the cutoff frequency of the lowpass. The required cutoff value to achieve a signal perceived as clean depends on the selected component amplitudes and frequencies, but also the highest played note, and is difficult to derive automatically. Such automation might not even be desirable, as it would prevent the user from deliberately introducing a lo-fi character into the waveform.

The output signal is slightly saturated to ensure a more consistent loudness. The L-th harmonic always has a full level or is muted, see frequency table.

CHAOS: controls

SHAPE

Adjusts the amount of phase modulation (PM) in the feedback path.

SHIFT+SHAPE

Adjusts the amount of frequency modulation (FM) in the feedback path.

SHAPE LFO

Depending on mode, the SHAPE LFO modulates the PM amount, the FM amount, or both.

PAR1: Mode

First, we introduce the frequency selection table. As shown, the L-th harmonic is mostly the fundamental, but can also be an overtone and is even muted for the highest-indexed modes 11-16. The frequency table is repeated six times, each time with a different choice for the used waveform and LFO target, resulting in 96 different modes. In practice, mode selection can be done by ear rather than looking at these tables.

PAR2: Amp1 [-100%…100%]

Sets the amplitude and the polarity of the M-th harmonic.

PAR3: Amp2 [-100%…100%]

Sets the amplitude and the polarity of the N-th harmonic.

PAR4: Drift1 [0…100%]

Adjusts the drift for the M-th harmonic.

PAR5: Drift2 [0…100%]

Adjusts the drift for the N-th harmonic.

PAR6: Lowpass [-100%…100%]

Sets the cutoff frequency and also switches between lowpass mode and direct mode. For positive values, the lowpass-filtered wave is used as the signal into the output saturator. For negative values, the wave is taken directly, while the lowpass filter is applied only in the feedback path. The lowest cutoff frequency (highest impact of the filter) is given at +-100%. Up to a certain point, lower cutoff frequencies improve loop stability.

Sequence oscillator collection

The sequence oscillator is a new type which can create more complex waveforms without having to store them as sample data. Just like in FM synthesis, all waveforms are calculated in real time. The basic scheme of such an oscillator is shown below.

The task of a static oscillator is to produce a periodic wave with a desired static single-cycle waveform, defining the timbre. This task can be divided into two subtasks, namely to establish an oscillation signal and to calculate a waveform based on this signal.

In a digital system, the oscillation can easily be realized with a phase counter. For each sample in time, this counter is incremented by a value representing the current frequency, and overflows after every cycle period. The rest of the oscillator unit has to calculate the desired output waveform, taking the sawtooth-like phase counter values as an input.

The sequence oscillator – as a special type of a waveform calculation scheme – splits the single-cycle period into L segments of equal length. Within each segment, an interpolator is responsible for calculating the waveform between two given samples A and B which represent the edges of the segment and can only have the bipolar values +1 or -1. The interpolated waveform in the segment depends only on these two samples and no other.

Technical notes

All of the oscillators are based on the same DSP framework, applying oversampling and frequency-dependent waveform smoothing to avoid audible aliasing. For most oscillators, some slop and drift is incorporated to mimic the behavior of analog VCOs.

Regarding aliasing, the oscillator models CRUDE and CHAOS are exceptions. The CRUDE oscillator with its deliberate LOFI character can experience aliasing for high notes, depending on the settings. It has been designed with a different attitude. For the CHAOS oscillator, aliasing can be suppressed with the lowpass filter in the feedback path. The cutoff frequency is set by the user.

All oscillator models use the following available eight parameters:

PAR1–PAR6 shall denote the parameters which are accessed using menu diving.

SHAPE denotes the shape mod knob assigned to the digital oscillator and has a finer resolution.

SHIFT+SHAPE is the same knob, but used together with the SHIFT button.

SHAPE LFO represents the synth LFO when (a) this LFO is assigned to SHAPE using the front panel switch and when (b) the LFO includes the user oscillator, as can be set in the menu (selecting either all oscillators or only the user oscillator as a destination). Then it acts as a modulation source seen by the user oscillator. The intensity with positive or negative polarity is controlled via the INT knob and the optional SHIFT button. In general, the user has the choice between a global LFO or an LFO per voice, switchable using the LFO voice sync setting. For the XD, a simple linear envelope with attack=0 using the LFO sawtooth-setting, or attack=release using the LFO triangle-setting can be imitated with one-shot mode enabled and the settings “voice sync” = “off” and “key sync” = “on” in the LFO menu. In this case, the speed of the LFO defines the inverse of the release. This feature is essential for the oscillators which do not include an envelope. For the Prologue, this “envelope” will be repeated.

Regarding usability, the chosen design philosophy for many of the models has been to get the most functionality out of the general six parameters assigned to a user oscillator in the menu. This approach has sometimes led to “creative” workarounds which might seem a bit peculiar at first.

In particular, bipolar parameters are used in many cases which come with a small inconvenience. For the current release of the official Logue API, a small bug is still present which is related to bipolar parameters. When a user oscillator is freshly loaded for a new patch, the internal states of all bipolar parameters are at position “-100%” and not at “0%”, although “0%” is shown in the screen during the first menu iteration. Fortunately, this circumstance can be utilized to quickly reset each bipolar parameter to 0. This can be done during the first iteration only by simply incrementing each bipolar value from “0%” to “%1” and back to “0%”. If left unchanged, the parameter will remain and finally be shown at “-100%” which is usually not a good starting point. The advantages of bipolar parameters are manifold, allowing negative envelope amounts etc.