Synthesis Theory

Synthesis Theory

This chapter explains the acoustic and musical principles behind Quesynth. For the exact discrete-time equations, see Mathematics and DSP.

1. Sound as a spectrum and an envelope

A periodic sound can be described as a fundamental frequency plus partials at integer multiples of that fundamental. Their relative amplitudes and phases form the spectrum, which the listener perceives primarily as timbre. A second description—the amplitude and spectral change over time—determines whether the same spectrum is heard as a pluck, pad, brass note, or organ tone.

Subtractive synthesis organizes these properties into three decisions:

1. Source: select harmonically useful oscillator waveforms and pitches.
2. Spectrum: remove or emphasize frequency regions with the filter.
3. Contour: move level, cutoff, pitch, or another destination over time.

The resulting patch is easier to control when these decisions are made in that order.

2. Oscillators and harmonic content

Waveform	Ideal harmonic structure	Typical use
Sine	Fundamental only	Sub-bass, FM source, reinforcement
Triangle	Odd harmonics falling rapidly	Soft leads, flutes, rounded basses
Sawtooth	All integer harmonics, approximately 1/k amplitude	Brass, strings, pads, bright basses
Pulse	Harmonics set by pulse width	Hollow, nasal, animated, or reed-like tones
Noise	Broad non-periodic spectrum	Breath, percussion, attacks, texture

Two nearby oscillator frequencies create beating at approximately |f_1 - f_2|. Slow beating adds width and motion; faster beating becomes roughness and eventually a perceived interval. Quesynth unison extends this principle by placing several oscillator/filter layers around a played pitch and distributing them across the stereo field.

Aliasing and band limitation

Ideal saw and pulse waves contain infinitely many harmonics, but sampled audio can represent frequencies only below the Nyquist frequency f_s/2. Components above that limit fold into the audible band as inharmonic aliases. Quesynth applies a PolyBLEP correction around oscillator discontinuities to reduce this energy while retaining the waveform's intended brightness.

Oscillator interactions

• Hard sync resets one oscillator from another. The slave retains its pitch control, but its cycle is repeatedly truncated, creating a moving harmonic spectrum when the pitch ratio changes.
• Ring modulation multiplies the oscillators. It produces sum and difference components and is therefore useful for metallic or bell-like spectra.
• Frequency modulation (FM) varies an oscillator's instantaneous phase advance. Small amounts add sidebands near the original harmonics; larger amounts produce increasingly complex, potentially inharmonic spectra.
• Pulse-width modulation moves the two edges of a pulse relative to each other. The pitch remains fixed while the harmonic balance changes.

These interactions can create substantial high-frequency energy. Reduce level or filter cutoff before adding more modulation if a patch becomes harsh.

3. Mixing and the sub oscillator

The oscillator mix establishes the spectrum delivered to the filter. Equal pitch and phase relationships may reinforce or cancel particular harmonics; equal knob positions do not therefore guarantee equal perceived loudness. The sub oscillator adds energy below oscillator 1 and is most effective when the main oscillator still provides enough upper harmonics for pitch definition.

Set source levels before compensating with the amplifier. Excessive level at this stage can drive the filter saturation even when the final output is quiet.

4. Filters, cutoff, and resonance

A filter changes the balance of frequency regions:

Response	Passes	Common application
Low-pass	Frequencies below cutoff	Remove brightness; classic subtractive contour
High-pass	Frequencies above cutoff	Remove rumble or thin a layer
Band-pass	A region around cutoff	Nasal, vocal, or focused tones
Notch	Frequencies away from cutoff	Phase-like movement and spectral space
Ladder low-pass	Four-pole low-pass response with feedback resonance	Steep, resonant analogue-style shaping

Cutoff is the principal spectral control. A 12 dB/octave response removes high frequencies more gradually than a 24 dB/octave response. Resonance feeds energy back around the cutoff and creates a peak whose sharpness is related to quality factor Q; greater resonance also changes level and transient behavior.

Quesynth uses topology-preserving state-variable sections for the 12 dB low-pass, high-pass, and band-pass responses. The LP24 and LPDL states currently use the four-pole zero-delay-feedback ladder path. LPDL does not yet have a distinct diode-specific nonlinear model.

Key tracking

Without key tracking, one fixed cutoff removes progressively more harmonics as notes rise. Positive tracking raises cutoff with played pitch, preserving a more consistent timbre across the keyboard. Use less than full tracking when higher notes should become naturally softer.

Filter saturation

Saturation is nonlinear: it changes both level and spectrum. Low settings add odd-harmonic density and apparent presence; high settings compress peaks and can make resonance more aggressive. Because this process occurs inside the voice, reducing the downstream amplifier does not undo distortion already generated by the filter.

5. Envelopes and articulation

An ADSR envelope has four stages:

• Attack: time from note-on to maximum level
• Decay: time from maximum level toward sustain
• Sustain: held level while the note remains active
• Release: time from note-off toward silence

The amplitude envelope defines the note's principal articulation. The filter envelope defines how brightness changes through the same gesture. Their timing need not match: a short filter decay over a sustained amplifier produces a bright attack followed by a darker body; a slower filter attack creates a swelling spectrum inside an already audible note.

The modulation envelope has no fixed acoustic role. Route it to pitch for dives or rises, pulse width for one-shot timbral movement, or another available destination for an independent contour.

6. LFOs and modulation depth

An LFO is an oscillator used as a control source. Its waveform describes the motion:

• sine and triangle produce smooth periodic movement;
• saw and ramp produce directional sweeps with a reset;
• square alternates between two states;
• sample-and-hold produces stepped random values.

Rate determines how often the motion repeats; amount determines its excursion. Tempo synchronization expresses the period in beats so the modulation follows the host tempo. Modulation sources add at a destination, so two modest routes can produce a large combined excursion. Begin with one route, establish its range, then introduce the next.

Vibrato is pitch modulation, tremolo is amplitude modulation, and wah-like motion is cutoff modulation. These names describe destinations rather than different signal types.

7. Polyphony, unison, and stereo image

Polyphony creates independent note voices. Unison creates several layers within each note voice. Their costs multiply: a four-note chord with six unison layers requires twenty-four oscillator/filter layers before effects.

Quesynth follows the measured reference behavior and sums unison layers without equal-power normalization. Consequently, unison may increase output level as well as width. Detune, phase spread, and pan spread also change cancellation and peak level, so gain should be checked after configuring the stack.

Mono and legato modes change envelope retriggering and portamento behavior. Use legato for connected lead or bass phrases; use polyphony when overlapping releases or chords are part of the articulation.

8. Effects and gain staging

The post-voice chain is:

voice mix → parametric EQ → effect unit → delay → chorus → master output

Order matters. Distortion before delay repeats the distorted signal; chorus after delay moves the combined dry and echo image. Equalization before nonlinear effects also changes which frequencies drive those effects most strongly.

Maintain headroom at four checkpoints: oscillator mix, resonant filter output, effect-unit output, and the final wet/dry sum. Lowering master volume prevents output clipping but cannot remove distortion produced earlier in the chain.

9. A repeatable patch-design method

1. Initialize the patch and set the desired playing mode.
2. Choose one oscillator waveform and confirm the pitch range.
3. Add oscillator 2, sub, or noise only when each has a defined role.
4. Set the static filter cutoff and resonance.
5. Shape the amplitude envelope, then the filter envelope.
6. Add one modulation route at a time and check its full excursion.
7. Configure unison and recheck level, mono compatibility, and stereo width.
8. Add effects in chain order while preserving output headroom.
9. Audition low, middle, and high notes at several velocities.

For practical starting settings, continue with Patch archetypes.

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