In 1984, Yamaha's DX7 cost around $2,000 and sat behind a locked FM synthesis patent that no competitor could legally replicate. Stanford University had licensed John Chowning's FM algorithm to Yamaha in 1973, and Yamaha held those rights until 1995. Every other digital synthesizer manufacturer faced the same problem: FM-style timbral complexity was the sound of the era, but the core technique was off-limits.
Casio's answer was Phase Distortion synthesis, introduced the same year in the CZ series. The CZ-101 sold for $495, fit into a gig bag, and produced evolving, harmonic-rich timbres through a mechanism that shared no code with FM but achieved many of the same practical results. Understanding how it works reveals something genuinely interesting about the relationship between phase, time, and harmonic content.
The Core Idea: A Bent Phase Accumulator
Standard digital oscillators work by incrementing a phase counter at a constant rate and looking up the corresponding value in a sine wave table. At 440 Hz with a 48 kHz sample rate, the counter advances by 440/48000 of the table length each sample. The output is a perfect sine wave.
Phase distortion keeps the pitch constant while making the phase counter increment non-linearly. Instead of advancing at a fixed rate, the counter rushes through some parts of the cycle and slows through others. The sine table still gets read from beginning to end exactly once per cycle, so the fundamental frequency stays correct, but the output waveform is no longer a sine wave.
The specific shape of this non-linearity determines the resulting harmonic content. Casio implemented it using piecewise linear functions, meaning the phase curve is made of straight line segments with sharp bends. A simple two-segment function, steep then shallow, squeezes the first half of the sine cycle into a shorter time and stretches the second half, producing a waveform closer to a sawtooth. Three-segment functions produce square and pulse variations. The "sharpness" of these bends controls how many harmonics appear.
This is the key insight the DCW exploits. DCW stands for Digitally Controlled Wave, and Casio described it as the CZ's equivalent of a voltage-controlled filter in analogue synthesis. At a DCW setting of zero, the phase function is linear and the output is a pure sine. As DCW increases toward its maximum of 99, the phase function becomes more sharply bent, and the output acquires progressively stronger upper harmonics. The DCW envelope, an independent 8-stage envelope generator, sweeps the DCW value over time. This is behaviourally almost identical to a filter opening and closing, but the mechanism is purely about how fast the sine table gets read at different moments in each cycle.
Eight Waveforms, Thirty-Three Sounds
Each CZ oscillator selects from eight base waveform types, which differ in the shape of their phase distortion function:
- Sine: no distortion at maximum DCW, more of a rounded shape at intermediate settings
- Saw: asymmetric two-segment curve that compresses one half-cycle
- Square and pulse: symmetric compression with plateau regions
- Double sine: two compressed sine arches per cycle, adding octave content
- Sawtooth-pulse hybrid: combines characteristics of both
The eighth and most distinctive category is resonance waveforms. These are implemented differently from the others. Rather than distorting the phase of a single sine cycle, resonance waveforms play a higher-frequency sine at a frequency related to the "resonant" parameter, but hard-synchronise it to the fundamental period. The waveform resets to zero at the start of each fundamental cycle, which is the same trick used by hard sync in analogue oscillators. Sweeping the resonant frequency while keeping the fundamental fixed produces the rising harmonic overtone effect associated with filter resonance sweeps, but generated entirely without a filter. This is why the CZ can produce sounds that aurally suggest a swept resonant filter even though the architecture contains no filter stage whatsoever.
The 33 total sounds come from using each of the 8 base types alone, plus 25 cascade combinations, where non-resonant waveform types chain with other waveform types.
How This Differs from FM
The practical difference matters for programming. FM synthesis with sinusoidal operators produces Bessel function-derived spectra: the harmonic structure depends on a frequency ratio between carrier and modulator, and changing the modulation index produces complex, non-intuitive harmonic jumps. FM is powerful but difficult to predict.
Phase distortion produces what researchers have called more linear spectra. The relationship between the DCW value and the harmonic content follows a more direct curve: more distortion means more upper harmonics, and the relationship is smooth rather than the complex modulation index behaviour of FM. This made the CZ easier to program intuitively. To create something that sounds like a filter closing, set the DCW envelope to start high and decay downward. The relationship maps directly to analogue-style thinking.
That said, PD and FM are mathematically related. Phase distortion is essentially a restricted case of phase modulation synthesis, with the constraint that the modulating function must be synchronised to the carrier period rather than running at an independent frequency. This restriction is partly what makes PD more predictable and partly what limits it compared to full FM. The CZ cannot produce the dense, inharmonic metallic spectra that made the DX7 famous for electric piano and bell sounds, because those require carrier-modulator ratios at non-integer multiples.
Two Oscillators, One Voice
Each CZ voice contains two complete DCO-DCW-DCA chains, each with its own 8-stage envelopes for pitch, wave distortion, and amplitude. The two oscillators can run independently at different pitch relationships, or their outputs can be ring-modulated together, which multiplies their waveforms and creates sum and difference frequency components that neither oscillator produces alone.
Ring modulation between a distorted sawtooth and a resonance waveform, both with different DCW envelope shapes, can produce sounds with evolving harmonic structures that would require three or four FM operators to approximate. The CZ-101's four-voice polyphony in dual-oscillator mode versus eight voices in single-oscillator mode reflects the CPU cost of running both chains simultaneously on 1984 hardware.
The Patent Expired, but PD Didn't Die
Yamaha's FM synthesis patent lapsed in 1995. After that point, any manufacturer could implement FM freely, and many did. Phase distortion synthesis continued in software. Modern implementations appear in plugins and virtual instruments specifically because PD produces a characteristic sound, not just a cheaper approximation of FM. The linear spectra and the filter-sweep behaviour of the DCW give it a textural quality that feels closer to analogue subtractive synthesis than FM does.
Casio's VZ series, introduced in 1988, extended the concept further with eight waveform types per oscillator and a more complex routing architecture, though it never achieved the commercial success of the CZ line.
The CZ-101 sold approximately 68,500 units. For a $495 instrument built around a legal workaround to a competitor's patent, it left a surprisingly durable mark on the sound of 1980s electronic music, and on the engineering history of synthesis.